Supplemental Readings A

A.1 Introduction the flow from supersonic to subsonic speeds in a transonic SBLI. Although it is preferable to design inlets with weaker We will now discuss the basic details about air-breathing terminating shock waves, constraints on overall system size engine intakes which are frequently used in Ramjets and generally limit the compression that can be achieved through Scramjets. In addition, a small discussion about supersonic oblique shock waves. combustion is also provided which help the reader in under- Such strong interactions pose considerable problems for standing the combustion at supersonic Mach numbers. We inlet efficiency. The strong normal or near-normal shock have already referred them many times earlier in the text for waves incur considerable entropy increase and stagnation purposes of explaining the various phenomena. Moreover, we pressure loss, which is a direct performance loss for the sys- do not discuss all possible topics in this appendix but will tem. Further, since the boundary layer already has experienced choose those that are essential for explaining the theories as a number of adverse pressure gradient regions in the previ- presented in the text. ous SBLIs, in turn, the boundary layer becomes more vul- nerable to flow separation, when encountered the final shock wave. Flow separation has an obvious detrimental impact on A.2 Air-Breathing Engine Intakes inlet performance. In addition to the introduction of addi- For jet aircraft operating at supersonic speeds, it is neces- tional stagnation pressure losses, it introduces considerable sary to decelerate and compress the incoming air to subsonic nonuniformity in the flow entering the subsonic diffuser or speeds before entering into the combustor. It is achieved via the combustor. the intake. The simplest form of compression is via a normal Moreover, any flow separations are also likely to introduce shock ahead of a pitot inlet, but this incurs significant stag- considerable unsteadiness into the flow, which can lead to nation pressure losses, rendering this form of intake imprac- unacceptable dynamic loads on the engine. If the terminal tical for M > 2. A better approach is to generate a series (near-normal) shock oscillation is so extreme that it reaches of oblique shock waves that can increase the pressure and the converging part of the inlet geometry, it becomes unstable. reduce the Mach number before eventually changing the flow At this point, it moves rapidly upstream, making more of the state to subsonic through a terminating near-normal shock. flow inside the inlet subsonic, until it is eventually expelled For a given incoming flow Mach number, a series of multiple from the intake causing unstart (or buzz, if this phenomenon is shock waves incurs a smaller entropy production and, thus, periodic). This is comparable to shock stall or shock-induced lower losses than a single normal shock wave. Depending on buffet on transonic wings; such a violent event is extremely whether the oblique shock waves are generated outside the damaging to the engine. Toavoid the problems associated with intake or within the inlet duct, such designs are referred to as strong transonic SBLIs in inlets, the researchers make use of external or internal compression inlets. flow control to enable the boundary layer to stay attached even In either case, the shock wave interacts with the boundary when the shock waves have considerable strength. The most layer growing along the inlet surface. Most of the interactions popular control method is boundary layer suction, or bleed. feature oblique shock waves with supersonic flow on both In any air-breathing engines, an inlet, a combustion cham- sides of the interaction. However, in each inlet design, there ber, and a nozzle are the three main components. Furthermore, is a final terminating, near-normal shock wave that switches it is established that 1% loss in inlet stagnation pressure even-

π tually leads to about 1–1.5% loss of engine gross thrust (Intake where D is the ratio of stagnation pressure, and p0,exit and Aerodynamics by J. Seddon and E. Goldsmith 1999). There- p0,entry, respectively, are the stagnation pressure at the inlet fore, an efficient performance of the engine components is of exit and the stagnation pressure at the inlet lip. Also, to a very prime importance for good performance of the whole engine. high degree of approximation the flow in the inlet is assumed Also, designing the engine components with high accuracy is to be adiabatic, that is, no exchange of heat transfer between more critical in the regions of increasing static pressure than the inlet and its surroundings. We have, the areas where static pressure decreases. This is because of boundary layer separation in the presence of adverse pressure τ = T0,exit = D 1(A.2) gradient. Clearly, the inlet design is more challenging than the T0,entry nozzles which are subjected to favorable pressure gradients. τ where D is the ratio of stagnation temperature, and T0,exit and T0,entry, respectively, are the stagnation temperature at the A.3 Engine Inlets exit and the stagnation temperature at the lip. The design of subsonic inlet is greatly influenced by the two major require- An inlet is the device which recovers pressure energy by ments; to prevent the separation of boundary layer at high reducing the kinetic energy of the flow. Depending on the angles of attack and need of high mass flow during landing flight Mach numbers, they are categorized into; subsonic or and takeoff; and to suppress the formation of both internal supersonic inlets. Inlets find tremendous application predom- and external shock waves at transonic flight Mach numbers. inantly in jet engines. But these two requirements are contradictory to each other, because a thick inlet lip is the best suited for high angle of attack engine operation, whereas a thin lip is suitable to high A.3.1 Subsonic Inlets Mach number requirements. With the advent of modern com- puting, it is now feasible to obtain analytical estimation of the It is known that the flow entering into the compressor of a tur- complex flow fields and the associated losses to develop the bojet engine must have the Mach number (M) in the range of best compromised inlet designs. 0.4−0.7, where the upper limit is suitable for transonic compressors or fans. Further, if the engine has to operate for the A.3.1.1 Flow through the Inlet (Internal Flow) subsonic level flight at M = 0.85, then the inlet must cause the Based on varied flight Mach numbers and mass flow require- flow deceleration from 0.85 to about 0.6. It should be noted ments of the engine, an inlet has to operate at different that the flow undergoes both external and internal deceleration freestream conditions. To investigate the inlet performance, in an intake. The properly designed intake should minimize or let us consider two typical subsonic freestream conditions eliminate boundary layer separation even during the pitch and and their corresponding thermodynamic processes on T − S yaw motions of the aircraft. Also, there should be minimum diagrams of an aggregate fluid lump as shown in Fig. A.1. stagnation pressure loss in an inlet and it must deliver a uni- In this figure, freestream conditions are depicted by sub- form flow to the compressor. A nonuniform flow at the entry script “a” upstream of the inlet and Aa is the streamtube cross- to the compressor not only affects its efficiency drastically but sectional area. The concept of streamtube introduced here is also, it may lead to flow-induced vibrations thereby causing very useful and resembles an aerodynamic duct. The airflow the failure of blades. In addition, as the diffuser is required to enteringintotheinletmayeitherundergoaccelerationordecel- have a stable operation in both subsonic and supersonic flow eration in the aforesaid aerodynamic duct. During level cruise regimes, its design becomes more challenging. motion, where an aircraft flies at high Mach number with rela- Typically, a subsonic inlet suffers mainly from the follow- tivelylowermassflowattheinlet,airexperiencessomedeceler- ing three types of losses: ationexternaltointake,showninFig.A.1a.Thus,anincreasein cross-sectionalareaofthestreamtubefromfreestreamtointake 1. Losses due to wall friction. entry can be observed. In other flight modes, such as during 2. Losses due to shock waves (at high subsonic or transonic takeoff and landing, the mass flow requirement is high but the flight conditions). aircraftspeedislow.Intheselow-speedhigh-thrustflightoper- 3. Losses due to separation the flow. ations, the streamtube resembles a converging duct as shown in Fig. A.1b, which illustrates the external acceleration of air As the flow passes through the inlet, all the above factors before entering into the inlet. Essentially, in both of the afore- cause loss of stagnation pressure. That is, saidcases,theairundergoesachangeofstateoutsidetheintake following an isentropic process as there is no physical surface π = p0,exit < D 1(A.1)involved to introduce friction. p0,entry Appendix A: Supplemental Readings 395

p 0a p T 0a 02 p 0a 02 2 1 2 02s 2 a 2s

A a Enthalpy (h) p 1 1 p a a

Ta Inlet

Entropy (s) (a) During level cruise motion (high Mach number ﬂight or low air mass ﬂow rate). p 0a p p T0a 0a 02 2 1 2 02s 2 a 2s

A a

Enthalpy (h) p a a p 1 1

Ta Inlet

Entropy (s) (b) During landing or take-off (low Mach number flight or high air mass flow rate).

Fig. A.1 Streamline patterns and the corresponding h − s diagrams for subsonic inlets

The external acceleration, shown in Fig. A.1b, lowers the be too large; otherwise, it will cause shock-induced boundary static pressure at the entry to the inlet and thus increases the layer separation resulting in high nacelle drag. internal pressure rise across the diffuser for the flow velocities From the physics point of view, the flow process in an at stations “a” and “2”. If the rise in internal pressure is too inlet and a diffuser is similar. In both, pressure rises and large, the diffuser may stall due to boundary layer separation fluid momentum decreases, with now work being done as the leading to increased loss of stagnation pressure. Conversely, fluid passes through the device. However, it should be noted the external deceleration causes less increase in static pres- that despite having quantum of experimental and computa- sure inside the diffuser and consequently, the boundary layer tional results on diffusers, they are not directly applicable as is subjected to lower adverse pressure gradient and thereby, subsonic aircraft inlets. This is because the maximum pres- less prone to separation (Fig. A.1a). Therefore, the inlet area sure recovery across a diffuser is accompanied by a highly is chosen so as to minimize the external acceleration during nonuniform velocity profile at the exit and even it has some takeoff with the result that external deceleration occurs dur- unsteadiness in the flow. Whereas in subsonic aircraft inlets, ing level cruise operation. In these conditions, the upstream it is necessary to have steady and uniform flow velocity enter- streamtube area Aa is less than the diffuser area at station “1”, ing the compressor. Therefore, the design of inlet does not i.e., Aa < A1 and some amount of flow spillage takes place depend on the results obtained through research on diffuser; over the inlet surface, which accelerates as it passes over the rather, it relies on the potential flow coupled with boundary surface. Further, at high subsonic Mach number operations, layer analysis followed by wind tunnel testing over a wide this acceleration and subsequent deceleration of the flow must range of test conditions. 396 Appendix A: Supplemental Readings

Fig. A.2 Probable locations of boundary layer separation

In actual inlets, the boundary layer may separate in any and the static pressure. Further, Ai and Amax, respectively, of the flow zones: “1”, “2”, or “3”, as shown in Fig.A.2. are the minimum and maximum areas of the inlet, subscript The acceleration and subsequent deceleration of the flow at “a” depicts the freestream condition. For simplicity, we will outer surface results in the boundary layer separation in zone assume the flow to be one-dimensional and incompressible. “1”, which eventually leads to high nacelle drag. On inter- The net momentum flux out of C∀ will be nal surfaces, two probable locations of flow separation are as + ρ 2 − ρ 2 follows: zone “2” and zone “3”, depending on the duct geom- m˚ sva vi Ai va Amax (A.3) etry and operating conditions. The flow separation in zone “3” occurs due to large adverse pressure gradient caused by the The mass flow rate m˚ s escaping from the sides of C∀ is flow acceleration around the nose of the centerbody and subsequent deceleration at the rear end as the curvature decreases. m˚ s= ρvaAmax − ρviAi (A.4)

A.3.1.2 Flow over the Inlet (External Flow) Thus, Eq. (A.3) can be written as It is seen that both internal and external flow deceleration ρ 2 − poses great challenges in the design of inlets and hence Ai vi viva (A.5) requires an optimization between the two. To investigate the effect of external deceleration of subsonic flow on the Further, the net force in axial direction, acting on the control inlet design, let us consider a typical streamline pattern over volume, is the inlet as shown in Fig. A.3. The flow acceleration on the external surface will cause a low-pressure zone which can paAmax−piAi − Fx (A.6) adversely affect the boundary layer in two ways. In a flow domain where the entire flow is subsonic, the decrease in where Fx is the component of F in x−direction. In absence of pressure will be followed by a region of rising pressure lead- friction, Fx can be expressed as ing to boundary layer separation. Under this condition, one might expect to have a point of minimum pressure or maxi- ˆ Aˆmax ˆ ˆ mum flow velocity downstream of which boundary layer may Fx = p i .ndA= pdAx (A.7) be separated. If the flow domain is partly supersonic, then it inlet A will end up abruptly forming a shock wave which will interact i the boundary layer on the wall causing the latter to separate. where î and n,ˆ respectively, are the unit vectors in the flow Thus, in this case, also, the local Mach number must be below direction and in outward pointing direction normal to inlet a limiting value in order to prevent the boundary layer separa- area. Introducing above equation into Eq. (A.6), we have tion. Whatever may be the case, the detachment of boundary layer is an undesired phenomenon which will adversely affect Aˆmax the overall pressure recovery as the flow passes downstream p A − p A − pdA (A.8) in the aircraft engine. It also generates a net rearward force or a max i i x drag on the body. Ai In Fig.A.3,˚m and F, respectively, are the mass flow rate s Combining this result with Eq. (A.3), the momentum equation crossing from the sides of control volume (C∀) and net force will be written as acting on the inlet, v and p, respectively, are the flow velocity Appendix A: Supplemental Readings 397

minimum (pmin) and the ﬂow velocity is maximum (umax). Hence, the pressure must rise from pmin to ambient pressure Aˆmax (pa) at some downstream location. Thus, on the outer surface − − = ρ 2 − paAmax piAi pdAx Ai vi viva of the inlet the average pressure can be deﬁned as Ai ´ Amax (p − p) dA Ai a x From algebraic rearrangement of the terms, we have pa − p = = f (pa − pmin) (Amax − Ai)

where f is a factor between 0 and 1. Therefore, Th can be Aˆmax written as ( − ) = ρ 2 − + ( − ) pa p dAx Ai vi viva pi pa Ai

Ai Th = f (pa − pmin)(Amax − Ai)

Applying Bernoulli’s equation between entry and exit of the Equation (A.9) can be rewritten as inlet f (p − p )(A − A ) v 2 v2 − v2 a min max i = − i a i 1 1 pi − pa = ρ ρv2A va 2 2 a i or Thus, 2 1 − vi Aˆ A va max 2 − 2 max = 1 + va v 2 ( − ) = ρ 2 − + ρ i Ai v pa p dAx Ai vi viva f max C , 2 va p max Ai (p −p ) , = a min or where Cp max 1 ρ 2 is the pressure coefficient which 2 va must not be too large; otherwise, boundary layer will separate. Aˆmax 1 v 2 Hence, the above equation can be written as (p − p) dA = ρv2A 1 − i a x a i 2 va 2 Ai vi 1 − 1 − Cp,max Amax va ´ = 1 + (A.10) It should be noted that the term Amax (p − p) dA is the Ai fCp,max Ai a x increment in component of thrust (Th) which acts on the It should be noted that the value of factor, (f), depends on front external surface of the inlet due to reduction in static the shape of the inlet. For example, taking f = 0.5, we can pressure. Thus, show the size of external surface required to prevent boundary layer separation for a given vi , as shown in Fig. A.4. Also, it Aˆmax va is interesting to note that to prevent excessive drag caused due Th = (p − p) dA a x to flow separation, the size of nacelle should be increased with Ai increase of external deceleration, i.e., by decreasing the velocity ratio vi . Nevertheless, the condition of higher drag for or va the larger nacelle still holds even without separation. Further, 2 = 1ρ 2 − vi the effect of relatively moderate velocity ratios vi > 0.8 Th va Ai 1 va 2 va on minimum nacelle size is rather small. Alternatively, the or employment of partial internal deceleration is found to be quite useful to reduce the maximum diameter of the inlet 2 Amax Th v because it allows a reduction in both Ai and . = 1 − i (A.9) Ai 1 2 Even though the above analysis is carried out assuming a ρu Ai va 2 a simplified flow field around the inlet, yet, it showed that the From Eq. (A.9), it is evident that the thrust generated by the performance of an inlet depends on the pressure gradient on engine can be increased by lowering the flow speed at the both internal and external surfaces as well as on area ratio Amax . The pressure rise on the outer surface is limited by entry to the inlet. Furthermore, we have seen that on the outer Ai surface of the inlet, there exists a point where the pressure is external compression and Amax whereas the internal pressure Ai 398 Appendix A: Supplemental Readings

CV va m s v F a p a

va v A A max p i i a

p F a va

Fig. A.3 Calculation of thrust over inlet surface

3.0 0.4 0.5 C 0.6 pmax 2.0 A max A i

1.0

020. 0.4 0.6 0.8 1.0 vi va Fig. A.4 Variation of area ratio Amax with velocity ratio vi for f = 0.5 Ai vmax rise depends on the flow deceleration between entry to the inlet If the flow velocity leaving the diffuser exit is assumed to and entry to the compressor in turbojet engine (or combustion be small, i.e., v2 ≈ 0, then we have chamber in case of a ramjet). For a more practical analysis, − one must consider compressibility effects. h02s ha ηd = (A.11) h0a − ha A.3.1.3 Performance Criteria of Inlets Assuming the gas to be perfect (say, air), we can The performance of an inlet is evaluated either in terms of write isentropic efficiency or in terms of stagnation pressure ratio. To get a clear idea, let us look into them in detail in the fol- h = C T(A.12) lowing sections. p Isentropic Efficiency We have The performance of an inlet is estimated in terms of isen- − η = T02s Ta tropic efficiency, also known as diffuser efficiency (η ).Itis d (A.13) d T0a − Ta defined as the ratio of enthalpy change of the flow between the entrance and exit of the diffuser to the kinetic energy of the where 02s depicts the isentropic state that would be reached flow. A typical flow process in an inlet, depicted by Mollier by isentropic compression to the actual outlet stagnation pres- diagram is shown in Fig. A.5. sure. Further, from isentropic relations Appendix A: Supplemental Readings 399

p 0a p T 02 p 0a 0a 02 2 2 1 v 02s 2 2 2 2 1 2s 1 2 v a 2 1 Enthalpy (h) p 1 1 p a

T a a Inlet

Entropy (s)

Fig. A.5 Mollier (h − s) diagram of ﬂow states in the subsonic inlet

T γ − 1 02 = + 2 tion pressure ratio (rd) across the shock wave. For a typical 1 Ma (A.14) Ta 2 subsonic diffuser, the variations of rd and ηd with ﬂight Mach number (M) are given in Fig. A.6. where Ma is the freestream Mach number. Also,

γ−1 T p γ 02s = 02s (A.15) A.3.2 Supersonic Inlets Ta pa Similar to flying at subsonic speed, for supersonic flight also, (η ) Therefore, the isentropic efficiency of the inlet d is given it remains necessary; at least for present designs, the flow by Eq. (A.16). coming out of an inlet must be subsonic only. The com-

γ−1 pressors capable of ingesting supersonic stream, however, γ p02 − may provide very high mass flow rate per unit area and p 1 a high-pressure ratio per stage. However, the development of a η = (A.16) d γ− supersonic compressor without excessive loss of stagnation 1 M2 2 pressure across the shock waves is still far from reality. Thus, till date, the Mach number of the airstream (in axial direc- Stagnation Pressure Ratio tion) approaching to a subsonic compressor must not be more The diffuser effectiveness is also evaluated in terms of stag- than 0.4; however, for transonic stage, it can go up to a max- nation pressure ratio (rd), defined as imum of about 0.6. Here, the transonic stage refers to the relative speed of the axial flow with respect to the blade p02 rd = (A.17) tip, and thus, the absolute speed will still be less than 0.4 p0a only. The challenges posed by an incoming supersonic stream From algebraic rearrangements in the designing of compressor are not present in a ramjet. γ Also, it is possible to have combustion at supersonic Mach γ − γ−1 p02 = p02 × p0a = ( ) + 1 2 rd 1 Ma numbers eliminating aerodynamic losses such as shock asso- pa p0a pa 2 ciated losses. The ramjet which permits combustion at supersonic speeds is better known as supersonic combustion ram- Introducing above in Eq. (A.16), we have jet (scramjet), the concept which could not be applied so far 2 γ − 1 γ−1 due to difficulty in having a stable combustion without exces- η = 1 + M2 (r ) γ − 1 (A.18) d (γ − ) 2 a d sive aerodynamic losses. Therefore, at present, the supersonic 1 Ma 2 inlets are designed to decelerate a supersonic flow to subsonic From Eq. (A.18), it is clear that for a given freestream Mach speeds bearable by existing compressors of turbojet engines number (Ma) the diffuser efficiency depends only the stagna- or fans of ramjet combustors. 400 Appendix A: Supplemental Readings

1.0 r d

0.95

η 0.90 d

0.85 0 0.2 0.4 0.6 0.8 1.0 M

Fig. A.6 Performance curves of a typical subsonic diffuser

A.3.3 Hypersonic Inlets ing that delivers the air from inlet to combustor is called the diffuser, whereas it is termed as isolator for scramjet engines. The emerging hypersonic air-breathing propulsion systems, The burnt mixture in the combustor is subsequently expanded currently under development, will provide a means for sus- in a convergent–divergent nozzle, exiting once again at super- tained and accelerating flight within the atmosphere at hypersonic speeds. At hypersonic Mach numbers, the losses asso- sonic Mach numbers. These propulsion systems could be used ciated with decelerating the incident airstream to subsonic in long range cruise missiles to intercept the time-sensitive tar- speeds become quite large and hence, the supersonic combus- gets, responsive hypersonic aircraft for global payload deliv- tion ramjet (scramjet) is preferred. In scramjets, the incoming ery and reusable launch vehicles to achieve cost-effective flow is still compressed by the inlet, but the combustion is space access. allowed to occur at supersonic Mach numbers. The hypersonic propulsion systems are broadly classified The inlets which are used to compress the requisite amount into; air-breathing and non-air-breathing. The liquid and solid of airstream at hypersonic Mach numbers are called hyper- propellant rocket motors fall under the category of non-air- sonic inlets. The following precautions should be exercised to breathing propulsion systems because they do not require improve the overall pressure recovery achieved in hypersonic atmospheric oxygen in the combustion process. Instead, they inlets: carry both fuel and oxidizer either separately in liquid fuel tanks or combined within a solid propellant grain which • The static pressure rise can be maximized by minimizing are burned within a high-pressure chamber to produce hot the viscous losses on the walls and by reducing the stag- gaseous products that are expanded through an exhaust nozzle nation pressure loss. to produce thrust. The commonly used air-breathing engines • The inlet contribution in overall drag should be minimized. are; turbojet, turbofan, turboprop, and ramjet and scramjet, as • The inlet performance should not be affected much by schematically shown in Fig. A.7. Because of material limita- varying the angle of attack. tions on allowable turbine blade temperature, the maximum • The inlet must be able to withstand the back pressure flight speed attained by a turbojet engine is usually limited caused due to heat transfer. to Mach 3.5. The primary air-breathing engine used to fly at Mach numbers approaching to 5, is the ramjet. At super- In hypersonic inlets, the incoming airstream should be com- sonic speeds, a ramjet-powered vehicle utilizes an inlet that is pressed to about three times, before it is being ducted to the designed to ingest the atmospheric air and compress it for an combustion chamber. The incident airstream is decelerated efficient combustion. Once the air is compressed, it is ducted in a highly convergent duct and for a given Mach number the into a combustion chamber where it is mixed with fuel, and duct can achieve two different flow configurations. The inlet is the mixture is burnt to raise the temperature and pressure said to be unstarted, when a strong bow shock is located ahead inside the engine. In subsonic combustion ramjets, the duct- of the inlet lip, causing the hypersonic airstream to become Appendix A: Supplemental Readings 401

Compressor Turbine

Combustor Airstream Exhaust Gases

Diffuser Nozzle

(a) Turbojet engine.

Engine cowl Airstream

Turbine Fan Burner Exhaust gases

Compressor Crankshaft Nozzle

Burner

Inlet

(b) Turbofan engine. HPT Low pressure High pressure compressor compressor Combustor LPT Nozzle Airstream

Exhaust Inlet gases

HPT− High Pressure Turbine w LPT− Low Pressure Turbine (c) Turboprop engine.

Fuel injector Flame holder Airstream Exhaust gases

Diffuser Combustion Nozzle chamber

Inlet (d) Ramjet engine.

Fig. A.7 Schematic layout of some air-breathing engines subsonic and permitting the requisite amount of flow spillage. In a hypersonic inlet, the pressure recovery is achieved But, when there are no bow shock and no flow spillage and by compressing the flow by a series of oblique shock waves, the flow is supersonic throughout in the inlet, the condition is as shown in Fig. A.8. The interaction of these shock waves referred to as start condition. with boundary layer on the wall is termed as shock-boundary 402 Appendix A: Supplemental Readings

Oblique shock wave

Separation bubble

M > 5 M > 1 M > 1

Cowl Separated boundary layer

Fig. A.8 Schematic layout of a hypersonic inlet layer interactions (SBLIs). The impingement of an oblique can be viewed as the working of a convergent–divergent noz- shock wave on the boundary layer imposes an adverse pres- zle in reverse. This is why, the convergent–divergent diffuser sure gradient, which decelerates the flow and eventually leads is also referred to as reverse nozzle diffuser. The major dif- to boundary layer thickening. Interaction of boundary layer ference between the reverse nozzle diffuser and the second with shock reflections is assumed to be responsible for the throat is that in the former the aerodynamic streamtube effect flow separation and causing inlet unstart. However, the sepa- is felt ahead of it, whereas in the latter there is no such effect is rated boundary layer subsequently reattaches to the surface at felt when used in supersonic wind tunnel. The application of some downstream location. The recirculatory zone between supersonic diffuser is associated with many practical difficul- the points of separation and reattachment of the boundary ties. For example, it has to operate successfully over a wide layer is known as “separation bubble”, which acts as blockage range of flight Mach numbers without excessive nacelle drag. and in the worst case may even lead to inlet unstart. Further, The losses due to interaction of shock and boundary layer on the “bubble” would also increase the heat transfer as well as internal and external surfaces further aggravate the situation. the wall friction, thereby, deteriorating the flow quality enter- Also, under certain conditions, the flow field becomes highly ing into the combustion chamber. Therefore, one must have oscillatory. a deep understanding in order to explore the techniques used The rise of static pressure by decelerating the flow is often to minimize or eliminate the detrimental effects of boundary critical for the jet engine operation as the nozzle inlet pres- layer separation. sure affects the exhaust velocity. It is established that 1% loss Furthermore, the established techniques to start the super- in inlet stagnation pressure eventually leads to about 1–1.5% sonic inlets such as variable intake geometry, bleeding, cowl loss of engine gross thrust (Intake Aerodynamics by J. Sed- deflection, micro-vortex generators, etc., are not directly don and E. Goldsmith 1999). Thus, an efficient design of a applicable to hypersonic inlets. The large temperature diffuser is quite crucial for the whole engine operation. Since gradients present at hypersonic Mach numbers cause severe the maximum rise in static pressure is the isentropic stagna- structural problems in any complex mechanical control tion pressure and therefore, it is highly desirable to have a system requiring an efficient cooling mechanism. shock-free diffuser operation. Furthermore, in supersonic wind tunnels, the normal shock wave located in the test section should be pushed through the A.4 Supersonic Diffusers second throat to minimize the pressure losses caused due to compression front. This is achieved either by increasing the It is known that for supersonic flow decreasing area of a duct operating stagnation pressure or by temporarily increasing the will result in deceleration of the flow. This concept is exploited second throat area. In supersonic inlets, the position of shock in the form of second throat in supersonic wind tunnels, where at the throat is achieved either by momentarily overspeeding a convergent–divergent duct immediately follows the test sec- the inlet or by using the variable area geometry diffuser. At tion. As the flow passes through the duct, it decelerates due this stage, we must realize that the positioning of the shock is to formation of a normal shock. In order to keep the pressure an independent phenomenon and is not affected by the bound- losses to a minimum, it is usual to position the shock ahead of ary layer at the wall. Therefore, in the foregoing discussion, the second throat where the Mach number is slightly greater we will neglect the effects of boundary layer and will investi- than one. Theoretically, the operation of a supersonic diffuser gate the starting problem of a convergent–divergent diffuser assuming the flow to be isentropic and in one dimension. Appendix A: Supplemental Readings 403

A A (a) i th A a

M < 1 M < 1 M < 1 M < 1 (e)

(b) M = M’ − dM M < 1 M = 1 M < 1

M < 1 M < 1 M = 1 M < 1 (f)

M = 1 M < 1 M = 1 M < 1 (g)

M = M M = 1 M < 1 (d) Strong Shock D

Weak Shock M > 1 M < 1 M = 1 M < 1

Flow Spillage

Fig. A.9 Start-up and acceleration of a one-dimensional ﬁxed-geometry convergent–divergent inlet

A.4.1 The Starting Problem where M is the freestream Mach number. From Eq. (A.10), it is evident that for sufficiently high subsonic speeds, we have Let us examine the flow through a fixed-geometry inlet which is being accelerated from subsonic to supersonic speeds in Aa = Aa < Ai ∗ steps, shown schematically in Fig. A.9. We will assume the A Ath Ath flow to be isentropic and in one dimension. Thus, the losses occur only across the shock wave. Despite it being a simpli- Thus, at high subsonic speeds, the streamtube capture area ( ) ( ) fied analysis, the results are applicable to actual flow through Aa is less than the inlet lip area Ai and therefore, flow diffusers where the boundary layer is sucked through wall spillage will occur around the inlet. As the flow further accel- ( = ) porosities. erates the freestream Mach number becomes one M 1 ,a When the low subsonic flow passes through the inlet, it weak shock appears ahead of the inlet, as shown in Fig.A.9c. undergoes deceleration before entering the inlet, as shown in At sonic or supersonic flight Mach numbers, the spillage Fig. A.9a. Since the presence of inlet is felt upstream due to mechanism is essentially non-isentropic. In other words, in order to “sense” the presence of inlet and the flow around it, subsonic speed, the streamtube capture area (Aa) is dictated by the downstream conditions. As the flow accelerates, the the spilled air must be reduced to subsonic velocity ahead of streamtube upstream of the inlet gets adjusted, as shown in the inlet. Consequently, a bow shock stands sufficiently far Fig. A.9b, consequently, the flow is accelerated to sonic veloc- away from the inlet causing the required spillage (Fig. A.9d). The bow shock formation in this case can be understood as ity at the minimum area location, i.e., at inlet throat (Ath). Under this condition, the mass flow rate through the intake is follows. We will consider the case when the freestream first limited by choking at the throat and since the flow is assumed attains the supersonic speed without formation of the shock ∗ wave. Under this condition, the entire flow at the inlet lip has isentropic, Ath = A . The upstream capture area (Aa) can be expressed as to enter without deviation and thus, the streamtube capture area (Aa) will same as the inlet lip area (Ai). But Fig. A.10 γ+1 shows that at low supersonic Mach numbers the allowable γ − 2(γ−1) Aa = Aa = 1 2 + 1 2 ( ) ∗ 1 M (A.19) capture area Aa , which is limited by choking at At is less A Ath M γ + 1 2 than Ai. Consequently, there will be an accumulation of mass 404 Appendix A: Supplemental Readings

Area−ratio for isentropic flow

10.0

(f) 6.0 A Area−ratio A a a for detached shock A* Ath 2.0 A i (a) (g) Ath (b) (e) (c) (d) Area−ratio 1.0

0.8

0.4 0.1 0.2 0.4 0.6 1.0 MM’ 6.0 10.0 D

Mach Number

A Fig. A.10 Variation of A∗ with M for a one-dimensional fixed-geometry supersonic inlet and a rise in pressure in the inlet. The pressure will be build up In turn, the shock will move upstream and exactly at design rapidly causing a shock of sufficient strength moved upstream speed the shock will be positioned right at the throat, where the against the supersonic flow and optimally located to allow the Mach number is just unity. The shock becomes very weak and required spillage. hence, the isentropic flow condition is attained throughout the Once the shock is formed the flow becomes non-isentropic inlet. and thus, when the freestream velocity reaches to design Mach However, in actual flight operations, the shock must be 1 number (MD), as schematically shown in Fig.A.9d, the isen- positioned slightly downstream of the throat as the opera- tropic mass flow rate as of previous cases will not pass through tions at design conditions are unstable and a slight decrease At. This follows from the equation, which indicates that the in Mach number will push the shock in convergent portion, choked mass flow rate m˚ max through a given area At is and hence, the overspeeding operation will have to be repeated proportional to p0 and also from the fact that fluid experi- to swallow the shock. Also, because of transient waves, the ences a stagnation pressure loss in traversing the shock. From shock may be pushed further upstream or in the worst case Fig. A.10, it can be seen that the inlet lip area (Ai) is still upstream of inlet tip. Consequently, the losses will be signif- large and the flow spillage is continued even beyond MD. icantly higher and the entire inlet will experience only sub- However, once the flow is accelerated to a sufficiently high sonic flow. Furthermore, one must realize that except for mod- Mach number M, the inlet is able to ingest the entire inci- est design Mach numbers, to swallow the shock at higher dent mass flow without spillage. At the Mach number slightly speeds substantial overspeeding will be required. Thus, at less than M, i.e., at M − dM shock will be positioned just high freestream Mach numbers, the flow overspeeding will the inlet lip as shown in Fig. A.9e, whereas a slight increase not be a feasible solution to the problems associated with the in Mach number, i.e., for M + dM shock will be pushed to starting of an inlet. enter the inlet convergence. The shock, however, cannot find a An alternative approach to swallow the shock is to use a stable position within the inlet convergence and thus, it moves variable geometry inlet at constant flight Mach number. Let quickly downstream to come to rest within the divergent sec- us analyze the flow in the inlet from one-dimensional point of tion (Fig. A.9f), an equilibrium position decided by the down- view. Suppose that the inlet is accelerated to the design Mach stream conditions. Here, an isentropic flow is established to number (MD) with starting shock present as shown schemat- ∗ the throat and since the throat becomes choked (A < At),the ically in Fig. A.11a. Under this condition, if the area ratio Aa > Aa ( ) Ai Ai area ratio A∗ A will be given by point f of Fig. A.10. is decreased to a value at which entire mass flow t Ath Ath That is, an incident supersonic flow decelerates from Ai to At downstream of the shock can be ingested, the shock will be and subsequently, accelerates in the inlet divergence and thus, having attained an isentropic flow throughout till the loca- 1 Keeping the shock, slightly downstream to the throat, maintains the tion of shock the Mach number is reduced from M to MD. throat Mach number slightly greater than the unity. Appendix A: Supplemental Readings 405

(a) A th

A / A i th (f) M = 1 M < 1 M = 1 M < 1

A / A’ (d) A / A* i th

(b) 1.0

M > 1 M = 1 M < 1

1.0 M D M

Fig. A.11 Shock swallowing using variable area supersonic inlet

(a)Low Backpressure (b) Low Backpressure A i

M = M M > M M < 1 M = M D M = M’i M < 1 D D

Best Backpressure Best Backpressure

M = M M < 1 M = M M = M’i M < 1 D D

Fig. A.12 Fixed-geometry diffuser with the normal shock waves inside (a) simple diverging passage and (b) Kantrowitz–Donaldson inlet swallowed to downstream location of the throat (Fig. A.11b). number at the throat, greater than unity. These requirements Essentially, the variation in area ratio causes a temporary are achieved through an improved design of inlet called increase in the throat area from At to At and thereby, establish- Kantrowitz–Donaldson inlet, shown in the Fig.A.12.This ing an isentropic flow within the inlet convergence. Here, the configuration has the maximum internal convergence that will throat will experience the Mach number greater than one, i.e., just permit the shock swallowing at MD. The inlet operates > Mth 1 and relatively a stronger shock forms at the father under supercritical condition with adequate mass flow rate downstream location to the throat. If area ratio is brought such that the shock is stabilized slightly downstream of the back to its original value, the isentropic flow can be achieved throat in a position, where it is unaffected by the upstream throughout the inlet, consequently, the operating point moves and downstream disturbances (Fig. A.12b). from (d) to (f) in Fig. A.11. Despite having an advantage in obtaining a stabilized From the above discussion, it might appear to design a fixed shock system in inlet divergence, the Kantrowitz–Donaldson geometry inlet so that the shock wave, positioned upstream inlet suffers a major drawback as the local Mach number of to the inlet lip, would be swallowed just as the inlet is accel- the flow approaching to the compression front will be greater erated to the design Mach number (MD). This would, how- than at the throat. Consequently, the shock will be of higher ever, require a larger throat area and would lead to a Mach strength. 406 Appendix A: Supplemental Readings

The operating condition in which a shock is positioned temperature may experience a significant decrease in tem- ahead of the inlet, and where there is a flow spillage, is called perature, and thus, the dissociated products may recombine subcritical operation. When the shock is just at the inlet lip, themselves. Therefore, the chemical kinetics of recombina- the operation is called critical operation. However, once the tion process would have a strong influence on the thrust as shock is swallowed to the inlet divergence, it is termed as well as on the propulsive efficiency of the ramjet. supercritical operation. To avoid the dissociation and stagnation pressure losses associated with deceleration of supersonic or hypersonic flow to subsonic level in ramjets, the concept of supersonic com- A.5 Supersonic Combustion and Scramjet bustion ramjet (scramjet) is proposed. With combustion at the Isolator supersonic Mach numbers, the static temperature of fluid is relatively lower, and hence, the dissociation losses decrease, The pressure loss associated with the deceleration of a super- since the dissociation of a gas depends on the static tempera- sonic or hypersonic flow passing through the shock waves ture. On the other hand, heat transfer through the wall depends may be substantial. Thus, the losses incurred in the ramjet mainly on the stagnation temperature, and thus, the wall cool- combustor even at subsonic Mach numbers will be high. Fur- ing problem is not eliminated by performing the combus- ther, if the ramjet engines are used to fly at hypersonic Mach tion at supersonic Mach numbers. As a remedy, the cooling numbers, in addition to pressure losses caused by the shocks, caused by liquid hydrogen on its way from the fuel tank to the the static temperature of the flow would also be extremely engine has been predicted as a means of keeping the engine high. The high temperature not only makes the cooling of the and vehicle cool enough to sustain the period of hypersonic vehicle difficult, but it also leads to the dissociation of oxygen flight. and nitrogen gases in the air, which in turn increases the com- Furthermore, the supersonic combustion requires the mix- bustion losses. Furthermore, for hypersonic flights (M > 8), ing of injected fuel with supersonic airstream without exces- the temperature of the air in the combustor will be quite large sive losses due to shock waves. In literature, it has been and will become a strong function of pressure. However, the demonstrated that the hydrogen fuel in its gaseous state when rise in pressure is quite advantageous as it suppresses the injected at an angle to the airflow direction, the combined per- dissociation of mixture in the combustion chamber despite turbations of fuel injection, fuel–air mixing and combustion an increase in temperature. Consequently, the temperature of results in a complex shock cell pattern that is associated with the combustion products is likewise pressure dependent. It is rather gradual pressure rise. Subsequently, after the initial found that for a Mach 10 flight at the combustion pressure pressure rise, the mixture is accelerated to supersonic Mach of 10 atm, there is no temperature rise due to combustion, numbers in the convergent–divergent nozzle. Sometimes, the because all the heat released in the combustion is absorbed pressure rise associated with shock cell train may be high in dissociation (Mechanics and Thermodynamics of Propul- enough to cause separation of the incoming boundary layer. sion, Hill and Peterson, Addison-Wesley, 1992). Indeed, at These flow-induced disturbances may travel upstream and on sufficiently high Mach numbers the temperature of the com- reaching the intake they can seriously distort the flow to such bustion products may be even lower than that of the incoming an extent as to even cause breakdown of the flow through the airstream. The low Mach number at which fuel and air are inlet. Therefore, it is essential to prevent the upstream prop- converted into dissociation products may show that there is agation of perturbation in the combustor. This is achieved sufficient residence time available in the combustion cham- by a constant area duct, positioned between the intake exit ber to attain an equilibrium composition. However, when the and combustor inlet, in which a series of oblique shocks are burnt gases are subsequently expanded in the nozzle, there’s present. These shock waves are relatively weak and thus, they no guarantee to ascertain an equilibrium composition in suc- do not cause any significant pressure loss. However, they cession with each step of temperature and pressure reduction, cause a considerable increase in static pressure of incoming owing to the rapidity of the expansion process. If the expan- flow, which is an advantage from the combustion performance sion is extremely rapid the mixture may be effectively frozen point of view. Also, these oblique shocks interact with the with the initial high-temperature composition. Thus, it is evi- boundary layer on the constant area duct, resulting in a com- dent that for flight Mach numbers of the order of 10, only an plex wave pattern which prevents the upstream propagation insignificant amount of combustion energy of the fuel would of the perturbation from the combustor. Thus, the constant be available for the acceleration of the combustion products area duct virtually isolates the inlet from getting disturbed by to generate thrust. Additionally, due to the rapid accelera- the instabilities from the combustor and hence, it is referred tion encountered in the nozzle, combustion products at high to as isolator. The Uncertainty Analysis B

B.1 Introduction • Each uncertainty component is quantified by a standard deviation. Uncertainty analysis or error analysis is essentially the • All biases are assumed to be corrected and any uncertainty procedure which involves estimating the uncertainty asso- is the uncertainty of the correction. ciated with the measured data in any experiment. The ISO • Zero corrections are allowed if the bias cannot be corrected definition of uncertainty is “Parameter, associated with the and an uncertainty is assessed. result of a measurement, that characterizes the dispersion • All uncertainty intervals are symmetric. of the values that could reasonably be attributed to the measurand”. As per ISO, the error components are classified into two major The quality of the performed experiments and the obtained groups, depending upon the source of data. Type A compo- data will be considered acceptable, based on proper docu- nents, which are evaluated by statistical methods and Type B menting of the experimental data along with the uncertainty. components evaluated by other means (or in other laborato- In any measured data, we attempt to find the true value by ries), which can be applied to both random error and bias. The making multiple measurements or by using different meth- sources of uncertainty evaluated by Type B components are ods of measurement. We may obtain slightly different values as follows: in each measurement. This range of measured values includes a true value, and it is represented as • Reference standards calibrated by another laboratory, • Physical constants used in the calculation of the reported Measured value = Best estimate ± Uncertainty value, • Environmental effects that cannot be sampled, Any uncertainty analysis must include both the accuracy and • Possible configuration/geometry misalignment in the precision in the measurement. The difference between pre- instrument, and cision and accuracy lies in the fact that the former indicates • Lack of resolution of the instrument. the quality of the measurement without any correctness in the measured value, whereas the latter estimates the deviation of the measured value from the expected value. Further, B.2 Uncertainty Estimation in the Static and the relative uncertainty accounts for precision, while the rel- Stagnation Pressures ative error accounts for the accuracy in measurement. Rela- tive uncertainty is given by the absolute value of the ratio of The general procedure for estimating the uncertainty in a cal- uncertainty to the measured quantity. Furthermore, the rela- culated quantity using the measured data is discussed in this tive error is the ratio of difference between the measured value section. In the experimental studies, discussed in Sects. 14.8.1 and expected value to the expected value. According to ISO and 14.8.2, the wall static pressure and the settling chamber standard, the basic tenets in uncertainty quantification are as stagnation pressure are calculated using the voltage output of follows: pressure transducers.

B.2.1 Standard Deviation and the Uncertainty B.2.2 Propagation of the Uncertainty

We know that the repeated measurements of a variable (x), Suppose we are interested in estimating the quantity F, which will give slightly different values during each measurement. is a function of a number of variables such as x, y, z, etc. Thus, A step-by-step procedure using statistical analysis, to deter- the overall uncertainty in F can be calculated by the measured mine the standard deviation and uncertainty in the measured uncertainties in x, y, z, ..., as σx, σy, σz, ..., respectively. variable is given below. In the experimental studies, discussed in Sects.14.8.1 and Generally, the average of a measured dataset can be con- 14.8.2, it is seen that the static and stagnation pressures are sidered as the best estimate of the ideal value. The average or the functions of a single variable, i.e., the measured transducer mean value of the repeatedly measured variable is given as output voltage V, i.e.,

X1 + X2 + ... + XN X = (B.1) V = mP + V0 (B.5) N

This mean value is not accurate since there will still be some If the transducer voltage constant is V0 and the slope is m, systematic errors due to the measuring equipment. Since it is the pressure can be written as quite tedious to calibrate the equipment perfectly, we express the uncertainty in the average value by calculating the average V − V deviation. P = 0 = VC + C (B.6) m 1 2

Differentiating above, we get |X − X| + |X − X| + ... + |X − X| d¯ = 1 2 N (B.2) N

The standard deviation is the most common way to charac- dP = C1 (B.7) terize the spread of a dataset. This can be calculated as dV Thus, the propagation of uncertainty is measured as ( − )2 + ( − )2 + ... + ( − )2 X1 X X2 X XN X S = (B.3) N − 1 dP σP = σV (B.8) dV when we report the mean value of N measurements, the uncertainty associated with this mean value is the standard devia- In addition, the measured static or stagnation pressure is given tion of the mean value, often called the standard error or the by uncertainty in measurement.

= P ± σP (B.9) S σX = √ (B.4) N Appendix B: The Uncertainty Analysis 409

Listing B.1 The MATLAB program for standard deviation and wall pressure calculations. 1 clc; clear all; 2 N = 5; %number of test runs 3 str1=’D:\Text Data\1. Plain\T=8mm\Text\’; 4 str2=’D:\Text Data\1. Plain\T=8mm\Plot\’; 5 str3=’Ori_XvsV ’; 6 str4=’ 001’; 7 str5=’.txt’; 8 str6=’_WError ’; 9 str7=’ 002’; 10 str8=’ 003’; 11 str9=’ 004’; 12 str10=’ 005’; 13 str11=’XvsP ’; 14 textname=strcat(str1 ,str11 ,str6 ,str5); 15 filename1=strcat(str1 ,str3 ,str4 ,str5); 16 filename2=strcat(str1 ,str3 ,str7 ,str5); 17 filename3=strcat(str1 ,str3 ,str8 ,str5); 18 filename4=strcat(str1 ,str3 ,str9 ,str5); 19 filename5=strcat(str1 ,str3 ,str10 ,str5); 20 M1=load(filename1); 21 length(M1); 22 x=M1(:,1); 23 v1=M1(:,2); 24 M2=load(filename2); 25 length(M2); 26 v2=M2(:,2); 27 M3=load(filename3); 28 length(M3); 29 v3=M3(:,2); 30 M4=load(filename4); 31 length(M4); 32 v4=M4(:,2); 33 M5=load(filename5); 34 length(M5); 35 v5=M5(:,2); 36 %average 37 v = (v1+v2+v3+v4+v5)/N 38 %deviation from the average 39 d1=(v1-v)./v 40 d2=(v2-v)./v 41 d3=(v3-v)./v 42 d4=(v4-v)./v 43 d5=(v5-v)./v 44 %average deviation 45 ad = (abs(d1)+abs(d2)+abs(d3)+abs(d4)+abs(d5))/N 46 %standard deviation 47 sd = sqrt(((d1.*d1)+(d2.*d2)+(d3.*d3)... 48 +(d4.*d4)+(d5.*d5))/(N-1)) 49 %standard error or uncertainity in voltage 50 se_v = sd/sqrt(N) 51 %Conversion of voltage to pressure 52 p=0.6v 53 %standard error or uncertainity in pressure 54 dp_dv=0.6 55 se_P=(abs(dP_dV)).*se_v 56 C=[x; v; sd; se; p; sep] 57 fileID = fopen(textname ,’w’); 58 fprintf(fileID , ’%4s %6s %6s %6s %6s %6s\r\n’,’x’,’v’,... 59 ’sd’,’se’,’p’,’sep’); 60 fprintf(fileID ,’%1.4f %1.4f %1.4f %1.4f %1.4f %1.4f\r\n’,C); 61 fclose(fileID); The Standard Atmosphere C

( ) ( ) ( ) −1 ( ) ρ −3 The properties of International Standard Atmosphere (ISA) h m hG m T K a ms p Pa kgm are tabulated in SI units. 725 725.08 283.44 337.5 92913.24 1.142 750 750.09 283.28 337.4 92633.61 1.139 775 775.09 283.11 337.31 92354.66 1.136 1. The geopotential (h) and geometric (hG) altitudes are mea- 800 800.1 282.95 337.21 92076.39 1.134 sured in meters (m). 825 825.11 282.79 337.11 91798.8 1.131 ( ) ( ) 2. The temperature T values are given in Kelvin K . 850 850.11 282.63 337.02 91521.88 1.128 − 3. The speed of sound (a) is given in ms 1. 875 875.12 282.46 336.92 91245.65 1.125 4. The pressure (p) data are in Pascals (Pa). 900 900.13 282.3 336.82 90970.09 1.123 5. The density (ρ) values are represented in kgm−3. 925 925.13 282.14 336.73 90695.2 1.12 950 950.14 281.98 336.63 90420.98 1.117 975 975.15 281.81 336.53 90147.44 1.114 1000 1000.16 281.65 336.43 89874.57 1.112 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm 1025 1025.16 281.49 336.34 89602.37 1.109 0 0 288.15 340.29 101325 1.225 1050 1050.17 281.33 336.24 89330.83 1.106 25 25 287.99 340.2 101025.03 1.222 1075 1075.18 281.16 336.14 89059.97 1.103 50 50 287.83 340.1 100725.78 1.219 1100 1100.19 281 336.05 88789.76 1.101 75 75 287.66 340.01 100427.25 1.216 1125 1125.2 280.84 335.95 88520.22 1.098 100 100 287.5 339.91 100129.44 1.213 1150 1150.21 280.68 335.85 88251.35 1.095 125 125 287.34 339.81 99832.34 1.21 1175 1175.22 280.51 335.75 87983.13 1.093 150 150 287.18 339.72 99535.96 1.207 1200 1200.23 280.35 335.66 87715.58 1.09 175 175 287.01 339.62 99240.29 1.205 1225 1225.24 280.19 335.56 87448.69 1.087 200 200.01 286.85 339.53 98945.33 1.202 1250 1250.25 280.03 335.46 87182.45 1.085 225 225.01 286.69 339.43 98651.08 1.199 1275 1275.26 279.86 335.36 86916.87 1.082 250 250.01 286.53 339.33 98357.54 1.196 1300 1300.27 279.7 335.27 86651.95 1.079 275 275.01 286.36 339.24 98064.7 1.193 1325 1325.28 279.54 335.17 86387.68 1.077 300 300.01 286.2 339.14 97772.58 1.19 1350 1350.29 279.38 335.07 86124.06 1.074 325 325.02 286.04 339.04 97481.16 1.187 1375 1375.3 279.21 334.98 85861.1 1.071 350 350.02 285.88 338.95 97190.44 1.184 1400 1400.31 279.05 334.88 85598.78 1.069 375 375.02 285.71 338.85 96900.42 1.182 1425 1425.32 278.89 334.78 85337.12 1.066 400 400.03 285.55 338.76 96611.11 1.179 1450 1450.33 278.73 334.68 85076.1 1.063 425 425.03 285.39 338.66 96322.5 1.176 1475 1475.34 278.56 334.58 84815.73 1.061 450 450.03 285.23 338.56 96034.58 1.173 1500 1500.35 278.4 334.49 84556 1.058 475 475.04 285.06 338.47 95747.36 1.17 1525 1525.37 278.24 334.39 84296.92 1.055 500 500.04 284.9 338.37 95460.84 1.167 1550 1550.38 278.08 334.29 84038.49 1.053 525 525.04 284.74 338.27 95175.01 1.164 1575 1575.39 277.91 334.19 83780.69 1.05 550 550.05 284.58 338.18 94889.88 1.162 1600 1600.4 277.75 334.1 83523.54 1.048 575 575.05 284.41 338.08 94605.44 1.159 1625 1625.41 277.59 334 83267.02 1.045 600 600.06 284.25 337.98 94321.68 1.156 1650 1650.43 277.43 333.9 83011.15 1.042 625 625.06 284.09 337.89 94038.62 1.153 1675 1675.44 277.26 333.8 82755.91 1.04 650 650.07 283.93 337.79 93756.25 1.15 1700 1700.45 277.1 333.71 82501.3 1.037 675 675.07 283.76 337.69 93474.56 1.148 700 700.08 283.6 337.6 93193.56 1.145

© Springer Nature Singapore Pte Ltd. 2019 411 M. Kaushik, Theoretical and Experimental Aerodynamics, https://doi.org/10.1007/978-981-13-1678-4 412 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 1725 1725.47 276.94 333.61 82247.33 1.035 3075 3076.48 268.16 328.28 69442.46 0.902 1750 1750.48 276.78 333.51 81994 1.032 3100 3101.51 268 328.18 69221.58 0.9 1775 1775.49 276.61 333.41 81741.3 1.029 3125 3126.53 267.84 328.08 69001.26 0.897 1800 1800.51 276.45 333.31 81489.22 1.027 3150 3151.56 267.68 327.98 68781.52 0.895 1825 1825.52 276.29 333.22 81237.78 1.024 3175 3176.58 267.51 327.88 68562.34 0.893 1850 1850.54 276.13 333.12 80986.97 1.022 3200 3201.61 267.35 327.78 68343.72 0.891 1875 1875.55 275.96 333.02 80736.78 1.019 3225 3226.63 267.19 327.68 68125.67 0.888 1900 1900.57 275.8 332.92 80487.22 1.017 3250 3251.66 267.03 327.58 67908.19 0.886 1925 1925.58 275.64 332.82 80238.28 1.014 3275 3276.68 266.86 327.48 67691.26 0.884 1950 1950.6 275.48 332.73 79989.97 1.012 3300 3301.71 266.7 327.38 67474.9 0.881 1975 1975.61 275.31 332.63 79742.28 1.009 3325 3326.74 266.54 327.28 67259.1 0.879 2000 2000.63 275.15 332.53 79495.22 1.006 3350 3351.76 266.38 327.18 67043.86 0.877 2025 2025.64 274.99 332.43 79248.77 1.004 3375 3376.79 266.21 327.08 66829.17 0.875 2050 2050.66 274.83 332.33 79002.94 1.001 3400 3401.82 266.05 326.98 66615.05 0.872 1875 1875.55 275.96 333.02 80736.78 1.019 3425 3426.84 265.89 326.88 66401.47 0.87 1900 1900.57 275.8 332.92 80487.22 1.017 3450 3451.87 265.73 326.78 66188.46 0.868 1925 1925.58 275.64 332.82 80238.28 1.014 3475 3476.9 265.56 326.68 65975.99 0.865 1950 1950.6 275.48 332.73 79989.97 1.012 3500 3501.92 265.4 326.58 65764.08 0.863 1975 1975.61 275.31 332.63 79742.28 1.009 3525 3526.95 265.24 326.48 65552.73 0.861 2000 2000.63 275.15 332.53 79495.22 1.006 3550 3551.98 265.08 326.38 65341.92 0.859 2025 2025.64 274.99 332.43 79248.77 1.004 3575 3577.01 264.91 326.28 65131.66 0.857 2050 2050.66 274.83 332.33 79002.94 1.001 3600 3602.04 264.75 326.18 64921.95 0.854 2075 2075.68 274.66 332.23 78757.73 0.999 3625 3627.06 264.59 326.08 64712.78 0.852 2100 2100.69 274.5 332.14 78513.14 0.996 3650 3652.09 264.43 325.98 64504.16 0.85 2125 2125.71 274.34 332.04 78269.16 0.994 3675 3677.12 264.26 325.88 64296.09 0.848 2150 2150.73 274.18 331.94 78025.79 0.991 3700 3702.15 264.1 325.78 64088.56 0.845 2175 2175.74 274.01 331.84 77783.04 0.989 3725 3727.18 263.94 325.68 63881.58 0.843 2200 2200.76 273.85 331.74 77540.9 0.986 3750 3752.21 263.78 325.58 63675.13 0.841 2225 2225.78 273.69 331.64 77299.37 0.984 3775 3777.24 263.61 325.48 63469.23 0.839 2250 2250.79 273.53 331.55 77058.46 0.981 3800 3802.27 263.45 325.38 63263.86 0.837 2275 2275.81 273.36 331.45 76818.14 0.979 3825 3827.3 263.29 325.28 63059.04 0.834 2300 2300.83 273.2 331.35 76578.44 0.976 3850 3852.33 263.13 325.18 62854.75 0.832 2325 2325.85 273.04 331.25 76339.34 0.974 3875 3877.36 262.96 325.08 62650.99 0.83 2350 2350.87 272.88 331.15 76100.85 0.972 3900 3902.39 262.8 324.98 62447.78 0.828 2375 2375.89 272.71 331.05 75862.96 0.969 3925 3927.42 262.64 324.88 62245.09 0.826 2400 2400.9 272.55 330.95 75625.68 0.967 3950 3952.45 262.48 324.78 62042.94 0.823 2425 2425.92 272.39 330.86 75388.99 0.964 3975 3977.48 262.31 324.68 61841.32 0.821 2450 2450.94 272.23 330.76 75152.91 0.962 4000 4002.51 262.15 324.58 61640.24 0.819 2475 2475.96 272.06 330.66 74917.42 0.959 4025 4027.54 261.99 324.48 61439.68 0.817 2500 2500.98 271.9 330.56 74682.53 0.957 4050 4052.58 261.83 324.38 61239.65 0.815 2525 2526 271.74 330.46 74448.24 0.954 4075 4077.61 261.66 324.28 61040.15 0.813 2550 2551.02 271.58 330.36 74214.55 0.952 4100 4102.64 261.5 324.18 60841.17 0.811 2575 2576.04 271.41 330.26 73981.45 0.95 4125 4127.67 261.34 324.08 60642.72 0.808 2600 2601.06 271.25 330.16 73748.94 0.947 4150 4152.71 261.18 323.97 60444.8 0.806 2625 2626.08 271.09 330.07 73517.02 0.945 4175 4177.74 261.01 323.87 60247.39 0.804 2650 2651.1 270.93 329.97 73285.7 0.942 4200 4202.77 260.85 323.77 60050.52 0.802 2675 2676.12 270.76 329.87 73054.96 0.94 4225 4227.8 260.69 323.67 59854.16 0.8 2700 2701.14 270.6 329.77 72824.81 0.938 4250 4252.84 260.53 323.57 59658.32 0.798 2725 2726.17 270.44 329.67 72595.25 0.935 4275 4277.87 260.36 323.47 59463 0.796 2750 2751.19 270.28 329.57 72366.28 0.933 4300 4302.9 260.2 323.37 59268.2 0.794 2775 2776.21 270.11 329.47 72137.89 0.93 4325 4327.94 260.04 323.27 59073.92 0.791 2800 2801.23 269.95 329.37 71910.09 0.928 4350 4352.97 259.88 323.17 58880.15 0.789 2825 2826.25 269.79 329.27 71682.87 0.926 4375 4378.01 259.71 323.07 58686.9 0.787 2850 2851.28 269.63 329.17 71456.23 0.923 4400 4403.04 259.55 322.97 58494.16 0.785 2875 2876.3 269.46 329.07 71230.17 0.921 4425 4428.08 259.39 322.86 58301.93 0.783 2900 2901.32 269.3 328.98 71004.69 0.919 4450 4453.11 259.23 322.76 58110.22 0.781 2925 2926.34 269.14 328.88 70779.79 0.916 4475 4478.15 259.06 322.66 57919.02 0.779 2950 2951.37 268.98 328.78 70555.47 0.914 4500 4503.18 258.9 322.56 57728.32 0.777 2975 2976.39 268.81 328.68 70331.72 0.911 4525 4528.22 258.74 322.46 57538.14 0.775 3000 3001.41 268.65 328.58 70108.54 0.909 4550 4553.25 258.58 322.36 57348.46 0.773 3025 3026.44 268.49 328.48 69885.95 0.907 4575 4578.29 258.41 322.26 57159.29 0.771 3050 3051.46 268.33 328.38 69663.92 0.904 4600 4603.32 258.25 322.16 56970.63 0.769 Appendix C: The Standard Atmosphere 413 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 4625 4628.36 258.09 322.05 56782.47 0.766 6100 6105.85 248.5 316.02 46537.67 0.652 4650 4653.4 257.93 321.95 56594.81 0.764 6125 6130.89 248.34 315.91 46377.94 0.651 4675 4678.43 257.76 321.85 56407.66 0.762 6150 6155.94 248.18 315.81 46218.66 0.649 4700 4703.47 257.6 321.75 56221 0.76 6175 6180.99 248.01 315.71 46059.82 0.647 4725 4728.51 257.44 321.65 56034.85 0.758 6200 6206.04 247.85 315.6 45901.43 0.645 4750 4753.54 257.28 321.55 55849.2 0.756 6225 6231.09 247.69 315.5 45743.48 0.643 4775 4778.58 257.11 321.45 55664.04 0.754 6250 6256.14 247.53 315.39 45585.96 0.642 4800 4803.62 256.95 321.34 55479.39 0.752 6275 6281.19 247.36 315.29 45428.89 0.64 4825 4828.66 256.79 321.24 55295.23 0.75 6300 6306.24 247.2 315.19 45272.25 0.638 4850 4853.69 256.63 321.14 55111.56 0.748 6325 6331.29 247.04 315.08 45116.06 0.636 4875 4878.73 256.46 321.04 54928.39 0.746 6350 6356.34 246.88 314.98 44960.29 0.634 4900 4903.77 256.3 320.94 54745.71 0.744 6375 6381.39 246.71 314.88 44804.97 0.633 4925 4928.81 256.14 320.83 54563.53 0.742 6400 6406.44 246.55 314.77 44650.08 0.631 4950 4953.85 255.98 320.73 54381.83 0.74 6425 6431.49 246.39 314.67 44495.62 0.629 4975 4978.89 255.81 320.63 54200.63 0.738 6450 6456.54 246.23 314.57 44341.6 0.627 5000 5003.93 255.65 320.53 54019.91 0.736 6475 6481.59 246.06 314.46 44188.01 0.626 5025 5028.97 255.49 320.43 53839.69 0.734 6500 6506.64 245.9 314.36 44034.85 0.624 5050 5054.01 255.33 320.33 53659.95 0.732 6525 6531.69 245.74 314.25 43882.12 0.622 5075 5079.05 255.16 320.22 53480.69 0.73 6550 6556.74 245.58 314.15 43729.81 0.62 5100 5104.09 255 320.12 53301.92 0.728 6575 6581.79 245.41 314.05 43577.94 0.619 5125 5129.13 254.84 320.02 53123.64 0.726 6600 6606.84 245.25 313.94 43426.5 0.617 5150 5154.17 254.68 319.92 52945.84 0.724 6625 6631.9 245.09 313.84 43275.48 0.615 5175 5179.21 254.51 319.82 52768.52 0.722 6650 6656.95 244.93 313.73 43124.88 0.613 5200 5204.25 254.35 319.71 52591.68 0.72 6675 6682 244.76 313.63 42974.71 0.612 5225 5229.29 254.19 319.61 52415.33 0.718 6700 6707.05 244.6 313.53 42824.97 0.61 5250 5254.33 254.03 319.51 52239.45 0.716 6725 6732.11 244.44 313.42 42675.65 0.608 5275 5279.37 253.86 319.41 52064.05 0.714 6750 6757.16 244.28 313.32 42526.75 0.606 5300 5304.41 253.7 319.3 51889.13 0.713 6775 6782.21 244.11 313.21 42378.27 0.605 5325 5329.45 253.54 319.2 51714.68 0.711 6800 6807.27 243.95 313.11 42230.21 0.603 5350 5354.5 253.38 319.1 51540.71 0.709 6825 6832.32 243.79 313 42082.57 0.601 5375 5379.54 253.21 319 51367.21 0.707 6850 6857.37 243.63 312.9 41935.34 0.6 5400 5404.58 253.05 318.9 51194.19 0.705 6875 6882.43 243.46 312.8 41788.54 0.598 5425 5429.62 252.89 318.79 51021.63 0.703 6900 6907.48 243.3 312.69 41642.15 0.596 5450 5454.67 252.73 318.69 50849.55 0.701 6925 6932.54 243.14 312.59 41496.18 0.595 5475 5479.71 252.56 318.59 50677.94 0.699 6950 6957.59 242.98 312.48 41350.62 0.593 5500 5504.75 252.4 318.49 50506.8 0.697 6975 6982.64 242.81 312.38 41205.47 0.591 5525 5529.8 252.24 318.38 50336.13 0.695 7000 7007.7 242.65 312.27 41060.74 0.59 5550 5554.84 252.08 318.28 50165.92 0.693 7025 7032.75 242.49 312.17 40916.42 0.588 5575 5579.88 251.91 318.18 49996.19 0.691 7050 7057.81 242.33 312.06 40772.51 0.586 5600 5604.93 251.75 318.08 49826.91 0.689 7075 7082.87 242.16 311.96 40629.02 0.584 5625 5629.97 251.59 317.97 49658.1 0.688 7100 7107.92 242 311.86 40485.93 0.583 5650 5655.02 251.43 317.87 49489.76 0.686 7125 7132.98 241.84 311.75 40343.25 0.581 5675 5680.06 251.26 317.77 49321.87 0.684 7150 7158.03 241.68 311.65 40200.97 0.579 5700 5705.1 251.1 317.66 49154.45 0.682 7175 7183.09 241.51 311.54 40059.1 0.578 5725 5730.15 250.94 317.56 48987.49 0.68 7200 7208.15 241.35 311.44 39917.64 0.576 5750 5755.19 250.78 317.46 48820.99 0.678 7225 7233.2 241.19 311.33 39776.59 0.575 5775 5780.24 250.61 317.36 48654.94 0.676 7250 7258.26 241.03 311.23 39635.93 0.573 5800 5805.28 250.45 317.25 48489.36 0.674 7275 7283.32 240.86 311.12 39495.68 0.571 5825 5830.33 250.29 317.15 48324.23 0.673 7300 7308.37 240.7 311.02 39355.84 0.57 5850 5855.38 250.13 317.05 48159.56 0.671 7325 7333.43 240.54 310.91 39216.39 0.568 5875 5880.42 249.96 316.94 47995.34 0.669 7350 7358.49 240.38 310.81 39077.34 0.566 5900 5905.47 249.8 316.84 47831.57 0.667 7375 7383.55 240.21 310.7 38938.7 0.565 5925 5930.52 249.64 316.74 47668.26 0.665 7400 7408.61 240.05 310.6 38800.45 0.563 5950 5955.56 249.48 316.63 47505.4 0.663 7425 7433.66 239.89 310.49 38662.6 0.561 5975 5980.61 249.31 316.53 47342.99 0.662 7450 7458.72 239.73 310.39 38525.14 0.56 6000 6005.66 249.15 316.43 47181.03 0.66 7475 7483.78 239.56 310.28 38388.09 0.558 6025 6030.7 248.99 316.33 47019.52 0.658 7500 7508.84 239.4 310.18 38251.42 0.557 6050 6055.75 248.83 316.22 46858.45 0.656 7525 7533.9 239.24 310.07 38115.16 0.555 6075 6080.8 248.66 316.12 46697.84 0.654 7550 7558.96 239.08 309.96 37979.28 0.553 414 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 7575 7584.02 238.91 309.86 37843.8 0.552 8950 8962.59 229.98 304.01 30971.81 0.469 7600 7609.08 238.75 309.75 37708.71 0.55 8975 8987.66 229.81 303.9 30856.96 0.468 7625 7634.14 238.59 309.65 37574.01 0.549 9000 9012.73 229.65 303.79 30742.46 0.466 7650 7659.2 238.43 309.54 37439.7 0.547 9025 9037.8 229.49 303.69 30628.3 0.465 7675 7684.26 238.26 309.44 37305.78 0.545 9050 9062.87 229.33 303.58 30514.48 0.464 7700 7709.32 238.1 309.33 37172.24 0.544 9075 9087.95 229.16 303.47 30401.01 0.462 7725 7734.38 237.94 309.23 37039.1 0.542 9100 9113.02 229 303.36 30287.87 0.461 7750 7759.44 237.78 309.12 36906.34 0.541 9125 9138.09 228.84 303.26 30175.08 0.459 7775 7784.5 237.61 309.02 36773.96 0.539 9150 9163.16 228.68 303.15 30062.63 0.458 7800 7809.56 237.45 308.91 36641.98 0.538 9175 9188.23 228.51 303.04 29950.52 0.457 7825 7834.62 237.29 308.8 36510.37 0.536 9200 9213.3 228.35 302.93 29838.75 0.455 7850 7859.68 237.13 308.7 36379.15 0.534 9225 9238.38 228.19 302.82 29727.31 0.454 7875 7884.75 236.96 308.59 36248.31 0.533 9250 9263.45 228.03 302.72 29616.21 0.452 7900 7909.81 236.8 308.49 36117.85 0.531 9275 9288.52 227.86 302.61 29505.45 0.451 7925 7934.87 236.64 308.38 35987.77 0.53 9300 9313.6 227.7 302.5 29395.03 0.45 7950 7959.93 236.48 308.27 35858.07 0.528 9325 9338.67 227.54 302.39 29284.94 0.448 7975 7985 236.31 308.17 35728.75 0.527 9350 9363.74 227.38 302.28 29175.18 0.447 8000 8010.06 236.15 308.06 35599.81 0.525 9375 9388.82 227.21 302.18 29065.76 0.446 8025 8035.12 235.99 307.96 35471.25 0.524 9400 9413.89 227.05 302.07 28956.67 0.444 8050 8060.18 235.83 307.85 35343.06 0.522 9425 9438.96 226.89 301.96 28847.91 0.443 8075 8085.25 235.66 307.74 35215.24 0.521 9450 9464.04 226.73 301.85 28739.48 0.442 8100 8110.31 235.5 307.64 35087.81 0.519 9475 9489.11 226.56 301.74 28631.38 0.44 8125 8135.38 235.34 307.53 34960.74 0.518 9500 9514.19 226.4 301.64 28523.62 0.439 8150 8160.44 235.18 307.43 34834.05 0.516 9525 9539.26 226.24 301.53 28416.18 0.438 8175 8185.5 235.01 307.32 34707.73 0.514 9550 9564.34 226.08 301.42 28309.07 0.436 8200 8210.57 234.85 307.21 34581.78 0.513 9575 9589.41 225.91 301.31 28202.28 0.435 8225 8235.63 234.69 307.11 34456.2 0.511 9600 9614.49 225.75 301.2 28095.82 0.434 8250 8260.7 234.53 307 34330.99 0.51 9625 9639.56 225.59 301.09 27989.69 0.432 8275 8285.76 234.36 306.89 34206.15 0.508 9650 9664.64 225.43 300.99 27883.88 0.431 8300 8310.83 234.2 306.79 34081.68 0.507 9675 9689.71 225.26 300.88 27778.4 0.43 8325 8335.89 234.04 306.68 33957.57 0.505 9700 9714.79 225.1 300.77 27673.24 0.428 8350 8360.96 233.88 306.58 33833.83 0.504 9725 9739.87 224.94 300.66 27568.4 0.427 8375 8386.02 233.71 306.47 33710.46 0.502 9750 9764.94 224.78 300.55 27463.89 0.426 8400 8411.09 233.55 306.36 33587.45 0.501 9775 9790.02 224.61 300.44 27359.69 0.424 8425 8436.16 233.39 306.26 33464.8 0.5 9800 9815.1 224.45 300.33 27255.82 0.423 8450 8461.22 233.23 306.15 33342.52 0.498 9825 9840.17 224.29 300.23 27152.26 0.422 8475 8486.29 233.06 306.04 33220.6 0.497 9850 9865.25 224.13 300.12 27049.03 0.42 8500 8511.36 232.9 305.94 33099.04 0.495 9875 9890.33 223.96 300.01 26946.11 0.419 8525 8536.42 232.74 305.83 32977.84 0.494 9900 9915.41 223.8 299.9 26843.51 0.418 8550 8561.49 232.58 305.72 32857 0.492 9925 9940.49 223.64 299.79 26741.23 0.417 8575 8586.56 232.41 305.62 32736.52 0.491 9950 9965.56 223.48 299.68 26639.26 0.415 8600 8611.62 232.25 305.51 32616.4 0.489 9975 9990.64 223.31 299.57 26537.61 0.414 8625 8636.69 232.09 305.4 32496.63 0.488 10000 10015.72 223.15 299.46 26436.27 0.413 8650 8661.76 231.93 305.29 32377.22 0.486 10025 10040.8 222.99 299.35 26335.24 0.411 8675 8686.83 231.76 305.19 32258.17 0.485 10050 10065.88 222.83 299.25 26234.53 0.41 8700 8711.9 231.6 305.08 32139.47 0.483 10075 10090.96 222.66 299.14 26134.13 0.409 8725 8736.97 231.44 304.97 32021.13 0.482 10100 10116.04 222.5 299.03 26034.04 0.408 8750 8762.03 231.28 304.87 31903.13 0.481 10125 10141.12 222.34 298.92 25934.26 0.406 8775 8787.1 231.11 304.76 31785.49 0.479 10150 10166.2 222.18 298.81 25834.8 0.405 8800 8812.17 230.95 304.65 31668.21 0.478 10175 10191.28 222.01 298.7 25735.64 0.404 8825 8837.24 230.79 304.54 31551.27 0.476 10200 10216.36 221.85 298.59 25636.79 0.403 8850 8862.31 230.63 304.44 31434.68 0.475 10225 10241.44 221.69 298.48 25538.24 0.401 8875 8887.38 230.46 304.33 31318.44 0.473 10250 10266.52 221.53 298.37 25440.01 0.4 8900 8912.45 230.3 304.22 31202.55 0.472 10275 10291.6 221.36 298.26 25342.08 0.399 8925 8937.52 230.14 304.12 31087.01 0.471 10300 10316.68 221.2 298.15 25244.45 0.398 Appendix C: The Standard Atmosphere 415 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 10325 10341.76 221.04 298.04 25147.13 0.396 11700 11721.53 216.65 295.07 20266.83 0.326 10350 10366.84 220.88 297.93 25050.12 0.395 11725 11746.62 216.65 295.07 20187.1 0.325 10375 10391.92 220.71 297.82 24953.4 0.394 11750 11771.71 216.65 295.07 20107.67 0.323 10400 10417 220.55 297.71 24857 0.393 11775 11796.8 216.65 295.07 20028.56 0.322 10425 10442.09 220.39 297.6 24760.89 0.391 11800 11821.9 216.65 295.07 19949.76 0.321 10450 10467.17 220.23 297.49 24665.08 0.39 11825 11846.99 216.65 295.07 19871.27 0.32 10475 10492.25 220.06 297.38 24569.57 0.389 11850 11872.08 216.65 295.07 19793.08 0.318 10500 10517.33 219.9 297.27 24474.37 0.388 11875 11897.18 216.65 295.07 19715.21 0.317 10525 10542.42 219.74 297.16 24379.46 0.387 11900 11922.27 216.65 295.07 19637.64 0.316 10550 10567.5 219.58 297.05 24284.85 0.385 11925 11947.36 216.65 295.07 19560.38 0.315 10575 10592.58 219.41 296.94 24190.54 0.384 11950 11972.46 216.65 295.07 19483.42 0.313 10600 10617.67 219.25 296.83 24096.52 0.383 11975 11997.55 216.65 295.07 19406.76 0.312 10625 10642.75 219.09 296.72 24002.8 0.382 12000 12022.65 216.65 295.07 19330.41 0.311 10650 10667.83 218.93 296.61 23909.38 0.38 12025 12047.74 216.65 295.07 19254.35 0.31 10675 10692.92 218.76 296.5 23816.25 0.379 12050 12072.83 216.65 295.07 19178.6 0.308 10700 10718 218.6 296.39 23723.42 0.378 12075 12097.93 216.65 295.07 19103.14 0.307 10725 10743.09 218.44 296.28 23630.87 0.377 12100 12123.02 216.65 295.07 19027.98 0.306 10750 10768.17 218.28 296.17 23538.62 0.376 12125 12148.12 216.65 295.07 18953.11 0.305 10775 10793.25 218.11 296.06 23446.67 0.374 12150 12173.22 216.65 295.07 18878.54 0.304 10800 10818.34 217.95 295.95 23355 0.373 12175 12198.31 216.65 295.07 18804.27 0.302 10825 10843.42 217.79 295.84 23263.62 0.372 12200 12223.41 216.65 295.07 18730.28 0.301 10850 10868.51 217.63 295.73 23172.54 0.371 12225 12248.5 216.65 295.07 18656.59 0.3 10875 10893.59 217.46 295.62 23081.74 0.37 12250 12273.6 216.65 295.07 18583.19 0.299 10900 10918.68 217.3 295.51 22991.23 0.369 12275 12298.7 216.65 295.07 18510.07 0.298 10925 10943.77 217.14 295.4 22901.01 0.367 12300 12323.79 216.65 295.07 18437.24 0.296 10950 10968.85 216.98 295.29 22811.08 0.366 12325 12348.89 216.65 295.07 18364.7 0.295 10975 10993.94 216.81 295.18 22721.43 0.365 12350 12373.99 216.65 295.07 18292.45 0.294 11000 11019.03 216.65 295.07 22632.06 0.364 12375 12399.08 216.65 295.07 18220.48 0.293 11025 11044.11 216.65 295.07 22543.02 0.362 12400 12424.18 216.65 295.07 18148.79 0.292 11050 11069.2 216.65 295.07 22454.32 0.361 12425 12449.28 216.65 295.07 18077.38 0.291 11075 11094.29 216.65 295.07 22365.98 0.36 12450 12474.38 216.65 295.07 18006.26 0.277 11100 11119.37 216.65 295.07 22277.98 0.358 12475 12499.48 216.65 295.07 17935.42 0.288 11125 11144.46 216.65 295.07 22190.33 0.357 12500 12524.57 216.65 295.07 17864.85 0.287 11150 11169.55 216.65 295.07 22103.02 0.355 12525 12549.67 216.65 295.07 17794.56 0.286 11175 11194.64 216.65 295.07 22016.06 0.354 12550 12574.77 216.65 295.07 17724.55 0.285 11200 11219.72 216.65 295.07 21929.44 0.353 12575 12599.87 216.65 295.07 17654.81 0.284 11225 11244.81 216.65 295.07 21843.16 0.351 12600 12624.97 216.65 295.07 17585.35 0.283 11250 11269.9 216.65 295.07 21757.22 0.35 12625 12650.07 216.65 295.07 17516.16 0.282 11275 11294.99 216.65 295.07 21671.62 0.348 12650 12675.17 216.65 295.07 17447.25 0.281 11300 11320.08 216.65 295.07 21586.35 0.347 12675 12700.27 216.65 295.07 17378.6 0.279 11325 11345.17 216.65 295.07 21501.42 0.346 12700 12725.37 216.65 295.07 17310.22 0.278 11350 11370.26 216.65 295.07 21416.82 0.344 12725 12750.47 216.65 295.07 17242.12 0.277 11375 11395.35 216.65 295.07 21332.56 0.343 12750 12775.57 216.65 295.07 17174.28 0.276 11400 11420.44 216.65 295.07 21248.63 0.342 12775 12800.67 216.65 295.07 17106.71 0.275 11425 11445.53 216.65 295.07 21165.03 0.34 12800 12825.77 216.65 295.07 17039.4 0.274 11450 11470.62 216.65 295.07 21081.75 0.339 12825 12850.87 216.65 295.07 16972.36 0.273 11475 11495.71 216.65 295.07 20998.81 0.338 12850 12875.97 216.65 295.07 16905.59 0.272 11500 11520.8 216.65 295.07 20916.19 0.336 12875 12901.07 216.65 295.07 16839.07 0.271 11525 11545.89 216.65 295.07 20833.9 0.335 12900 12926.17 216.65 295.07 16772.82 0.27 11550 11570.98 216.65 295.07 20751.93 0.334 12925 12951.27 216.65 295.07 16706.83 0.269 11575 11596.07 216.65 295.07 20670.28 0.332 12950 12976.38 216.65 295.07 16641.1 0.268 11600 11621.16 216.65 295.07 20588.95 0.331 12975 13001.48 216.65 295.07 16575.62 0.267 11625 11646.25 216.65 295.07 20507.95 0.33 13000 13026.58 216.65 295.07 16510.41 0.265 11650 11671.34 216.65 295.07 20427.26 0.328 13025 13051.68 216.65 295.07 16445.45 0.264 11675 11696.43 216.65 295.07 20346.89 0.327 13050 13076.79 216.65 295.07 16380.74 0.263 416 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 13075 13101.89 216.65 295.07 16316.29 0.261 14450 14482.85 216.65 295.07 13135.82 0.211 13100 13126.99 216.65 295.07 16252.1 0.261 14475 14507.96 216.65 295.07 13084.13 0.21 13125 13152.09 216.65 295.07 16188.15 0.26 14500 14533.08 216.65 295.07 13032.66 0.21 13150 13177.2 216.65 295.07 16124.46 0.259 14525 14558.19 216.65 295.07 12981.38 0.209 13175 13202.3 216.65 295.07 16061.02 0.258 14550 14583.31 216.65 295.07 12930.31 0.208 13200 13227.41 216.65 295.07 15997.83 0.257 14575 14608.42 216.65 295.07 12879.43 0.207 13225 13252.51 216.65 295.07 15934.89 0.256 14600 14633.53 216.65 295.07 12828.76 0.206 13250 13277.61 216.65 295.07 15872.19 0.255 14625 14658.65 216.65 295.07 12778.28 0.205 13275 13302.72 216.65 295.07 15809.74 0.254 14650 14683.77 216.65 295.07 12728.01 0.205 13300 13327.82 216.65 295.07 15747.54 0.253 14675 14708.88 216.65 295.07 12677.93 0.204 13325 13352.93 216.65 295.07 15685.58 0.252 14700 14734 216.65 295.07 12628.05 0.203 13350 13378.03 216.65 295.07 15623.87 0.251 14725 14759.11 216.65 295.07 12578.37 0.202 13375 13403.14 216.65 295.07 15562.4 0.25 14750 14784.23 216.65 295.07 12528.88 0.201 13400 13428.24 216.65 295.07 15501.17 0.249 14775 14809.34 216.65 295.07 12479.58 0.201 13425 13453.35 216.65 295.07 15440.18 0.248 14800 14834.46 216.65 295.07 12430.48 0.2 13450 13478.45 216.65 295.07 15379.43 0.247 14825 14859.58 216.65 295.07 12381.57 0.199 13475 13503.56 216.65 295.07 15318.92 0.246 14850 14884.69 216.65 295.07 12332.86 0.198 13500 13528.67 216.65 295.07 15258.65 0.245 14875 14909.81 216.65 295.07 12284.34 0.198 13525 13553.77 216.65 295.07 15198.62 0.244 14900 14934.93 216.65 295.07 12236.01 0.197 13550 13578.88 216.65 295.07 15138.82 0.243 14925 14960.05 216.65 295.07 12187.86 0.196 13575 13603.99 216.65 295.07 15079.26 0.242 14950 14985.16 216.65 295.07 12139.91 0.195 13600 13629.09 216.65 295.07 15019.93 0.242 14975 15010.28 216.65 295.07 12092.15 0.194 13625 13654.2 216.65 295.07 14960.83 0.241 15000 15035.4 216.65 295.07 12044.57 0.194 13650 13679.31 216.65 295.07 14901.97 0.24 15025 15060.52 216.65 295.07 11997.18 0.193 13675 13704.42 216.65 295.07 14843.34 0.239 15050 15085.64 216.65 295.07 11949.98 0.192 13700 13729.52 216.65 295.07 14784.94 0.238 15075 15110.75 216.65 295.07 11902.96 0.191 13725 13754.63 216.65 295.07 14726.77 0.237 15100 15135.87 216.65 295.07 11856.13 0.191 13750 13779.74 216.65 295.07 14668.83 0.236 15125 15160.99 216.65 295.07 11809.48 0.19 13775 13804.85 216.65 295.07 14611.11 0.235 15150 15186.11 216.65 295.07 11763.02 0.189 13800 13829.96 216.65 295.07 14553.63 0.234 15175 15211.23 216.65 295.07 11716.74 0.188 13825 13855.07 216.65 295.07 14496.36 0.233 15200 15236.35 216.65 295.07 11670.64 0.188 13850 13880.17 216.65 295.07 14439.33 0.232 15225 15261.47 216.65 295.07 11624.72 0.187 13875 13905.28 216.65 295.07 14382.52 0.231 15250 15286.59 216.65 295.07 11578.99 0.186 13900 13930.39 216.65 295.07 14325.93 0.23 15275 15311.71 216.65 295.07 11533.43 0.185 13925 13955.5 216.65 295.07 14269.57 0.229 15300 15336.83 216.65 295.07 11488.05 0.185 13950 13980.61 216.65 295.07 14213.42 0.229 15325 15361.95 216.65 295.07 11442.85 0.184 13975 14005.72 216.65 295.07 14157.5 0.228 15350 15387.07 216.65 295.07 11397.83 0.183 14000 14030.83 216.65 295.07 14101.8 0.227 15375 15412.19 216.65 295.07 11352.99 0.183 14025 14055.94 216.65 295.07 14046.32 0.226 15400 15437.32 216.65 295.07 11308.32 0.182 14050 14081.05 216.65 295.07 13991.05 0.225 15425 15462.44 216.65 295.07 11263.83 0.181 14075 14106.16 216.65 295.07 13936.01 0.224 15450 15487.56 216.65 295.07 11219.51 0.18 14100 14131.27 216.65 295.07 13881.17 0.223 15475 15512.68 216.65 295.07 11175.37 0.18 14125 14156.39 216.65 295.07 13826.56 0.222 15500 15537.8 216.65 295.07 11131.4 0.179 14150 14181.5 216.65 295.07 13772.16 0.221 15525 15562.92 216.65 295.07 11087.6 0.178 14175 14206.61 216.65 295.07 13717.97 0.221 15550 15588.05 216.65 295.07 11043.98 0.178 14200 14231.72 216.65 295.07 13664 0.22 15575 15613.17 216.65 295.07 11000.53 0.177 14225 14256.83 216.65 295.07 13610.24 0.219 15600 15638.29 216.65 295.07 10957.25 0.176 14250 14281.94 216.65 295.07 13556.69 0.218 15625 15663.41 216.65 295.07 10914.14 0.175 14275 14307.06 216.65 295.07 13503.35 0.217 15650 15688.54 216.65 295.07 10871.19 0.175 14300 14332.17 216.65 295.07 13450.23 0.216 15675 15713.66 216.65 295.07 10828.42 0.174 14325 14357.28 216.65 295.07 13397.31 0.215 15700 15738.78 216.65 295.07 10785.82 0.173 14350 14382.39 216.65 295.07 13344.6 0.215 15725 15763.91 216.65 295.07 10743.38 0.173 14375 14407.51 216.65 295.07 13292.09 0.214 15750 15789.03 216.65 295.07 10701.11 0.172 14400 14432.62 216.65 295.07 13239.79 0.213 15775 15814.16 216.65 295.07 10659.01 0.171 14425 14457.73 216.65 295.07 13187.7 0.212 15800 15839.28 216.65 295.07 10617.07 0.171 Appendix C: The Standard Atmosphere 417 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 15825 15864.41 216.65 295.07 10575.3 0.17 17200 17246.56 216.65 295.07 8513.89 0.137 15850 15889.53 216.65 295.07 10533.69 0.169 17225 17271.7 216.65 295.07 8480.4 0.136 15875 15914.66 216.65 295.07 10492.25 0.169 17250 17296.83 216.65 295.07 8447.03 0.136 15900 15939.78 216.65 295.07 10450.97 0.168 17275 17321.97 216.65 295.07 8413.8 0.135 15925 15964.91 216.65 295.07 10409.85 0.167 17300 17347.1 216.65 295.07 8380.69 0.135 15950 15990.03 216.65 295.07 10368.89 0.167 17325 17372.24 216.65 295.07 8347.72 0.134 15975 16015.16 216.65 295.07 10328.09 0.166 17350 17397.38 216.65 295.07 8314.88 0.134 16000 16040.28 216.65 295.07 10287.46 0.165 17375 17422.51 216.65 295.07 8282.16 0.133 16025 16065.41 216.65 295.07 10246.98 0.165 17400 17447.65 216.65 295.07 8249.58 0.133 16050 16090.54 216.65 295.07 10206.67 0.164 17425 17472.79 216.65 295.07 8217.12 0.132 16075 16115.66 216.65 295.07 10166.51 0.163 17450 17497.93 216.65 295.07 8184.79 0.132 16100 16140.79 216.65 295.07 10126.51 0.163 17475 17523.06 216.65 295.07 8152.59 0.131 16125 16165.92 216.65 295.07 10086.67 0.162 17500 17548.2 216.65 295.07 8120.51 0.131 16150 16191.04 216.65 295.07 10046.98 0.162 17525 17573.34 216.65 295.07 8088.56 0.13 16175 16216.17 216.65 295.07 10007.45 0.161 17550 17598.48 216.65 295.07 8056.74 0.13 16200 16241.3 216.65 295.07 9968.08 0.16 17575 17623.62 216.65 295.07 8025.04 0.129 16225 16266.43 216.65 295.07 9928.86 0.16 17600 17648.75 216.65 295.07 7993.46 0.129 16250 16291.55 216.65 295.07 9889.8 0.159 17625 17673.89 216.65 295.07 7962.01 0.128 16275 16316.68 216.65 295.07 9850.88 0.158 17650 17699.03 216.65 295.07 7930.69 0.128 16300 16341.81 216.65 295.07 9812.13 0.158 17675 17724.17 216.65 295.07 7899.48 0.127 16325 16366.94 216.65 295.07 9773.52 0.157 17700 17749.31 216.65 295.07 7868.4 0.127 16350 16392.07 216.65 295.07 9735.07 0.157 17725 17774.45 216.65 295.07 7837.45 0.126 16375 16417.2 216.65 295.07 9696.77 0.156 17750 17799.59 216.65 295.07 7806.61 0.126 16400 16442.33 216.65 295.07 9658.61 0.155 17775 17824.73 216.65 295.07 7775.9 0.125 16425 16467.45 216.65 295.07 9620.61 0.155 17800 17849.87 216.65 295.07 7745.3 0.125 16450 16492.58 216.65 295.07 9582.76 0.154 17825 17875.01 216.65 295.07 7714.83 0.124 16475 16517.71 216.65 295.07 9545.06 0.153 17850 17900.15 216.65 295.07 7684.47 0.124 16500 16542.84 216.65 295.07 9507.5 0.153 17875 17925.29 216.65 295.07 7654.24 0.123 16525 16567.97 216.65 295.07 9470.1 0.152 17900 17950.43 216.65 295.07 7624.13 0.123 16550 16593.1 216.65 295.07 9432.84 0.152 17925 17975.57 216.65 295.07 7594.13 0.122 16575 16618.23 216.65 295.07 9395.72 0.151 17950 18000.72 216.65 295.07 7564.25 0.122 16600 16643.37 216.65 295.07 9358.76 0.15 17975 18025.86 216.65 295.07 7534.49 0.121 16625 16668.5 216.65 295.07 9321.94 0.15 18000 18051 216.65 295.07 7504.84 0.121 16650 16693.63 216.65 295.07 9285.26 0.149 18025 18076.14 216.65 295.07 7475.32 0.12 16675 16718.76 216.65 295.07 9248.73 0.149 18050 18101.28 216.65 295.07 7445.91 0.12 16700 16743.89 216.65 295.07 9212.34 0.148 18075 18126.43 216.65 295.07 7416.61 0.119 16725 16769.02 216.65 295.07 9176.09 0.148 18100 18151.57 216.65 295.07 7387.43 0.119 16750 16794.15 216.65 295.07 9139.99 0.147 18125 18176.71 216.65 295.07 7358.36 0.118 16775 16819.29 216.65 295.07 9104.03 0.146 18150 18201.85 216.65 295.07 7329.41 0.118 16800 16844.42 216.65 295.07 9068.21 0.146 18175 18227 216.65 295.07 7300.58 0.117 16825 16869.55 216.65 295.07 9032.53 0.145 18200 18252.14 216.65 295.07 7271.85 0.117 16850 16894.68 216.65 295.07 8996.99 0.145 18225 18277.28 216.65 295.07 7243.24 0.116 16875 16919.82 216.65 295.07 8961.6 0.144 18250 18302.43 216.65 295.07 7214.74 0.116 16900 16944.95 216.65 295.07 8926.34 0.144 18275 18327.57 216.65 295.07 7186.36 0.116 16925 16970.08 216.65 295.07 8891.22 0.143 18300 18352.72 216.65 295.07 7158.08 0.115 16950 16995.22 216.65 295.07 8856.23 0.142 18325 18377.86 216.65 295.07 7129.92 0.115 16975 17020.35 216.65 295.07 8821.39 0.142 18350 18403.01 216.65 295.07 7101.87 0.114 17000 17045.48 216.65 295.07 8786.68 0.141 18375 18428.15 216.65 295.07 7073.93 0.114 17025 17070.62 216.65 295.07 8752.11 0.141 18400 18453.29 216.65 295.07 7046.09 0.113 17050 17095.75 216.65 295.07 8717.68 0.14 18425 18478.44 216.65 295.07 7018.37 0.113 17075 17120.89 216.65 295.07 8683.38 0.14 18450 18503.59 216.65 295.07 6990.76 0.112 17100 17146.02 216.65 295.07 8649.21 0.139 18475 18528.73 216.65 295.07 6963.25 0.112 17125 17171.16 216.65 295.07 8615.18 0.139 18500 18553.88 216.65 295.07 6935.86 0.112 17150 17196.29 216.65 295.07 8581.29 0.138 18525 18579.02 216.65 295.07 6908.57 0.111 17175 17221.43 216.65 295.07 8547.52 0.137 18550 18604.17 216.65 295.07 6881.39 0.111 418 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 18575 18629.31 216.65 295.07 6854.31 0.11 19975 20037.82 216.65 295.07 5496.51 0.088 18600 18654.46 216.65 295.07 6827.34 0.11 20000 20062.98 216.65 295.07 5474.89 0.088 18625 18679.61 216.65 295.07 6800.48 0.109 20025 20088.14 216.68 295.09 5453.35 0.088 18650 18704.75 216.65 295.07 6773.73 0.109 20050 20113.3 216.7 295.1 5431.9 0.087 18675 18729.9 216.65 295.07 6747.08 0.108 20075 20138.46 216.73 295.12 5410.53 0.087 18700 18755.05 216.65 295.07 6720.53 0.108 20100 20163.61 216.75 295.14 5389.25 0.087 18725 18780.2 216.65 295.07 6694.09 0.108 20125 20188.77 216.78 295.15 5368.06 0.086 18750 18805.34 216.65 295.07 6667.75 0.107 20150 20213.93 216.8 295.17 5346.95 0.086 18775 18830.49 216.65 295.07 6641.52 0.107 20175 20239.09 216.83 295.19 5325.93 0.086 18800 18855.64 216.65 295.07 6615.39 0.106 20200 20264.25 216.85 295.21 5304.99 0.085 18825 18880.79 216.65 295.07 6589.36 0.106 20225 20289.41 216.88 295.22 5284.14 0.085 18850 18905.94 216.65 295.07 6563.43 0.106 20250 20314.57 216.9 295.24 5263.38 0.085 18875 18931.09 216.65 295.07 6537.61 0.105 20275 20339.73 216.93 295.26 5242.69 0.084 18900 18956.23 216.65 295.07 6511.89 0.105 20300 20364.89 216.95 295.27 5222.09 0.084 18925 18981.38 216.65 295.07 6486.27 0.104 20325 20390.05 216.98 295.29 5201.58 0.084 18950 19006.53 216.65 295.07 6460.75 0.104 20350 20415.21 217 295.31 5181.14 0.083 18975 19031.68 216.65 295.07 6435.33 0.103 20375 20440.37 217.03 295.32 5160.79 0.083 19000 19056.83 216.65 295.07 6410.01 0.103 20400 20465.53 217.05 295.34 5140.52 0.083 19025 19081.98 216.65 295.07 6384.79 0.103 20425 20490.69 217.08 295.36 5120.34 0.082 19050 19107.13 216.65 295.07 6359.67 0.102 20450 20515.85 217.1 295.38 5100.23 0.082 19075 19132.28 216.65 295.07 6334.64 0.102 20475 20541.01 217.13 295.39 5080.21 0.082 19100 19157.43 216.65 295.07 6309.72 0.101 20500 20566.18 217.15 295.41 5060.26 0.081 19125 19182.58 216.65 295.07 6284.9 0.101 20525 20591.34 217.18 295.43 5040.4 0.081 19150 19207.73 216.65 295.07 6260.17 0.101 20550 20616.5 217.2 295.44 5020.62 0.081 19175 19232.89 216.65 295.07 6235.54 0.1 20575 20641.66 217.23 295.46 5000.92 0.08 19200 19258.04 216.65 295.07 6211 0.1 20600 20666.82 217.25 295.48 4981.29 0.08 19225 19283.19 216.65 295.07 6186.57 0.099 20625 20691.99 217.28 295.49 4961.75 0.08 19250 19308.34 216.65 295.07 6162.23 0.099 20650 20717.15 217.3 295.51 4942.29 0.079 19275 19333.49 216.65 295.07 6137.98 0.099 20675 20742.31 217.33 295.53 4922.9 0.079 19300 19358.64 216.65 295.07 6113.83 0.098 20700 20767.48 217.35 295.55 4903.59 0.079 19325 19383.8 216.65 295.07 6089.78 0.098 20725 20792.64 217.38 295.56 4884.36 0.078 19350 19408.95 216.65 295.07 6065.82 0.098 20750 20817.8 217.4 295.58 4865.21 0.078 19375 19434.1 216.65 295.07 6041.95 0.097 20775 20842.97 217.43 295.6 4846.14 0.078 19400 19459.25 216.65 295.07 6018.18 0.097 20800 20868.13 217.45 295.61 4827.14 0.077 19425 19484.41 216.65 295.07 5994.5 0.096 20825 20893.29 217.48 295.63 4808.22 0.077 19450 19509.56 216.65 295.07 5970.92 0.096 20850 20918.46 217.5 295.65 4789.37 0.077 19475 19534.71 216.65 295.07 5947.43 0.096 20875 20943.62 217.53 295.66 4770.6 0.076 19500 19559.87 216.65 295.07 5924.03 0.095 20900 20968.79 217.55 295.68 4751.91 0.076 19525 19585.02 216.65 295.07 5900.72 0.095 20925 20993.95 217.58 295.7 4733.29 0.076 19550 19610.18 216.65 295.07 5877.5 0.095 20950 21019.12 217.6 295.72 4714.75 0.075 19575 19635.33 216.65 295.07 5854.38 0.094 20975 21044.28 217.63 295.73 4696.28 0.075 19600 19660.48 216.65 295.07 5831.34 0.094 21000 21069.45 217.65 295.75 4677.89 0.075 19625 19685.64 216.65 295.07 5808.4 0.093 21025 21094.61 217.68 295.77 4659.57 0.075 19650 19710.79 216.65 295.07 5785.55 0.093 21050 21119.78 217.7 295.78 4641.32 0.074 19675 19735.95 216.65 295.07 5762.78 0.093 21075 21144.95 217.73 295.8 4623.15 0.074 19700 19761.1 216.65 295.07 5740.11 0.092 21100 21170.11 217.75 295.82 4605.05 0.074 19725 19786.26 216.65 295.07 5717.53 0.092 21125 21195.28 217.78 295.83 4587.02 0.073 19750 19811.42 216.65 295.07 5695.03 0.092 21150 21220.45 217.8 295.85 4569.07 0.073 19775 19836.57 216.65 295.07 5672.62 0.091 21175 21245.61 217.83 295.87 4551.19 0.073 19800 19861.73 216.65 295.07 5650.31 0.091 21200 21270.78 217.85 295.89 4533.38 0.072 19825 19886.88 216.65 295.07 5628.07 0.09 21225 21295.95 217.88 295.9 4515.64 0.072 19850 19912.04 216.65 295.07 5605.93 0.09 21250 21321.12 217.9 295.92 4497.98 0.072 19875 19937.2 216.65 295.07 5583.88 0.09 21275 21346.28 217.93 295.94 4480.38 0.072 19900 19962.35 216.65 295.07 5561.91 0.089 21300 21371.45 217.95 295.95 4462.86 0.071 19925 19987.51 216.65 295.07 5540.02 0.089 19950 20012.67 216.65 295.07 5518.23 0.089 Appendix C: The Standard Atmosphere 419 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 21325 21396.62 217.98 295.97 4445.41 0.071 22700 22781.17 219.35 296.9 3586.03 0.057 21350 21421.79 218 295.99 4428.02 0.071 22725 22806.35 219.38 296.92 3572.09 0.057 21375 21446.96 218.03 296 4410.71 0.07 22750 22831.53 219.4 296.94 3558.21 0.056 21400 21472.12 218.05 296.02 4393.47 0.07 22775 22856.71 219.43 296.95 3544.39 0.056 21425 21497.29 218.08 296.04 4376.29 0.07 22800 22881.89 219.45 296.97 3530.62 0.056 21450 21522.46 218.1 296.06 4359.19 0.07 22825 22907.07 219.48 296.99 3516.91 0.056 21475 21547.63 218.13 296.07 4342.15 0.069 22850 22932.25 219.5 297 3503.25 0.056 21500 21572.8 218.15 296.09 4325.18 0.069 22875 22957.43 219.53 297.02 3489.64 0.055 21525 21597.97 218.18 296.11 4308.28 0.069 22900 22982.61 219.55 297.04 3476.09 0.055 21550 21623.14 218.2 296.12 4291.45 0.069 22925 23007.79 219.58 297.05 3462.6 0.055 21575 21648.31 218.23 296.14 4274.69 0.068 22950 23032.97 219.6 297.07 3449.16 0.055 21600 21673.48 218.25 296.16 4257.99 0.068 22975 23058.15 219.63 297.09 3435.77 0.054 21625 21698.65 218.28 296.17 4241.36 0.068 23000 23083.33 219.65 297.11 3422.43 0.054 21650 21723.82 218.3 296.19 4224.8 0.067 23025 23108.51 219.68 297.12 3409.15 0.054 21675 21748.99 218.33 296.21 4208.3 0.067 23050 23133.7 219.7 297.14 3395.93 0.054 21700 21774.16 218.35 296.23 4191.87 0.067 23075 23158.88 219.73 297.16 3382.75 0.054 21725 21799.34 218.38 296.24 4175.51 0.067 23100 23184.06 219.75 297.17 3369.63 0.053 21750 21824.51 218.4 296.26 4159.21 0.066 23125 23209.24 219.78 297.19 3356.56 0.053 21775 21849.68 218.43 296.28 4142.98 0.066 23150 23234.43 219.8 297.21 3343.54 0.053 21800 21874.85 218.45 296.29 4126.81 0.066 23175 23259.61 219.83 297.22 3330.57 0.053 21825 21900.02 218.48 296.31 4110.71 0.066 23200 23284.79 219.85 297.24 3317.66 0.053 21850 21925.19 218.5 296.33 4094.67 0.065 23225 23309.97 219.88 297.26 3304.8 0.052 21875 21950.37 218.53 296.34 4078.7 0.065 23250 23335.16 219.9 297.27 3291.98 0.052 21900 21975.54 218.55 296.36 4062.79 0.065 23275 23360.34 219.93 297.29 3279.22 0.052 21925 22000.71 218.58 296.38 4046.95 0.065 23300 23385.53 219.95 297.31 3266.51 0.052 21950 22025.89 218.6 296.39 4031.16 0.064 23325 23410.71 219.98 297.33 3253.86 0.052 21975 22051.06 218.63 296.41 4015.45 0.064 23350 23435.89 220 297.34 3241.25 0.051 22000 22076.23 218.65 296.43 3999.79 0.064 23375 23461.08 220.03 297.36 3228.69 0.051 22025 22101.41 218.68 296.45 3984.2 0.063 23400 23486.26 220.05 297.38 3216.18 0.051 22050 22126.58 218.7 296.46 3968.67 0.063 23425 23511.45 220.08 297.39 3203.72 0.051 22075 22151.75 218.73 296.48 3953.2 0.063 23450 23536.63 220.1 297.41 3191.32 0.051 22100 22176.93 218.75 296.5 3937.79 0.063 23475 23561.82 220.13 297.43 3178.96 0.05 22125 22202.1 218.78 296.51 3922.45 0.062 23500 23587 220.15 297.44 3166.65 0.05 22150 22227.28 218.8 296.53 3907.17 0.062 23525 23612.19 220.18 297.46 3154.39 0.05 22175 22252.45 218.83 296.55 3891.95 0.062 23550 23637.37 220.2 297.48 3142.17 0.05 22200 22277.63 218.85 296.56 3876.79 0.062 23575 23662.56 220.23 297.49 3130.01 0.05 22225 22302.8 218.88 296.58 3861.69 0.061 23600 23687.75 220.25 297.51 3117.9 0.049 22250 22327.98 218.9 296.6 3846.65 0.061 23625 23712.93 220.28 297.53 3105.83 0.049 22275 22353.15 218.93 296.61 3831.67 0.061 23650 23738.12 220.3 297.54 3093.81 0.049 22300 22378.33 218.95 296.63 3816.75 0.061 23675 23763.31 220.33 297.56 3081.84 0.049 22325 22403.51 218.98 296.65 3801.9 0.06 23700 23788.49 220.35 297.58 3069.92 0.049 22350 22428.68 219 296.67 3787.1 0.06 23725 23813.68 220.38 297.6 3058.04 0.048 22375 22453.86 219.03 296.68 3772.36 0.06 23750 23838.87 220.4 297.61 3046.21 0.048 22400 22479.03 219.05 296.7 3757.68 0.06 23775 23864.05 220.43 297.63 3034.43 0.048 22425 22504.21 219.08 296.72 3743.05 0.06 23800 23889.24 220.45 297.65 3022.7 0.048 22450 22529.39 219.1 296.73 3728.49 0.059 23825 23914.43 220.48 297.66 3011.01 0.048 22475 22554.57 219.13 296.75 3713.99 0.059 23850 23939.62 220.5 297.68 2999.37 0.047 22500 22579.74 219.15 296.77 3699.54 0.059 23875 23964.81 220.53 297.7 2987.78 0.047 22525 22604.92 219.18 296.78 3685.15 0.059 23900 23990 220.55 297.71 2976.23 0.047 22550 22630.1 219.2 296.8 3670.82 0.058 23925 24015.18 220.58 297.73 2964.73 0.047 22575 22655.28 219.23 296.82 3656.54 0.058 23950 24040.37 220.6 297.75 2953.27 0.047 22600 22680.45 219.25 296.83 3642.33 0.058 23975 24065.56 220.63 297.76 2941.86 0.046 22625 22705.63 219.28 296.85 3628.17 0.058 24000 24090.75 220.65 297.78 2930.49 0.046 22650 22730.81 219.3 296.87 3614.06 0.057 24025 24115.94 220.68 297.8 2919.17 0.046 22675 22755.99 219.33 296.89 3600.02 0.057 24050 24141.13 220.7 297.81 2907.9 0.046 420 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 24075 24166.32 220.73 297.83 2896.67 0.046 25450 25552.07 222.1 298.76 2342.93 0.037 24100 24191.51 220.75 297.85 2885.48 0.046 25475 25577.27 222.13 298.77 2333.94 0.037 24125 24216.7 220.78 297.87 2874.34 0.045 25500 25602.47 222.15 298.79 2324.98 0.036 24150 24241.89 220.8 297.88 2863.24 0.045 25525 25627.68 222.18 298.81 2316.06 0.036 24175 24267.08 220.83 297.9 2852.19 0.045 25550 25652.88 222.2 298.83 2307.17 0.036 24200 24292.27 220.85 297.92 2841.18 0.045 25575 25678.08 222.23 298.84 2298.32 0.036 24225 24317.46 220.88 297.93 2830.21 0.045 25600 25703.28 222.25 298.86 2289.51 0.036 24250 24342.66 220.9 297.95 2819.29 0.044 25625 25728.48 222.28 298.88 2280.73 0.036 24275 24367.85 220.93 297.97 2808.41 0.044 25650 25753.69 222.3 298.89 2271.98 0.036 24300 24393.04 220.95 297.98 2797.58 0.044 25675 25778.89 222.33 298.91 2263.27 0.035 24325 24418.23 220.98 298 2786.78 0.044 25700 25804.09 222.35 298.93 2254.59 0.035 24350 24443.42 221 298.02 2776.03 0.044 25725 25829.29 222.38 298.94 2245.95 0.035 24375 24468.62 221.03 298.03 2765.33 0.044 25750 25854.5 222.4 298.96 2237.34 0.035 24400 24493.81 221.05 298.05 2754.66 0.043 25775 25879.7 222.43 298.98 2228.76 0.035 24425 24519 221.08 298.07 2744.04 0.043 25800 25904.9 222.45 298.99 2220.22 0.035 24450 24544.19 221.1 298.08 2733.46 0.043 25825 25930.11 222.48 299.01 2211.71 0.035 24475 24569.39 221.13 298.1 2722.92 0.043 25850 25955.31 222.5 299.03 2203.24 0.034 24500 24594.58 221.15 298.12 2712.42 0.043 25875 25980.52 222.53 299.04 2194.8 0.034 24525 24619.77 221.18 298.14 2701.97 0.043 25900 26005.72 222.55 299.06 2186.39 0.034 24550 24644.97 221.2 298.15 2691.56 0.042 25925 26030.93 222.58 299.08 2178.02 0.034 24575 24670.16 221.23 298.17 2681.19 0.042 25950 26056.13 222.6 299.09 2169.68 0.034 24600 24695.35 221.25 298.19 2670.85 0.042 25975 26081.34 222.63 299.11 2161.37 0.034 24625 24720.55 221.28 298.2 2660.57 0.042 26000 26106.54 222.65 299.13 2153.09 0.034 24650 24745.74 221.3 298.22 2650.32 0.042 26025 26131.75 222.68 299.14 2144.85 0.034 24675 24770.94 221.33 298.24 2640.11 0.042 26050 26156.95 222.7 299.16 2136.64 0.033 24700 24796.13 221.35 298.25 2629.94 0.041 26075 26182.16 222.73 299.18 2128.46 0.033 24725 24821.33 221.38 298.27 2619.81 0.041 26100 26207.36 222.75 299.19 2120.32 0.033 24750 24846.52 221.4 298.29 2609.73 0.041 26125 26232.57 222.78 299.21 2112.2 0.033 24775 24871.72 221.43 298.3 2599.68 0.041 26150 26257.78 222.8 299.23 2104.12 0.033 24800 24896.91 221.45 298.32 2589.67 0.041 26175 26282.98 222.83 299.25 2096.07 0.033 24825 24922.11 221.48 298.34 2579.7 0.041 26200 26308.19 222.85 299.26 2088.05 0.033 24850 24947.31 221.5 298.35 2569.77 0.04 26225 26333.4 222.88 299.28 2080.07 0.033 24875 24972.5 221.53 298.37 2559.88 0.04 26250 26358.6 222.9 299.3 2072.11 0.032 24900 24997.7 221.55 298.39 2550.03 0.04 26275 26383.81 222.93 299.31 2064.19 0.032 24925 25022.9 221.58 298.4 2540.22 0.04 26300 26409.02 222.95 299.33 2056.29 0.032 24950 25048.09 221.6 298.42 2530.45 0.04 26325 26434.23 222.98 299.35 2048.43 0.032 24975 25073.29 221.63 298.44 2520.72 0.04 26350 26459.43 223 299.36 2040.6 0.032 25000 25098.49 221.65 298.46 2511.02 0.039 26375 26484.64 223.03 299.38 2032.8 0.032 25025 25123.68 221.68 298.47 2501.37 0.039 26400 26509.85 223.05 299.4 2025.03 0.032 25050 25148.88 221.7 298.49 2491.75 0.039 26425 26535.06 223.08 299.41 2017.29 0.032 25075 25174.08 221.73 298.51 2482.17 0.039 26450 26560.27 223.1 299.43 2009.58 0.031 25100 25199.28 221.75 298.52 2472.63 0.039 26475 26585.48 223.13 299.45 2001.91 0.031 25125 25224.48 221.78 298.54 2463.12 0.039 26500 26610.69 223.15 299.46 1994.26 0.031 25150 25249.67 221.8 298.56 2453.65 0.039 26525 26635.9 223.18 299.48 1986.64 0.031 25175 25274.87 221.83 298.57 2444.22 0.038 26550 26661.11 223.2 299.5 1979.05 0.031 25200 25300.07 221.85 298.59 2434.83 0.038 26575 26686.32 223.23 299.51 1971.49 0.031 25225 25325.27 221.88 298.61 2425.48 0.038 26600 26711.53 223.25 299.53 1963.97 0.031 25250 25350.47 221.9 298.62 2416.16 0.038 26625 26736.74 223.28 299.55 1956.47 0.031 25275 25375.67 221.93 298.64 2406.88 0.038 26650 26761.95 223.3 299.56 1949 0.03 25300 25400.87 221.95 298.66 2397.63 0.038 26675 26787.16 223.33 299.58 1941.56 0.03 25325 25426.07 221.98 298.67 2388.43 0.037 26700 26812.37 223.35 299.6 1934.15 0.03 25350 25451.27 222 298.69 2379.25 0.037 26725 26837.58 223.38 299.61 1926.77 0.03 25375 25476.47 222.03 298.71 2370.12 0.037 26750 26862.79 223.4 299.63 1919.41 0.03 25400 25501.67 222.05 298.72 2361.02 0.037 26775 26888 223.43 299.65 1912.09 0.03 25425 25526.87 222.08 298.74 2351.96 0.037 26800 26913.21 223.45 299.66 1904.8 0.03 Appendix C: The Standard Atmosphere 421 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 26825 26938.42 223.48 299.68 1897.53 0.03 28200 28325.38 224.85 300.6 1538.79 0.024 26850 26963.64 223.5 299.7 1890.29 0.029 28225 28350.6 224.88 300.62 1532.96 0.024 26875 26988.85 223.53 299.71 1883.08 0.029 28250 28375.82 224.9 300.64 1527.15 0.024 26900 27014.06 223.55 299.73 1875.9 0.029 28275 28401.05 224.93 300.65 1521.36 0.024 26925 27039.27 223.58 299.75 1868.75 0.029 28300 28426.27 224.95 300.67 1515.59 0.023 26950 27064.49 223.6 299.77 1861.62 0.029 28325 28451.49 224.98 300.69 1509.85 0.023 26975 27089.7 223.63 299.78 1854.53 0.029 28350 28476.72 225 300.7 1504.13 0.023 27000 27114.91 223.65 299.8 1847.46 0.029 28375 28501.94 225.03 300.72 1498.43 0.023 27025 27140.13 223.68 299.82 1840.42 0.029 28400 28527.17 225.05 300.74 1492.75 0.023 27050 27165.34 223.7 299.83 1833.4 0.029 28425 28552.39 225.08 300.75 1487.1 0.023 27075 27190.55 223.73 299.85 1826.42 0.028 28450 28577.61 225.1 300.77 1481.47 0.023 27100 27215.77 223.75 299.87 1819.46 0.028 28475 28602.84 225.13 300.79 1475.86 0.023 27125 27240.98 223.78 299.88 1812.53 0.028 28500 28628.06 225.15 300.8 1470.27 0.023 27150 27266.19 223.8 299.9 1805.62 0.028 28525 28653.29 225.18 300.82 1464.7 0.023 27175 27291.41 223.83 299.92 1798.74 0.028 28550 28678.52 225.2 300.84 1459.16 0.023 27200 27316.62 223.85 299.93 1791.89 0.028 28575 28703.74 225.23 300.85 1453.64 0.022 27225 27341.84 223.88 299.95 1785.07 0.028 28600 28728.97 225.25 300.87 1448.13 0.022 27250 27367.05 223.9 299.97 1778.27 0.028 28625 28754.19 225.28 300.89 1442.65 0.022 27275 27392.27 223.93 299.98 1771.5 0.028 28650 28779.42 225.3 300.9 1437.19 0.022 27300 27417.49 223.95 300 1764.76 0.027 28675 28804.65 225.33 300.92 1431.76 0.022 27325 27442.7 223.98 300.02 1758.04 0.027 28700 28829.87 225.35 300.94 1426.34 0.022 27350 27467.92 224 300.03 1751.35 0.027 28725 28855.1 225.38 300.95 1420.95 0.022 27375 27493.13 224.03 300.05 1744.69 0.027 28750 28880.33 225.4 300.97 1415.57 0.022 27400 27518.35 224.05 300.07 1738.05 0.027 28775 28905.55 225.43 300.99 1410.22 0.022 27425 27543.57 224.08 300.08 1731.44 0.027 28800 28930.78 225.45 301 1404.89 0.022 27450 27568.78 224.1 300.1 1724.85 0.027 28825 28956.01 225.48 301.02 1399.57 0.022 27475 27594 224.13 300.12 1718.29 0.027 28850 28981.24 225.5 301.04 1394.28 0.022 27500 27619.22 224.15 300.13 1711.75 0.027 28875 29006.46 225.53 301.05 1389.01 0.021 27525 27644.43 224.18 300.15 1705.25 0.026 28900 29031.69 225.55 301.07 1383.76 0.021 27550 27669.65 224.2 300.17 1698.76 0.026 28925 29056.92 225.58 301.09 1378.53 0.021 27575 27694.87 224.23 300.18 1692.3 0.026 28950 29082.15 225.6 301.1 1373.32 0.021 27600 27720.09 224.25 300.2 1685.87 0.026 28975 29107.38 225.63 301.12 1368.13 0.021 27625 27745.31 224.28 300.22 1679.46 0.026 29000 29132.61 225.65 301.14 1362.96 0.021 27650 27770.52 224.3 300.23 1673.08 0.026 29025 29157.84 225.68 301.15 1357.82 0.021 27675 27795.74 224.33 300.25 1666.72 0.026 29050 29183.07 225.7 301.17 1352.69 0.021 27700 27820.96 224.35 300.27 1660.39 0.026 29075 29208.3 225.73 301.19 1347.58 0.021 27725 27846.18 224.38 300.28 1654.08 0.026 29100 29233.53 225.75 301.2 1342.49 0.021 27750 27871.4 224.4 300.3 1647.79 0.026 29125 29258.76 225.78 301.22 1337.42 0.021 27775 27896.62 224.43 300.32 1641.53 0.025 29150 29283.99 225.8 301.24 1332.37 0.021 27800 27921.84 224.45 300.33 1635.3 0.025 29175 29309.22 225.83 301.25 1327.34 0.02 27825 27947.06 224.48 300.35 1629.09 0.025 29200 29334.45 225.85 301.27 1322.33 0.02 27850 27972.28 224.5 300.37 1622.9 0.025 29225 29359.68 225.88 301.29 1317.34 0.02 27875 27997.5 224.53 300.38 1616.74 0.025 29250 29384.91 225.9 301.3 1312.37 0.02 27900 28022.72 224.55 300.4 1610.6 0.025 29275 29410.14 225.93 301.32 1307.42 0.02 27925 28047.94 224.58 300.42 1604.49 0.025 29300 29435.37 225.95 301.34 1302.48 0.02 27950 28073.16 224.6 300.43 1598.4 0.025 29325 29460.6 225.98 301.35 1297.57 0.02 27975 28098.38 224.63 300.45 1592.33 0.025 29350 29485.84 226 301.37 1292.68 0.02 28000 28123.6 224.65 300.47 1586.29 0.025 29375 29511.07 226.03 301.39 1287.8 0.02 28025 28148.82 224.68 300.48 1580.27 0.025 29400 29536.3 226.05 301.4 1282.94 0.02 28050 28174.04 224.7 300.5 1574.28 0.024 29425 29561.53 226.08 301.42 1278.1 0.02 28075 28199.27 224.73 300.52 1568.3 0.024 29450 29586.77 226.1 301.44 1273.29 0.02 28100 28224.49 224.75 300.53 1562.35 0.024 29475 29612 226.13 301.45 1268.49 0.02 28125 28249.71 224.78 300.55 1556.43 0.024 29500 29637.23 226.15 301.47 1263.7 0.019 28150 28274.93 224.8 300.57 1550.53 0.024 29525 29662.46 226.18 301.49 1258.94 0.019 28175 28300.15 224.83 300.59 1544.65 0.024 29550 29687.7 226.2 301.5 1254.2 0.019 422 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 29575 29712.93 226.23 301.52 1249.47 0.019 30950 31101.09 227.6 302.43 1015.83 0.016 29600 29738.17 226.25 301.54 1244.76 0.019 30975 31126.33 227.63 302.45 1012.02 0.015 29625 29763.4 226.28 301.55 1240.07 0.019 31000 31151.58 227.65 302.47 1008.23 0.015 29650 29788.63 226.3 301.57 1235.4 0.019 31025 31176.82 227.68 302.48 1004.46 0.015 29675 29813.87 226.33 301.59 1230.75 0.019 31050 31202.07 227.7 302.5 1000.7 0.015 29700 29839.1 226.35 301.6 1226.11 0.019 31075 31227.31 227.73 302.52 996.95 0.015 29725 29864.34 226.38 301.62 1221.49 0.019 31100 31252.56 227.75 302.53 993.22 0.015 29750 29889.57 226.4 301.64 1216.89 0.019 31125 31277.81 227.78 302.55 989.5 0.015 29775 29914.81 226.43 301.65 1212.31 0.019 31150 31303.05 227.8 302.57 985.8 0.015 29800 29940.04 226.45 301.67 1207.75 0.019 31175 31328.3 227.83 302.58 982.11 0.015 29825 29965.28 226.48 301.69 1203.2 0.019 31200 31353.54 227.85 302.6 978.43 0.015 29850 29990.51 226.5 301.7 1198.67 0.018 31225 31378.79 227.88 302.62 974.77 0.015 29875 30015.75 226.53 301.72 1194.16 0.018 31250 31404.04 227.9 302.63 971.13 0.015 29900 30040.99 226.55 301.74 1189.67 0.018 31275 31429.29 227.93 302.65 967.49 0.015 29925 30066.22 226.58 301.75 1185.19 0.018 31300 31454.53 227.95 302.67 963.88 0.015 29950 30091.46 226.6 301.77 1180.73 0.018 31325 31479.78 227.98 302.68 960.27 0.015 29975 30116.7 226.63 301.79 1176.29 0.018 31350 31505.03 228 302.7 956.68 0.015 30000 30141.93 226.65 301.8 1171.87 0.018 31375 31530.28 228.03 302.72 953.1 0.015 30025 30167.17 226.68 301.82 1167.46 0.018 31400 31555.52 228.05 302.73 949.54 0.015 30050 30192.41 226.7 301.84 1163.07 0.018 31425 31580.77 228.08 302.75 945.99 0.014 30075 30217.65 226.73 301.85 1158.7 0.018 31450 31606.02 228.1 302.77 942.46 0.014 30100 30242.88 226.75 301.87 1154.34 0.018 31475 31631.27 228.13 302.78 938.93 0.014 30125 30268.12 226.78 301.89 1150 0.018 31500 31656.52 228.15 302.8 935.43 0.014 30150 30293.36 226.8 301.9 1145.68 0.018 31525 31681.77 228.18 302.82 931.93 0.014 30175 30318.6 226.83 301.92 1141.37 0.018 31550 31707.02 228.2 302.83 928.45 0.014 30200 30343.84 226.85 301.94 1137.08 0.017 31575 31732.27 228.23 302.85 924.98 0.014 30225 30369.08 226.88 301.95 1132.81 0.017 31600 31757.52 228.25 302.87 921.53 0.014 30250 30394.31 226.9 301.97 1128.55 0.017 31625 31782.77 228.28 302.88 918.08 0.014 30275 30419.55 226.93 301.99 1124.31 0.017 31650 31808.02 228.3 302.9 914.66 0.014 30300 30444.79 226.95 302 1120.09 0.017 31675 31833.27 228.33 302.92 911.24 0.014 30325 30470.03 226.98 302.02 1115.88 0.017 31700 31858.52 228.35 302.93 907.84 0.014 30350 30495.27 227 302.04 1111.69 0.017 31725 31883.77 228.38 302.95 904.45 0.014 30375 30520.51 227.03 302.05 1107.52 0.017 31750 31909.02 228.4 302.97 901.07 0.014 30400 30545.75 227.05 302.07 1103.36 0.017 31775 31934.27 228.43 302.98 897.71 0.014 30425 30570.99 227.08 302.09 1099.22 0.017 31800 31959.52 228.45 303 894.36 0.014 30450 30596.23 227.1 302.1 1095.09 0.017 31825 31984.77 228.48 303.02 891.02 0.014 30475 30621.47 227.13 302.12 1090.98 0.017 31850 32010.03 228.5 303.03 887.7 0.014 30500 30646.72 227.15 302.14 1086.88 0.017 31875 32035.28 228.53 303.05 884.39 0.013 30525 30671.96 227.18 302.15 1082.81 0.017 31900 32060.53 228.55 303.06 881.09 0.013 30550 30697.2 227.2 302.17 1078.74 0.017 31925 32085.78 228.58 303.08 877.8 0.013 30575 30722.44 227.23 302.19 1074.7 0.016 31950 32111.03 228.6 303.1 874.53 0.013 30600 30747.68 227.25 302.2 1070.66 0.016 31975 32136.29 228.63 303.11 871.27 0.013 30625 30772.92 227.28 302.22 1066.65 0.016 32000 32161.54 228.65 303.13 868.02 0.013 30650 30798.17 227.3 302.24 1062.65 0.016 32025 32186.79 228.72 303.18 864.78 0.013 30675 30823.41 227.33 302.25 1058.66 0.016 32050 32212.05 228.79 303.22 861.56 0.013 30700 30848.65 227.35 302.27 1054.69 0.016 32075 32237.3 228.86 303.27 858.35 0.013 30725 30873.89 227.38 302.28 1050.74 0.016 32100 32262.55 228.93 303.32 855.15 0.013 30750 30899.14 227.4 302.3 1046.8 0.016 32125 32287.81 229 303.36 851.97 0.013 30775 30924.38 227.43 302.32 1042.87 0.016 32150 32313.06 229.07 303.41 848.8 0.013 30800 30949.62 227.45 302.33 1038.97 0.016 32175 32338.32 229.14 303.46 845.64 0.013 30825 30974.87 227.48 302.35 1035.07 0.016 32200 32363.57 229.21 303.5 842.49 0.013 30850 31000.11 227.5 302.37 1031.19 0.016 32225 32388.83 229.28 303.55 839.36 0.013 30875 31025.35 227.53 302.38 1027.33 0.016 32250 32414.08 229.35 303.59 836.24 0.013 30900 31050.6 227.55 302.4 1023.48 0.016 32275 32439.34 229.42 303.64 833.13 0.013 30925 31075.84 227.58 302.42 1019.65 0.016 32300 32464.59 229.49 303.69 830.04 0.013 Appendix C: The Standard Atmosphere 423 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 32325 32489.85 229.56 303.73 826.96 0.013 33700 33879.21 233.41 306.27 675.07 0.01 32350 32515.1 229.63 303.78 823.88 0.012 33725 33904.47 233.48 306.32 672.61 0.01 32375 32540.36 229.7 303.83 820.83 0.012 33750 33929.74 233.55 306.36 670.15 0.01 32400 32565.61 229.77 303.87 817.78 0.012 33775 33955.01 233.62 306.41 667.71 0.01 32425 32590.87 229.84 303.92 814.75 0.012 33800 33980.28 233.69 306.45 665.27 0.01 32450 32616.13 229.91 303.97 811.73 0.012 33825 34005.54 233.76 306.5 662.84 0.01 32475 32641.38 229.98 304.01 808.72 0.012 33850 34030.81 233.83 306.55 660.43 0.01 32500 32666.64 230.05 304.06 805.72 0.012 33875 34056.08 233.9 306.59 658.02 0.01 32525 32691.9 230.12 304.1 802.73 0.012 33900 34081.35 233.97 306.64 655.62 0.01 32550 32717.15 230.19 304.15 799.76 0.012 33925 34106.61 234.04 306.68 653.23 0.01 32575 32742.41 230.26 304.2 796.8 0.012 33950 34131.88 234.11 306.73 650.85 0.01 32600 32767.67 230.33 304.24 793.85 0.012 33975 34157.15 234.18 306.78 648.48 0.01 32625 32792.93 230.4 304.29 790.91 0.012 34000 34182.42 234.25 306.82 646.12 0.01 32650 32818.19 230.47 304.34 787.99 0.012 34025 34207.69 234.32 306.87 643.77 0.01 32675 32843.44 230.54 304.38 785.07 0.012 34050 34232.96 234.39 306.91 641.43 0.01 32700 32868.7 230.61 304.43 782.17 0.012 34075 34258.23 234.46 306.96 639.1 0.009 32725 32893.96 230.68 304.47 779.28 0.012 34100 34283.5 234.53 307 636.77 0.009 32750 32919.22 230.75 304.52 776.4 0.012 34125 34308.77 234.6 307.05 634.46 0.009 32775 32944.48 230.82 304.57 773.53 0.012 34150 34334.04 234.67 307.1 632.15 0.009 32800 32969.74 230.89 304.61 770.67 0.012 34175 34359.31 234.74 307.14 629.86 0.009 32825 32995 230.96 304.66 767.83 0.012 34200 34384.58 234.81 307.19 627.57 0.009 32850 33020.26 231.03 304.7 764.99 0.012 34225 34409.85 234.88 307.23 625.29 0.009 32875 33045.52 231.1 304.75 762.17 0.011 34250 34435.12 234.95 307.28 623.02 0.009 32900 33070.78 231.17 304.8 759.36 0.011 34275 34460.39 235.02 307.32 620.76 0.009 32925 33096.04 231.24 304.84 756.56 0.011 34300 34485.66 235.09 307.37 618.51 0.009 32950 33121.3 231.31 304.89 753.77 0.011 34325 34510.93 235.16 307.42 616.27 0.009 32975 33146.56 231.38 304.94 750.99 0.011 34350 34536.21 235.23 307.46 614.03 0.009 33000 33171.82 231.45 304.98 748.23 0.011 34375 34561.48 235.3 307.51 611.81 0.009 33025 33197.08 231.52 305.03 745.47 0.011 34400 34586.75 235.37 307.55 609.59 0.009 33050 33222.34 231.59 305.07 742.73 0.011 34425 34612.02 235.44 307.6 607.39 0.009 33075 33247.6 231.66 305.12 739.99 0.011 34450 34637.29 235.51 307.64 605.19 0.009 33100 33272.87 231.73 305.17 737.27 0.011 34475 34662.57 235.58 307.69 603 0.009 33125 33298.13 231.8 305.21 734.56 0.011 34500 34687.84 235.65 307.74 600.81 0.009 33150 33323.39 231.87 305.26 731.86 0.011 34525 34713.11 235.72 307.78 598.64 0.009 33175 33348.65 231.94 305.3 729.17 0.011 34550 34738.39 235.79 307.83 596.48 0.009 33200 33373.92 232.01 305.35 726.49 0.011 34575 34763.66 235.86 307.87 594.32 0.009 33225 33399.18 232.08 305.4 723.82 0.011 34600 34788.93 235.93 307.92 592.17 0.009 33250 33424.44 232.15 305.44 721.16 0.011 34625 34814.21 236 307.96 590.03 0.009 33275 33449.7 232.22 305.49 718.51 0.011 34650 34839.48 236.07 308.01 587.9 0.009 33300 33474.97 232.29 305.53 715.88 0.011 34675 34864.76 236.14 308.06 585.78 0.009 33325 33500.23 232.36 305.58 713.25 0.011 34700 34890.03 236.21 308.1 583.66 0.009 33350 33525.49 232.43 305.63 710.63 0.011 34725 34915.31 236.28 308.15 581.56 0.009 33375 33550.76 232.5 305.67 708.03 0.011 34750 34940.58 236.35 308.19 579.46 0.009 33400 33576.02 232.57 305.72 705.43 0.011 34775 34965.86 236.42 308.24 577.37 0.009 33425 33601.29 232.64 305.76 702.85 0.011 34800 34991.13 236.49 308.28 575.29 0.008 33450 33626.55 232.71 305.81 700.27 0.01 34825 35016.41 236.56 308.33 573.21 0.008 33475 33651.82 232.78 305.86 697.7 0.01 34850 35041.68 236.63 308.38 571.15 0.008 33500 33677.08 232.85 305.9 695.15 0.01 34875 35066.96 236.7 308.42 569.09 0.008 33525 33702.35 232.92 305.95 692.61 0.01 34900 35092.23 236.77 308.47 567.04 0.008 33550 33727.61 232.99 305.99 690.07 0.01 34925 35117.51 236.84 308.51 565 0.008 33575 33752.88 233.06 306.04 687.55 0.01 34950 35142.79 236.91 308.56 562.97 0.008 33600 33778.14 233.13 306.09 685.03 0.01 34975 35168.06 236.98 308.6 560.94 0.008 33625 33803.41 233.2 306.13 682.53 0.01 35000 35193.34 237.05 308.65 558.92 0.008 33650 33828.67 233.27 306.18 680.03 0.01 35025 35218.62 237.12 308.69 556.91 0.008 33675 33853.94 233.34 306.22 677.55 0.01 35050 35243.89 237.19 308.74 554.91 0.008 424 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 35075 35269.17 237.26 308.79 552.92 0.008 36450 36659.74 241.11 311.28 454.32 0.007 35100 35294.45 237.33 308.83 550.93 0.008 36475 36685.03 241.18 311.33 452.72 0.007 35125 35319.73 237.4 308.88 548.95 0.008 36500 36710.32 241.25 311.37 451.12 0.007 35150 35345.01 237.47 308.92 546.98 0.008 36525 36735.61 241.32 311.42 449.52 0.006 35175 35370.28 237.54 308.97 545.02 0.008 36550 36760.89 241.39 311.46 447.94 0.006 35200 35395.56 237.61 309.01 543.06 0.008 36575 36786.18 241.46 311.51 446.35 0.006 35225 35420.84 237.68 309.06 541.11 0.008 36600 36811.47 241.53 311.55 444.78 0.006 35250 35446.12 237.75 309.1 539.17 0.008 36625 36836.76 241.6 311.6 443.21 0.006 35275 35471.4 237.82 309.15 537.24 0.008 36650 36862.05 241.67 311.64 441.64 0.006 35300 35496.68 237.89 309.2 535.31 0.008 36675 36887.34 241.74 311.69 440.09 0.006 35325 35521.96 237.96 309.24 533.4 0.008 36700 36912.63 241.81 311.73 438.53 0.006 35350 35547.24 238.03 309.29 531.49 0.008 36725 36937.93 241.88 311.78 436.99 0.006 35375 35572.52 238.1 309.33 529.58 0.008 36750 36963.22 241.95 311.82 435.45 0.006 35400 35597.8 238.17 309.38 527.69 0.008 36775 36988.51 242.02 311.87 433.91 0.006 35425 35623.08 238.24 309.42 525.8 0.008 36800 37013.8 242.09 311.91 432.39 0.006 35450 35648.36 238.31 309.47 523.92 0.008 36825 37039.09 242.16 311.96 430.86 0.006 35475 35673.64 238.38 309.51 522.04 0.008 36850 37064.38 242.23 312 429.35 0.006 35500 35698.92 238.45 309.56 520.18 0.008 36875 37089.67 242.3 312.05 427.84 0.006 35525 35724.2 238.52 309.6 518.32 0.008 36900 37114.97 242.37 312.09 426.33 0.006 35550 35749.48 238.59 309.65 516.46 0.008 36925 37140.26 242.44 312.14 424.83 0.006 35575 35774.76 238.66 309.7 514.62 0.008 36950 37165.55 242.51 312.18 423.34 0.006 35600 35800.04 238.73 309.74 512.78 0.007 36975 37190.84 242.58 312.23 421.85 0.006 35625 35825.33 238.8 309.79 510.95 0.007 37000 37216.14 242.65 312.27 420.37 0.006 35650 35850.61 238.87 309.83 509.13 0.007 37025 37241.43 242.72 312.32 418.89 0.006 35675 35875.89 238.94 309.88 507.31 0.007 37050 37266.72 242.79 312.36 417.42 0.006 35700 35901.17 239.01 309.92 505.5 0.007 37075 37292.01 242.86 312.41 415.95 0.006 35725 35926.46 239.08 309.97 503.7 0.007 37100 37317.31 242.93 312.45 414.49 0.006 35750 35951.74 239.15 310.01 501.9 0.007 37125 37342.6 243 312.5 413.04 0.006 35775 35977.02 239.22 310.06 500.11 0.007 37150 37367.9 243.07 312.54 411.59 0.006 35800 36002.3 239.29 310.1 498.33 0.007 37175 37393.19 243.14 312.59 410.15 0.006 35825 36027.59 239.36 310.15 496.55 0.007 37200 37418.48 243.21 312.63 408.71 0.006 35850 36052.87 239.43 310.19 494.78 0.007 37225 37443.78 243.28 312.68 407.28 0.006 35875 36078.16 239.5 310.24 493.02 0.007 37250 37469.07 243.35 312.72 405.85 0.006 35900 36103.44 239.57 310.29 491.27 0.007 37275 37494.37 243.42 312.77 404.43 0.006 35925 36128.72 239.64 310.33 489.52 0.007 37300 37519.66 243.49 312.81 403.01 0.006 35950 36154.01 239.71 310.38 487.78 0.007 37325 37544.96 243.56 312.86 401.6 0.006 35975 36179.29 239.78 310.42 486.04 0.007 37350 37570.26 243.63 312.9 400.19 0.006 36000 36204.58 239.85 310.47 484.32 0.007 37375 37595.55 243.7 312.95 398.79 0.006 36025 36229.86 239.92 310.51 482.6 0.007 37400 37620.85 243.77 312.99 397.4 0.006 36050 36255.15 239.99 310.56 480.88 0.007 37425 37646.14 243.84 313.04 396.01 0.006 36075 36280.43 240.06 310.6 479.17 0.007 37450 37671.44 243.91 313.08 394.62 0.006 36100 36305.72 240.13 310.65 477.47 0.007 37475 37696.74 243.98 313.13 393.25 0.006 36125 36331 240.2 310.69 475.78 0.007 37500 37722.03 244.05 313.17 391.87 0.006 36150 36356.29 240.27 310.74 474.09 0.007 37525 37747.33 244.12 313.22 390.5 0.006 36175 36381.58 240.34 310.78 472.41 0.007 37550 37772.63 244.19 313.26 389.14 0.006 36200 36406.86 240.41 310.83 470.73 0.007 37575 37797.93 244.26 313.31 387.78 0.006 36225 36432.15 240.48 310.87 469.06 0.007 37600 37823.22 244.33 313.35 386.43 0.006 36250 36457.44 240.55 310.92 467.4 0.007 37625 37848.52 244.4 313.4 385.08 0.005 36275 36482.72 240.62 310.96 465.74 0.007 37650 37873.82 244.47 313.44 383.74 0.005 36300 36508.01 240.69 311.01 464.09 0.007 37675 37899.12 244.54 313.49 382.4 0.005 36325 36533.3 240.76 311.06 462.45 0.007 37700 37924.42 244.61 313.53 381.06 0.005 36350 36558.59 240.83 311.1 460.81 0.007 37725 37949.71 244.68 313.58 379.74 0.005 36375 36583.87 240.9 311.15 459.18 0.007 37750 37975.01 244.75 313.62 378.41 0.005 36400 36609.16 240.97 311.19 457.56 0.007 37775 38000.31 244.82 313.67 377.1 0.005 36425 36634.45 241.04 311.24 455.94 0.007 37800 38025.61 244.89 313.71 375.78 0.005 Appendix C: The Standard Atmosphere 425 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 37825 38050.91 244.96 313.76 374.47 0.005 39200 39442.69 248.81 316.21 309.59 0.004 37850 38076.21 245.03 313.8 373.17 0.005 39225 39468 248.88 316.26 308.53 0.004 37875 38101.51 245.1 313.85 371.87 0.005 39250 39493.31 248.95 316.3 307.47 0.004 37900 38126.81 245.17 313.89 370.58 0.005 39275 39518.62 249.02 316.35 306.42 0.004 37925 38152.11 245.24 313.94 369.29 0.005 39300 39543.93 249.09 316.39 305.37 0.004 37950 38177.41 245.31 313.98 368.01 0.005 39325 39569.24 249.16 316.43 304.33 0.004 37975 38202.71 245.38 314.03 366.73 0.005 39350 39594.55 249.23 316.48 303.29 0.004 38000 38228.01 245.45 314.07 365.45 0.005 39375 39619.86 249.3 316.52 302.25 0.004 38025 38253.31 245.52 314.11 364.19 0.005 39400 39645.18 249.37 316.57 301.21 0.004 38050 38278.61 245.59 314.16 362.92 0.005 39425 39670.49 249.44 316.61 300.18 0.004 38075 38303.92 245.66 314.2 361.66 0.005 39450 39695.8 249.51 316.66 299.16 0.004 38100 38329.22 245.73 314.25 360.41 0.005 39475 39721.11 249.58 316.7 298.14 0.004 38125 38354.52 245.8 314.29 359.16 0.005 39500 39746.43 249.65 316.75 297.12 0.004 38150 38379.82 245.87 314.34 357.91 0.005 39525 39771.74 249.72 316.79 296.1 0.004 38175 38405.12 245.94 314.38 356.67 0.005 39550 39797.05 249.79 316.83 295.09 0.004 38200 38430.43 246.01 314.43 355.43 0.005 39575 39822.37 249.86 316.88 294.09 0.004 38225 38455.73 246.08 314.47 354.2 0.005 39600 39847.68 249.93 316.92 293.08 0.004 38250 38481.03 246.15 314.52 352.97 0.005 39625 39872.99 250 316.97 292.08 0.004 38275 38506.33 246.22 314.56 351.75 0.005 39650 39898.31 250.07 317.01 291.09 0.004 38300 38531.64 246.29 314.61 350.53 0.005 39675 39923.62 250.14 317.06 290.09 0.004 38325 38556.94 246.36 314.65 349.32 0.005 39700 39948.94 250.21 317.1 289.11 0.004 38350 38582.24 246.43 314.7 348.11 0.005 39725 39974.25 250.28 317.15 288.12 0.004 38375 38607.55 246.5 314.74 346.91 0.005 39750 39999.57 250.35 317.19 287.14 0.004 38400 38632.85 246.57 314.79 345.71 0.005 39775 40024.88 250.42 317.23 286.16 0.004 38425 38658.16 246.64 314.83 344.51 0.005 39800 40050.2 250.49 317.28 285.19 0.004 38450 38683.46 246.71 314.88 343.32 0.005 39825 40075.51 250.56 317.32 284.22 0.004 38475 38708.77 246.78 314.92 342.14 0.005 39850 40100.83 250.63 317.37 283.25 0.004 38500 38734.07 246.85 314.96 340.95 0.005 39875 40126.14 250.7 317.41 282.29 0.004 38525 38759.38 246.92 315.01 339.78 0.005 39900 40151.46 250.77 317.46 281.33 0.004 38550 38784.68 246.99 315.05 338.6 0.005 39925 40176.77 250.84 317.5 280.37 0.004 38575 38809.99 247.06 315.1 337.43 0.005 39950 40202.09 250.91 317.54 279.42 0.004 38600 38835.29 247.13 315.14 336.27 0.005 39975 40227.41 250.98 317.59 278.47 0.004 38625 38860.6 247.2 315.19 335.11 0.005 40000 40252.72 251.05 317.63 277.52 0.004 38650 38885.9 247.27 315.23 333.95 0.005 40025 40278.04 251.12 317.68 276.58 0.004 38675 38911.21 247.34 315.28 332.8 0.005 40050 40303.36 251.19 317.72 275.64 0.004 38700 38936.52 247.41 315.32 331.66 0.005 40075 40328.68 251.26 317.77 274.7 0.004 38725 38961.82 247.48 315.37 330.51 0.005 40100 40353.99 251.33 317.81 273.77 0.004 38750 38987.13 247.55 315.41 329.38 0.005 40125 40379.31 251.4 317.85 272.84 0.004 38775 39012.44 247.62 315.46 328.24 0.005 40150 40404.63 251.47 317.9 271.92 0.004 38800 39037.74 247.69 315.5 327.11 0.005 40175 40429.95 251.54 317.94 271 0.004 38825 39063.05 247.76 315.54 325.98 0.005 40200 40455.27 251.61 317.99 270.08 0.004 38850 39088.36 247.83 315.59 324.86 0.005 40225 40480.58 251.68 318.03 269.16 0.004 38875 39113.67 247.9 315.63 323.75 0.005 40250 40505.9 251.75 318.08 268.25 0.004 38900 39138.97 247.97 315.68 322.63 0.005 40275 40531.22 251.82 318.12 267.34 0.004 38925 39164.28 248.04 315.72 321.52 0.005 40300 40556.54 251.89 318.16 266.44 0.004 38950 39189.59 248.11 315.77 320.42 0.004 40325 40581.86 251.96 318.21 265.54 0.004 38975 39214.9 248.18 315.81 319.32 0.004 40350 40607.18 252.03 318.25 264.64 0.004 39000 39240.21 248.25 315.86 318.22 0.004 40375 40632.5 252.1 318.3 263.74 0.004 39025 39265.52 248.32 315.9 317.13 0.004 40400 40657.82 252.17 318.34 262.85 0.004 39050 39290.83 248.39 315.95 316.04 0.004 40425 40683.14 252.24 318.38 261.96 0.004 39075 39316.14 248.46 315.99 314.95 0.004 40450 40708.46 252.31 318.43 261.08 0.004 39100 39341.45 248.53 316.03 313.87 0.004 40475 40733.78 252.38 318.47 260.19 0.004 39125 39366.76 248.6 316.08 312.8 0.004 40500 40759.1 252.45 318.52 259.32 0.004 39150 39392.07 248.67 316.12 311.72 0.004 40525 40784.42 252.52 318.56 258.44 0.004 39175 39417.38 248.74 316.17 310.66 0.004 40550 40809.74 252.59 318.61 257.57 0.004 426 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 40575 40835.07 252.66 318.65 256.7 0.004 41950 42228.05 256.51 321.07 213.45 0.003 40600 40860.39 252.73 318.69 255.83 0.004 41975 42253.38 256.58 321.11 212.74 0.003 40625 40885.71 252.8 318.74 254.97 0.004 42000 42278.72 256.65 321.16 212.03 0.003 40650 40911.03 252.87 318.78 254.11 0.004 42025 42304.05 256.72 321.2 211.33 0.003 40675 40936.35 252.94 318.83 253.25 0.003 42050 42329.38 256.79 321.24 210.62 0.003 40700 40961.68 253.01 318.87 252.4 0.003 42075 42354.72 256.86 321.29 209.92 0.003 40725 40987 253.08 318.91 251.55 0.003 42100 42380.05 256.93 321.33 209.23 0.003 40750 41012.32 253.15 318.96 250.7 0.003 42125 42405.38 257 321.37 208.53 0.003 40775 41037.64 253.22 319 249.86 0.003 42150 42430.72 257.07 321.42 207.84 0.003 40800 41062.97 253.29 319.05 249.02 0.003 42175 42456.05 257.14 321.46 207.15 0.003 40825 41088.29 253.36 319.09 248.18 0.003 42200 42481.39 257.21 321.51 206.47 0.003 40850 41113.62 253.43 319.13 247.34 0.003 42225 42506.72 257.28 321.55 205.78 0.003 40875 41138.94 253.5 319.18 246.51 0.003 42250 42532.06 257.35 321.59 205.1 0.003 40900 41164.26 253.57 319.22 245.68 0.003 42275 42557.39 257.42 321.64 204.42 0.003 40925 41189.59 253.64 319.27 244.86 0.003 42300 42582.73 257.49 321.68 203.74 0.003 40950 41214.91 253.71 319.31 244.03 0.003 42325 42608.06 257.56 321.72 203.07 0.003 40975 41240.24 253.78 319.36 243.21 0.003 42350 42633.4 257.63 321.77 202.4 0.003 41000 41265.56 253.85 319.4 242.4 0.003 42375 42658.73 257.7 321.81 201.73 0.003 41025 41290.89 253.92 319.44 241.58 0.003 42400 42684.07 257.77 321.86 201.06 0.003 41050 41316.21 253.99 319.49 240.77 0.003 42425 42709.41 257.84 321.9 200.39 0.003 41075 41341.54 254.06 319.53 239.96 0.003 42450 42734.74 257.91 321.94 199.73 0.003 41100 41366.86 254.13 319.58 239.16 0.003 42475 42760.08 257.98 321.99 199.07 0.003 41125 41392.19 254.2 319.62 238.35 0.003 42500 42785.42 258.05 322.03 198.41 0.003 41150 41417.51 254.27 319.66 237.56 0.003 42525 42810.75 258.12 322.07 197.76 0.003 41175 41442.84 254.34 319.71 236.76 0.003 42550 42836.09 258.19 322.12 197.1 0.003 41200 41468.17 254.41 319.75 235.97 0.003 42575 42861.43 258.26 322.16 196.45 0.003 41225 41493.49 254.48 319.8 235.17 0.003 42600 42886.76 258.33 322.21 195.81 0.003 41250 41518.82 254.55 319.84 234.39 0.003 42625 42912.1 258.4 322.25 195.16 0.003 41275 41544.15 254.62 319.88 233.6 0.003 42650 42937.44 258.47 322.29 194.52 0.003 41300 41569.47 254.69 319.93 232.82 0.003 42675 42962.78 258.54 322.34 193.87 0.003 41325 41594.8 254.76 319.97 232.04 0.003 42700 42988.12 258.61 322.38 193.23 0.003 41350 41620.13 254.83 320.02 231.26 0.003 42725 43013.46 258.68 322.42 192.6 0.003 41375 41645.46 254.9 320.06 230.49 0.003 42750 43038.79 258.75 322.47 191.96 0.003 41400 41670.78 254.97 320.1 229.72 0.003 42775 43064.13 258.82 322.51 191.33 0.003 41425 41696.11 255.04 320.15 228.95 0.003 42800 43089.47 258.89 322.55 190.7 0.003 41450 41721.44 255.11 320.19 228.19 0.003 42825 43114.81 258.96 322.6 190.07 0.003 41475 41746.77 255.18 320.23 227.42 0.003 42850 43140.15 259.03 322.64 189.45 0.003 41500 41772.1 255.25 320.28 226.66 0.003 42875 43165.49 259.1 322.69 188.82 0.003 41525 41797.43 255.32 320.32 225.91 0.003 42900 43190.83 259.17 322.73 188.2 0.003 41550 41822.76 255.39 320.37 225.15 0.003 42925 43216.17 259.24 322.77 187.58 0.003 41575 41848.09 255.46 320.41 224.4 0.003 42950 43241.51 259.31 322.82 186.97 0.003 41600 41873.42 255.53 320.45 223.65 0.003 42975 43266.85 259.38 322.86 186.35 0.003 41625 41898.75 255.6 320.5 222.91 0.003 43000 43292.19 259.45 322.9 185.74 0.002 41650 41924.08 255.67 320.54 222.16 0.003 43025 43317.53 259.52 322.95 185.13 0.002 41675 41949.41 255.74 320.59 221.42 0.003 43050 43342.88 259.59 322.99 184.52 0.002 41700 41974.74 255.81 320.63 220.68 0.003 43075 43368.22 259.66 323.03 183.91 0.002 41725 42000.07 255.88 320.67 219.95 0.003 43100 43393.56 259.73 323.08 183.31 0.002 41750 42025.4 255.95 320.72 219.21 0.003 43125 43418.9 259.8 323.12 182.71 0.002 41775 42050.73 256.02 320.76 218.48 0.003 43150 43444.24 259.87 323.16 182.11 0.002 41800 42076.06 256.09 320.81 217.76 0.003 43175 43469.58 259.94 323.21 181.51 0.002 41825 42101.39 256.16 320.85 217.03 0.003 43200 43494.93 260.01 323.25 180.92 0.002 41850 42126.72 256.23 320.89 216.31 0.003 43225 43520.27 260.08 323.29 180.32 0.002 41875 42152.05 256.3 320.94 215.59 0.003 43250 43545.61 260.15 323.34 179.73 0.002 41900 42177.39 256.37 320.98 214.87 0.003 43275 43570.96 260.22 323.38 179.14 0.002 41925 42202.72 256.44 321.02 214.16 0.003 43300 43596.3 260.29 323.43 178.56 0.002 Appendix C: The Standard Atmosphere 427 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 43325 43621.64 260.36 323.47 177.97 0.002 44700 45015.84 264.21 325.85 148.79 0.002 43350 43646.99 260.43 323.51 177.39 0.002 44725 45041.19 264.28 325.89 148.31 0.002 43375 43672.33 260.5 323.56 176.81 0.002 44750 45066.55 264.35 325.94 147.83 0.002 43400 43697.67 260.57 323.6 176.23 0.002 44775 45091.9 264.42 325.98 147.35 0.002 43425 43723.02 260.64 323.64 175.65 0.002 44800 45117.26 264.49 326.02 146.88 0.002 43450 43748.36 260.71 323.69 175.08 0.002 44825 45142.61 264.56 326.07 146.4 0.002 43475 43773.71 260.78 323.73 174.5 0.002 44850 45167.97 264.63 326.11 145.93 0.002 43500 43799.05 260.85 323.77 173.93 0.002 44875 45193.33 264.7 326.15 145.46 0.002 43525 43824.4 260.92 323.82 173.37 0.002 44900 45218.68 264.77 326.2 144.99 0.002 43550 43849.74 260.99 323.86 172.8 0.002 44925 45244.04 264.84 326.24 144.53 0.002 43575 43875.09 261.06 323.9 172.23 0.002 44950 45269.39 264.91 326.28 144.06 0.002 43600 43900.43 261.13 323.95 171.67 0.002 44975 45294.75 264.98 326.33 143.6 0.002 43625 43925.78 261.2 323.99 171.11 0.002 45000 45320.11 265.05 326.37 143.13 0.002 43650 43951.12 261.27 324.03 170.55 0.002 45025 45345.46 265.12 326.41 142.67 0.002 43675 43976.47 261.34 324.08 170 0.002 45050 45370.82 265.19 326.46 142.22 0.002 43700 44001.82 261.41 324.12 169.44 0.002 45075 45396.18 265.26 326.5 141.76 0.002 43725 44027.16 261.48 324.16 168.89 0.002 45100 45421.54 265.33 326.54 141.3 0.002 43750 44052.51 261.55 324.21 168.34 0.002 45125 45446.89 265.4 326.58 140.85 0.002 43775 44077.86 261.62 324.25 167.79 0.002 45150 45472.25 265.47 326.63 140.4 0.002 43800 44103.21 261.69 324.29 167.24 0.002 45175 45497.61 265.54 326.67 139.95 0.002 43825 44128.55 261.76 324.34 166.7 0.002 45200 45522.97 265.61 326.71 139.5 0.002 43850 44153.9 261.83 324.38 166.16 0.002 45225 45548.33 265.68 326.76 139.05 0.002 43875 44179.25 261.9 324.42 165.61 0.002 45250 45573.69 265.75 326.8 138.6 0.002 43900 44204.6 261.97 324.47 165.08 0.002 45275 45599.05 265.82 326.84 138.16 0.002 43925 44229.94 262.04 324.51 164.54 0.002 45300 45624.41 265.89 326.89 137.71 0.002 43950 44255.29 262.11 324.55 164 0.002 45325 45649.76 265.96 326.93 137.27 0.002 43975 44280.64 262.18 324.6 163.47 0.002 45350 45675.12 266.03 326.97 136.83 0.002 44000 44305.99 262.25 324.64 162.94 0.002 45375 45700.48 266.1 327.01 136.39 0.002 44025 44331.34 262.32 324.68 162.41 0.002 45400 45725.84 266.17 327.06 135.96 0.002 44050 44356.69 262.39 324.73 161.88 0.002 45425 45751.2 266.24 327.1 135.52 0.002 44075 44382.04 262.46 324.77 161.35 0.002 45450 45776.56 266.31 327.14 135.09 0.002 44100 44407.39 262.53 324.81 160.83 0.002 45475 45801.93 266.38 327.19 134.65 0.002 44125 44432.74 262.6 324.86 160.31 0.002 45500 45827.29 266.45 327.23 134.22 0.002 44150 44458.09 262.67 324.9 159.79 0.002 45525 45852.65 266.52 327.27 133.79 0.002 44175 44483.44 262.74 324.94 159.27 0.002 45550 45878.01 266.59 327.32 133.37 0.002 44200 44508.79 262.81 324.99 158.75 0.002 45575 45903.37 266.66 327.36 132.94 0.002 44225 44534.14 262.88 325.03 158.24 0.002 45600 45928.73 266.73 327.4 132.51 0.002 44250 44559.49 262.95 325.07 157.72 0.002 45625 45954.09 266.8 327.44 132.09 0.002 44275 44584.84 263.02 325.12 157.21 0.002 45650 45979.46 266.87 327.49 131.67 0.002 44300 44610.19 263.09 325.16 156.7 0.002 45675 46004.82 266.94 327.53 131.25 0.002 44325 44635.54 263.16 325.2 156.19 0.002 45700 46030.18 267.01 327.57 130.83 0.002 44350 44660.89 263.23 325.25 155.69 0.002 45725 46055.54 267.08 327.62 130.41 0.002 44375 44686.25 263.3 325.29 155.18 0.002 45750 46080.91 267.15 327.66 130 0.002 44400 44711.6 263.37 325.33 154.68 0.002 45775 46106.27 267.22 327.7 129.58 0.002 44425 44736.95 263.44 325.38 154.18 0.002 45800 46131.63 267.29 327.75 129.17 0.002 44450 44762.3 263.51 325.42 153.68 0.002 45825 46157 267.36 327.79 128.75 0.002 44475 44787.66 263.58 325.46 153.18 0.002 45850 46182.36 267.43 327.83 128.34 0.002 44500 44813.01 263.65 325.51 152.69 0.002 45875 46207.72 267.5 327.87 127.94 0.002 44525 44838.36 263.72 325.55 152.2 0.002 45900 46233.09 267.57 327.92 127.53 0.002 44550 44863.72 263.79 325.59 151.7 0.002 45925 46258.45 267.64 327.96 127.12 0.002 44575 44889.07 263.86 325.64 151.21 0.002 45950 46283.82 267.71 328 126.72 0.002 44600 44914.42 263.93 325.68 150.72 0.002 45975 46309.18 267.78 328.05 126.31 0.002 44625 44939.78 264 325.72 150.24 0.002 46000 46334.55 267.85 328.09 125.91 0.002 44650 44965.13 264.07 325.77 149.75 0.002 46025 46359.91 267.92 328.13 125.51 0.002 44675 44990.48 264.14 325.81 149.27 0.002 46050 46385.28 267.99 328.17 125.11 0.002 428 Appendix C: The Standard Atmosphere −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 46075 46410.64 268.06 328.22 124.71 0.002 47450 47806.05 270.65 329.8 104.78 0.001 46100 46436.01 268.13 328.26 124.32 0.002 47475 47831.43 270.65 329.8 104.45 0.001 46125 46461.37 268.2 328.3 123.92 0.002 47500 47856.8 270.65 329.8 104.12 0.001 46150 46486.74 268.27 328.35 123.53 0.002 47525 47882.18 270.65 329.8 103.79 0.001 46175 46512.11 268.34 328.39 123.13 0.002 47550 47907.56 270.65 329.8 103.47 0.001 46200 46537.47 268.41 328.43 122.74 0.002 47575 47932.94 270.65 329.8 103.14 0.001 46225 46562.84 268.48 328.47 122.35 0.002 47600 47958.31 270.65 329.8 102.82 0.001 46250 46588.21 268.55 328.52 121.96 0.002 47625 47983.69 270.65 329.8 102.49 0.001 46275 46613.57 268.62 328.56 121.58 0.002 47650 48009.07 270.65 329.8 102.17 0.001 46300 46638.94 268.69 328.6 121.19 0.002 47675 48034.45 270.65 329.8 101.85 0.001 46325 46664.31 268.76 328.65 120.81 0.002 47700 48059.83 270.65 329.8 101.53 0.001 46350 46689.67 268.83 328.69 120.42 0.002 47725 48085.21 270.65 329.8 101.21 0.001 46375 46715.04 268.9 328.73 120.04 0.002 47750 48110.58 270.65 329.8 100.89 0.001 46400 46740.41 268.97 328.77 119.66 0.002 47775 48135.96 270.65 329.8 100.57 0.001 46425 46765.78 269.04 328.82 119.28 0.002 47800 48161.34 270.65 329.8 100.25 0.001 46450 46791.15 269.11 328.86 118.9 0.002 47825 48186.72 270.65 329.8 99.94 0.001 46475 46816.52 269.18 328.9 118.53 0.002 47850 48212.1 270.65 329.8 99.62 0.001 46500 46841.88 269.25 328.94 118.15 0.002 47875 48237.48 270.65 329.8 99.31 0.001 46525 46867.25 269.32 328.99 117.78 0.002 47900 48262.86 270.65 329.8 99 0.001 46550 46892.62 269.39 329.03 117.4 0.002 47925 48288.24 270.65 329.8 98.68 0.001 46575 46917.99 269.46 329.07 117.03 0.002 47950 48313.62 270.65 329.8 98.37 0.001 46600 46943.36 269.53 329.12 116.66 0.002 47975 48339 270.65 329.8 98.06 0.001 46625 46968.73 269.6 329.16 116.29 0.002 48000 48364.38 270.65 329.8 97.75 0.001 46650 46994.1 269.67 329.2 115.93 0.001 48025 48389.77 270.65 329.8 97.45 0.001 46675 47019.47 269.74 329.24 115.56 0.001 48050 48415.15 270.65 329.8 97.14 0.001 46700 47044.84 269.81 329.29 115.19 0.001 48075 48440.53 270.65 329.8 96.83 0.001 46725 47070.21 269.88 329.33 114.83 0.001 48100 48465.91 270.65 329.8 96.53 0.001 46750 47095.58 269.95 329.37 114.47 0.001 48125 48491.29 270.65 329.8 96.22 0.001 46775 47120.96 270.02 329.41 114.11 0.001 48150 48516.67 270.65 329.8 95.92 0.001 46800 47146.33 270.09 329.46 113.74 0.001 48175 48542.06 270.65 329.8 95.62 0.001 46825 47171.7 270.16 329.5 113.39 0.001 48200 48567.44 270.65 329.8 95.32 0.001 46850 47197.07 270.23 329.54 113.03 0.001 48225 48592.82 270.65 329.8 95.02 0.001 46875 47222.44 270.3 329.59 112.67 0.001 48250 48618.2 270.65 329.8 94.72 0.001 46900 47247.81 270.37 329.63 112.32 0.001 48275 48643.59 270.65 329.8 94.42 0.001 46925 47273.19 270.44 329.67 111.96 0.001 48300 48668.97 270.65 329.8 94.12 0.001 46950 47298.56 270.51 329.71 111.61 0.001 48325 48694.35 270.65 329.8 93.83 0.001 46975 47323.93 270.58 329.76 111.26 0.001 48350 48719.74 270.65 329.8 93.53 0.001 47000 47349.3 270.65 329.8 110.91 0.001 48375 48745.12 270.65 329.8 93.24 0.001 47025 47374.68 270.65 329.8 110.56 0.001 48400 48770.51 270.65 329.8 92.94 0.001 47050 47400.05 270.65 329.8 110.21 0.001 48425 48795.89 270.65 329.8 92.65 0.001 47075 47425.42 270.65 329.8 109.86 0.001 48450 48821.27 270.65 329.8 92.36 0.001 47100 47450.8 270.65 329.8 109.52 0.001 48475 48846.66 270.65 329.8 92.07 0.001 47125 47476.17 270.65 329.8 109.17 0.001 48500 48872.04 270.65 329.8 91.78 0.001 47150 47501.55 270.65 329.8 108.83 0.001 48525 48897.43 270.65 329.8 91.49 0.001 47175 47526.92 270.65 329.8 108.48 0.001 48550 48922.81 270.65 329.8 91.2 0.001 47200 47552.29 270.65 329.8 108.14 0.001 48575 48948.2 270.65 329.8 90.91 0.001 47225 47577.67 270.65 329.8 107.8 0.001 48600 48973.59 270.65 329.8 90.62 0.001 47250 47603.04 270.65 329.8 107.46 0.001 48625 48998.97 270.65 329.8 90.34 0.001 47275 47628.42 270.65 329.8 107.12 0.001 48650 49024.36 270.65 329.8 90.05 0.001 47300 47653.79 270.65 329.8 106.79 0.001 48675 49049.74 270.65 329.8 89.77 0.001 47325 47679.17 270.65 329.8 106.45 0.001 48700 49075.13 270.65 329.8 89.49 0.001 47350 47704.55 270.65 329.8 106.11 0.001 48725 49100.52 270.65 329.8 89.21 0.001 47375 47729.92 270.65 329.8 105.78 0.001 48750 49125.9 270.65 329.8 88.92 0.001 47400 47755.3 270.65 329.8 105.45 0.001 48775 49151.29 270.65 329.8 88.64 0.001 47425 47780.67 270.65 329.8 105.11 0.001 48800 49176.68 270.65 329.8 88.37 0.001 Appendix C: The Standard Atmosphere 429 −1 −3 −1 −3 h (m) hG (m) T (K) a ms p (Pa) ρ kgm h (m) hG (m) T (K) a ms p (Pa) ρ kgm 48825 49202.07 270.65 329.8 88.09 0.001 49400 49786.04 270.65 329.8 81.92 0.001 48850 49227.45 270.65 329.8 87.81 0.001 49425 49811.43 270.65 329.8 81.66 0.001 48875 49252.84 270.65 329.8 87.53 0.001 49450 49836.82 270.65 329.8 81.4 0.001 48900 49278.23 270.65 329.8 87.26 0.001 49475 49862.21 270.65 329.8 81.15 0.001 48925 49303.62 270.65 329.8 86.98 0.001 49500 49887.61 270.65 329.8 80.89 0.001 48950 49329.01 270.65 329.8 86.71 0.001 49525 49913 270.65 329.8 80.64 0.001 48975 49354.4 270.65 329.8 86.43 0.001 49550 49938.39 270.65 329.8 80.38 0.001 49000 49379.78 270.65 329.8 86.16 0.001 49575 49963.79 270.65 329.8 80.13 0.001 49025 49405.17 270.65 329.8 85.89 0.001 49600 49989.18 270.65 329.8 79.88 0.001 49050 49430.56 270.65 329.8 85.62 0.001 49625 50014.57 270.65 329.8 79.63 0.001 49075 49455.95 270.65 329.8 85.35 0.001 49650 50039.97 270.65 329.8 79.38 0.001 49100 49481.34 270.65 329.8 85.08 0.001 49675 50065.36 270.65 329.8 79.13 0.001 49125 49506.73 270.65 329.8 84.81 0.001 49700 50090.76 270.65 329.8 78.88 0.001 49150 49532.12 270.65 329.8 84.55 0.001 49725 50116.15 270.65 329.8 78.63 0.001 49175 49557.51 270.65 329.8 84.28 0.001 49750 50141.55 270.65 329.8 78.38 0.001 49200 49582.9 270.65 329.8 84.01 0.001 49775 50166.94 270.65 329.8 78.13 0.001 49225 49608.29 270.65 329.8 83.75 0.001 49800 50192.34 270.65 329.8 77.89 0.001 49250 49633.69 270.65 329.8 83.49 0.001 49825 50217.73 270.65 329.8 77.64 0.001 49275 49659.08 270.65 329.8 83.22 0.001 49850 50243.13 270.65 329.8 77.4 0.001 49300 49684.47 270.65 329.8 82.96 0.001 49875 50268.52 270.65 329.8 77.15 0.001 49325 49709.86 270.65 329.8 82.7 0.001 49900 50293.92 270.65 329.8 76.91 0.001 49350 49735.25 270.65 329.8 82.44 0.001 49925 50319.32 270.65 329.8 76.67 0.001 49375 49760.64 270.65 329.8 82.18 0.001 49950 50344.71 270.65 329.8 76.43 0.001 49975 50370.11 270.65 329.8 76.18 0.001 50000 50395.51 270.65 329.8 75.94 0.001 Isentropic Table (γ = 1.4) D

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 0.00 1.0000 1.0000 1.0000 1.0000 ∞ 0.40 0.8956 0.9690 0.9243 0.9844 1.5901 0.01 0.9999 1.0000 1.0000 1.0000 57.8738 0.41 0.8907 0.9675 0.9207 0.9836 1.5587 0.02 0.9997 0.9999 0.9998 1.0000 28.9421 0.42 0.8857 0.9659 0.9170 0.9828 1.5289 0.03 0.9994 0.9998 0.9996 0.9999 19.3005 0.43 0.8807 0.9643 0.9132 0.9820 1.5007 0.04 0.9989 0.9997 0.9992 0.9998 14.4815 0.44 0.8755 0.9627 0.9094 0.9812 1.4740 0.05 0.9983 0.9995 0.9988 0.9998 11.5914 0.45 0.8703 0.9611 0.9055 0.9803 1.4487 0.06 0.9975 0.9993 0.9982 0.9996 9.6659 0.46 0.8650 0.9594 0.9016 0.9795 1.4246 0.07 0.9966 0.9990 0.9976 0.9995 8.2915 0.47 0.8596 0.9577 0.8976 0.9786 1.4018 0.08 0.9955 0.9987 0.9968 0.9994 7.2616 0.48 0.8541 0.9559 0.8935 0.9777 1.3801 0.09 0.9944 0.9984 0.9960 0.9992 6.4613 0.49 0.8486 0.9542 0.8894 0.9768 1.3595 0.10 0.9930 0.9980 0.9950 0.9990 5.8218 0.50 0.8430 0.9524 0.8852 0.9759 1.3398 0.11 0.9916 0.9976 0.9940 0.9988 5.2992 0.51 0.8374 0.9506 0.8809 0.9750 1.3212 0.12 0.9900 0.9971 0.9928 0.9986 4.8643 0.52 0.8317 0.9487 0.8766 0.9740 1.3034 0.13 0.9883 0.9966 0.9916 0.9983 4.4969 0.53 0.8259 0.9468 0.8723 0.9730 1.2865 0.14 0.9864 0.9961 0.9903 0.9980 4.1824 0.54 0.8201 0.9449 0.8679 0.9721 1.2703 0.15 0.9844 0.9955 0.9888 0.9978 3.9103 0.55 0.8142 0.9430 0.8634 0.9711 1.2549 0.16 0.9823 0.9949 0.9873 0.9974 3.6727 0.56 0.8082 0.9410 0.8589 0.9700 1.2403 0.17 0.9800 0.9943 0.9857 0.9971 3.4635 0.57 0.8022 0.9390 0.8544 0.9690 1.2263 0.18 0.9776 0.9936 0.9840 0.9968 3.2779 0.58 0.7962 0.9370 0.8498 0.9680 1.2130 0.19 0.9751 0.9928 0.9822 0.9964 3.1123 0.59 0.7901 0.9349 0.8451 0.9669 1.2003 0.20 0.9725 0.9921 0.9803 0.9960 2.9635 0.60 0.7840 0.9328 0.8405 0.9658 1.1882 0.21 0.9697 0.9913 0.9783 0.9956 2.8293 0.61 0.7778 0.9307 0.8357 0.9647 1.1767 0.22 0.9668 0.9904 0.9762 0.9952 2.7076 0.62 0.7716 0.9286 0.8310 0.9636 1.1656 0.23 0.9638 0.9895 0.9740 0.9948 2.5968 0.63 0.7654 0.9265 0.8262 0.9625 1.1552 0.24 0.9607 0.9886 0.9718 0.9943 2.4956 0.64 0.7591 0.9243 0.8213 0.9614 1.1451 0.25 0.9575 0.9877 0.9694 0.9938 2.4027 0.65 0.7528 0.9221 0.8164 0.9603 1.1356 0.26 0.9541 0.9867 0.9670 0.9933 2.3173 0.66 0.7465 0.9199 0.8115 0.9591 1.1265 0.27 0.9506 0.9856 0.9645 0.9928 2.2385 0.67 0.7401 0.9176 0.8066 0.9579 1.1179 0.28 0.9470 0.9846 0.9619 0.9923 2.1656 0.68 0.7338 0.9153 0.8016 0.9567 1.1097 0.29 0.9433 0.9835 0.9592 0.9917 2.0979 0.69 0.7274 0.9131 0.7966 0.9555 1.1018 0.30 0.9395 0.9823 0.9564 0.9911 2.0351 0.70 0.7209 0.9107 0.7916 0.9543 1.0944 0.31 0.9355 0.9811 0.9535 0.9905 1.9765 0.71 0.7145 0.9084 0.7865 0.9531 1.0873 0.32 0.9315 0.9799 0.9506 0.9899 1.9219 0.72 0.7080 0.9061 0.7814 0.9519 1.0806 0.33 0.9274 0.9787 0.9476 0.9893 1.8707 0.73 0.7016 0.9037 0.7763 0.9506 1.0742 0.34 0.9231 0.9774 0.9445 0.9886 1.8229 0.74 0.6951 0.9013 0.7712 0.9494 1.0681 0.35 0.9188 0.9761 0.9413 0.9880 1.7780 0.75 0.6886 0.8989 0.7660 0.9481 1.0624 0.36 0.9143 0.9747 0.9380 0.9873 1.7358 0.76 0.6821 0.8964 0.7609 0.9468 1.0570 0.37 0.9098 0.9733 0.9347 0.9866 1.6961 0.77 0.6756 0.8940 0.7557 0.9455 1.0519 0.38 0.9052 0.9719 0.9313 0.9859 1.6587 0.78 0.6691 0.8915 0.7505 0.9442 1.0471 0.39 0.9004 0.9705 0.9278 0.9851 1.6234

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 0.79 0.6625 0.8890 0.7452 0.9429 1.0425 1.42 0.3055 0.7126 0.4287 0.8442 1.1262 0.80 0.6560 0.8865 0.7400 0.9416 1.0382 1.43 0.3012 0.7097 0.4244 0.8425 1.1320 0.81 0.6495 0.8840 0.7347 0.9402 1.0342 1.44 0.2969 0.7069 0.4201 0.8407 1.1379 0.82 0.6430 0.8815 0.7295 0.9389 1.0305 1.45 0.2927 0.7040 0.4158 0.8390 1.1440 0.83 0.6365 0.8789 0.7242 0.9375 1.0270 1.46 0.2886 0.7011 0.4116 0.8373 1.1501 0.84 0.6300 0.8763 0.7189 0.9361 1.0237 1.47 0.2845 0.6982 0.4074 0.8356 1.1565 0.85 0.6235 0.8737 0.7136 0.9347 1.0207 1.48 0.2804 0.6954 0.4032 0.8339 1.1629 0.86 0.6170 0.8711 0.7083 0.9333 1.0179 1.49 0.2764 0.6925 0.3991 0.8322 1.1695 0.87 0.6106 0.8685 0.7030 0.9319 1.0153 1.50 0.2724 0.6897 0.3950 0.8305 1.1762 0.88 0.6041 0.8659 0.6977 0.9305 1.0129 1.51 0.2685 0.6868 0.3909 0.8287 1.1830 0.89 0.5977 0.8632 0.6924 0.9291 1.0108 1.52 0.2646 0.6840 0.3869 0.8270 1.1899 0.90 0.5913 0.8606 0.6870 0.9277 1.0089 1.53 0.2608 0.6811 0.3829 0.8253 1.1970 0.91 0.5849 0.8579 0.6817 0.9262 1.0071 1.54 0.2570 0.6783 0.3789 0.8236 1.2042 0.92 0.5785 0.8552 0.6764 0.9248 1.0056 1.55 0.2533 0.6754 0.3750 0.8219 1.2116 0.93 0.5721 0.8525 0.6711 0.9233 1.0043 1.56 0.2496 0.6726 0.3710 0.8201 1.2190 0.94 0.5658 0.8498 0.6658 0.9219 1.0031 1.57 0.2459 0.6698 0.3672 0.8184 1.2266 0.95 0.5595 0.8471 0.6604 0.9204 1.0021 1.58 0.2423 0.6670 0.3633 0.8167 1.2344 0.96 0.5532 0.8444 0.6551 0.9189 1.0014 1.59 0.2388 0.6642 0.3595 0.8150 1.2422 0.97 0.5469 0.8416 0.6498 0.9174 1.0008 1.60 0.2353 0.6614 0.3557 0.8133 1.2502 0.98 0.5407 0.8389 0.6445 0.9159 1.0003 1.61 0.2318 0.6586 0.3520 0.8115 1.2584 0.99 0.5345 0.8361 0.6392 0.9144 1.0001 1.62 0.2284 0.6558 0.3483 0.8098 1.2666 1.00 0.5283 0.8333 0.6339 0.9129 1.0000 1.63 0.2250 0.6530 0.3446 0.8081 1.2750 1.01 0.5221 0.8306 0.6287 0.9113 1.0001 1.64 0.2217 0.6502 0.3409 0.8064 1.2836 1.02 0.5160 0.8278 0.6234 0.9098 1.0003 1.65 0.2184 0.6475 0.3373 0.8046 1.2922 1.03 0.5099 0.8250 0.6181 0.9083 1.0007 1.66 0.2151 0.6447 0.3337 0.8029 1.3010 1.04 0.5039 0.8222 0.6129 0.9067 1.0013 1.67 0.2119 0.6419 0.3302 0.8012 1.3100 1.05 0.4979 0.8193 0.6077 0.9052 1.0020 1.68 0.2088 0.6392 0.3266 0.7995 1.3190 1.06 0.4919 0.8165 0.6024 0.9036 1.0029 1.69 0.2057 0.6364 0.3232 0.7978 1.3283 1.07 0.4860 0.8137 0.5972 0.9020 1.0039 1.70 0.2026 0.6337 0.3197 0.7961 1.3376 1.08 0.4800 0.8108 0.5920 0.9005 1.0051 1.71 0.1996 0.6310 0.3163 0.7943 1.3471 1.09 0.4742 0.8080 0.5869 0.8989 1.0064 1.72 0.1966 0.6283 0.3129 0.7926 1.3567 1.10 0.4684 0.8052 0.5817 0.8973 1.0079 1.73 0.1936 0.6256 0.3095 0.7909 1.3665 1.11 0.4626 0.8023 0.5766 0.8957 1.0095 1.74 0.1907 0.6229 0.3062 0.7892 1.3764 1.12 0.4568 0.7994 0.5714 0.8941 1.0113 1.75 0.1878 0.6202 0.3029 0.7875 1.3865 1.13 0.4511 0.7966 0.5663 0.8925 1.0132 1.76 0.1850 0.6175 0.2996 0.7858 1.3967 1.14 0.4455 0.7937 0.5612 0.8909 1.0153 1.77 0.1822 0.6148 0.2964 0.7841 1.4070 1.15 0.4398 0.7908 0.5562 0.8893 1.0175 1.78 0.1794 0.6121 0.2931 0.7824 1.4175 1.16 0.4343 0.7879 0.5511 0.8877 1.0198 1.79 0.1767 0.6095 0.2900 0.7807 1.4282 1.17 0.4287 0.7851 0.5461 0.8860 1.0222 1.80 0.1740 0.6068 0.2868 0.7790 1.4390 1.18 0.4232 0.7822 0.5411 0.8844 1.0248 1.81 0.1714 0.6041 0.2837 0.7773 1.4499 1.19 0.4178 0.7793 0.5361 0.8828 1.0276 1.82 0.1688 0.6015 0.2806 0.7756 1.4610 1.20 0.4124 0.7764 0.5311 0.8811 1.0304 1.83 0.1662 0.5989 0.2776 0.7739 1.4723 1.21 0.4070 0.7735 0.5262 0.8795 1.0334 1.84 0.1637 0.5963 0.2745 0.7722 1.4836 1.22 0.4017 0.7706 0.5213 0.8778 1.0366 1.85 0.1612 0.5936 0.2715 0.7705 1.4952 1.23 0.3964 0.7677 0.5164 0.8762 1.0398 1.86 0.1587 0.5910 0.2686 0.7688 1.5069 1.24 0.3912 0.7648 0.5115 0.8745 1.0432 1.87 0.1563 0.5884 0.2656 0.7671 1.5187 1.25 0.3861 0.7619 0.5067 0.8729 1.0468 1.88 0.1539 0.5859 0.2627 0.7654 1.5308 1.26 0.3809 0.7590 0.5019 0.8712 1.0504 1.89 0.1516 0.5833 0.2598 0.7637 1.5429 1.27 0.3759 0.7561 0.4971 0.8695 1.0542 1.90 0.1492 0.5807 0.2570 0.7620 1.5553 1.28 0.3708 0.7532 0.4923 0.8679 1.0581 1.91 0.1470 0.5782 0.2542 0.7604 1.5677 1.29 0.3658 0.7503 0.4876 0.8662 1.0621 1.92 0.1447 0.5756 0.2514 0.7587 1.5804 1.30 0.3609 0.7474 0.4829 0.8645 1.0663 1.93 0.1425 0.5731 0.2486 0.7570 1.5932 1.31 0.3560 0.7445 0.4782 0.8628 1.0706 1.94 0.1403 0.5705 0.2459 0.7553 1.6062 1.32 0.3512 0.7416 0.4736 0.8611 1.0750 1.95 0.1381 0.5680 0.2432 0.7537 1.6193 1.35 0.3370 0.7329 0.4598 0.8561 1.0890 1.96 0.1360 0.5655 0.2405 0.7520 1.6326 1.36 0.3323 0.7300 0.4553 0.8544 1.0940 1.97 0.1339 0.5630 0.2378 0.7503 1.6461 1.37 0.3277 0.7271 0.4508 0.8527 1.0990 1.98 0.1318 0.5605 0.2352 0.7487 1.6597 1.38 0.3232 0.7242 0.4463 0.8510 1.1042 1.99 0.1298 0.5580 0.2326 0.7470 1.6735 1.39 0.3187 0.7213 0.4418 0.8493 1.1095 2.00 0.1278 0.5556 0.2300 0.7454 1.6875 1.40 0.3142 0.7184 0.4374 0.8476 1.1149 2.01 0.1258 0.5531 0.2275 0.7437 1.7016 1.41 0.3098 0.7155 0.4330 0.8459 1.1205 2.02 0.1239 0.5506 0.2250 0.7420 1.7160 2.03 0.1220 0.5482 0.2225 0.7404 1.7305 2.04 0.1201 0.5458 0.2200 0.7388 1.7451 Appendix D: Isentropic Table (γ = 1.4) 433

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 2.05 0.1182 0.5433 0.2176 0.7371 1.7600 2.67 0.0450 0.4122 0.1091 0.6421 3.0938 2.06 0.1164 0.5409 0.2152 0.7355 1.7750 2.68 0.0443 0.4104 0.1079 0.6406 3.1233 2.07 0.1146 0.5385 0.2128 0.7338 1.7902 2.69 0.0436 0.4086 0.1067 0.6392 3.1530 2.08 0.1128 0.5361 0.2104 0.7322 1.8056 2.70 0.0430 0.4068 0.1056 0.6378 3.1830 2.09 0.1111 0.5337 0.2081 0.7306 1.8212 2.71 0.0423 0.4051 0.1044 0.6364 3.2133 2.10 0.1094 0.5313 0.2058 0.7289 1.8369 2.72 0.0417 0.4033 0.1033 0.6350 3.2440 2.11 0.1077 0.5290 0.2035 0.7273 1.8529 2.73 0.0410 0.4015 0.1022 0.6337 3.2749 2.12 0.1060 0.5266 0.2013 0.7257 1.8690 2.74 0.0404 0.3998 0.1010 0.6323 3.3061 2.13 0.1043 0.5243 0.1990 0.7241 1.8853 2.75 0.0398 0.3980 0.0999 0.6309 3.3377 2.14 0.1027 0.5219 0.1968 0.7225 1.9018 2.76 0.0392 0.3963 0.0989 0.6295 3.3695 2.15 0.1011 0.5196 0.1946 0.7208 1.9185 2.77 0.0386 0.3945 0.0978 0.6281 3.4017 2.16 0.0996 0.5173 0.1925 0.7192 1.9354 2.78 0.0380 0.3928 0.0967 0.6268 3.4342 2.17 0.0980 0.5150 0.1903 0.7176 1.9525 2.79 0.0374 0.3911 0.0957 0.6254 3.4670 2.18 0.0965 0.5127 0.1882 0.7160 1.9698 2.80 0.0368 0.3894 0.0946 0.6240 3.5001 2.19 0.0950 0.5104 0.1861 0.7144 1.9873 2.81 0.0363 0.3877 0.0936 0.6227 3.5336 2.20 0.0935 0.5081 0.1841 0.7128 2.0050 2.82 0.0357 0.3860 0.0926 0.6213 3.5674 2.21 0.0921 0.5059 0.1820 0.7112 2.0229 2.83 0.0352 0.3844 0.0916 0.6200 3.6015 2.22 0.0906 0.5036 0.1800 0.7097 2.0409 2.84 0.0347 0.3827 0.0906 0.6186 3.6359 2.23 0.0892 0.5014 0.1780 0.7081 2.0592 2.85 0.0341 0.3810 0.0896 0.6173 3.6707 2.24 0.0878 0.4991 0.1760 0.7065 2.0777 2.86 0.0336 0.3794 0.0886 0.6159 3.7058 2.25 0.0865 0.4969 0.1740 0.7049 2.0964 2.87 0.0331 0.3777 0.0877 0.6146 3.7413 2.26 0.0851 0.4947 0.1721 0.7033 2.1153 2.88 0.0326 0.3761 0.0867 0.6133 3.7771 2.27 0.0838 0.4925 0.1702 0.7018 2.1345 2.89 0.0321 0.3745 0.0858 0.6119 3.8133 2.28 0.0825 0.4903 0.1683 0.7002 2.1538 2.90 0.0317 0.3729 0.0849 0.6106 3.8498 2.29 0.0812 0.4881 0.1664 0.6986 2.1734 2.91 0.0312 0.3712 0.0840 0.6093 3.8866 2.30 0.0800 0.4859 0.1646 0.6971 2.1931 2.92 0.0307 0.3696 0.0831 0.6080 3.9238 2.31 0.0787 0.4837 0.1628 0.6955 2.2131 2.93 0.0302 0.3681 0.0822 0.6067 3.9614 2.32 0.0775 0.4816 0.1609 0.6940 2.2333 2.94 0.0298 0.3665 0.0813 0.6054 3.9993 2.33 0.0763 0.4794 0.1592 0.6924 2.2538 2.95 0.0293 0.3649 0.0804 0.6041 4.0376 2.34 0.0751 0.4773 0.1574 0.6909 2.2744 2.96 0.0289 0.3633 0.0796 0.6028 4.0763 2.35 0.0740 0.4752 0.1556 0.6893 2.2953 2.97 0.0285 0.3618 0.0787 0.6015 4.1153 2.36 0.0728 0.4731 0.1539 0.6878 2.3164 2.98 0.0281 0.3602 0.0779 0.6002 4.1547 2.37 0.0717 0.4709 0.1522 0.6863 2.3377 2.99 0.0276 0.3587 0.0770 0.5989 4.1944 2.38 0.0706 0.4688 0.1505 0.6847 2.3593 3.00 0.0272 0.3571 0.0762 0.5976 4.2346 2.39 0.0695 0.4668 0.1488 0.6832 2.3811 3.01 0.0268 0.3556 0.0754 0.5963 4.2751 2.40 0.0684 0.4647 0.1472 0.6817 2.4031 3.02 0.0264 0.3541 0.0746 0.5951 4.3160 2.41 0.0673 0.4626 0.1456 0.6802 2.4254 3.03 0.0260 0.3526 0.0738 0.5938 4.3573 2.42 0.0663 0.4606 0.1439 0.6786 2.4479 3.04 0.0256 0.3511 0.0730 0.5925 4.3989 2.43 0.0653 0.4585 0.1424 0.6771 2.4706 3.05 0.0253 0.3496 0.0723 0.5913 4.4410 2.44 0.0643 0.4565 0.1408 0.6756 2.4936 3.06 0.0249 0.3481 0.0715 0.5900 4.4835 2.45 0.0633 0.4544 0.1392 0.6741 2.5168 3.07 0.0245 0.3466 0.0707 0.5887 4.5263 2.46 0.0623 0.4524 0.1377 0.6726 2.5403 3.08 0.0242 0.3452 0.0700 0.5875 4.5696 2.47 0.0613 0.4504 0.1362 0.6711 2.5640 3.09 0.0238 0.3437 0.0692 0.5862 4.6132 2.48 0.0604 0.4484 0.1346 0.6696 2.5880 3.10 0.0234 0.3422 0.0685 0.5850 4.6573 2.49 0.0594 0.4464 0.1332 0.6682 2.6122 3.11 0.0231 0.3408 0.0678 0.5838 4.7018 2.50 0.0585 0.4444 0.1317 0.6667 2.6367 3.12 0.0228 0.3393 0.0671 0.5825 4.7467 2.51 0.0576 0.4425 0.1302 0.6652 2.6615 3.13 0.0224 0.3379 0.0664 0.5813 4.7920 2.52 0.0567 0.4405 0.1288 0.6637 2.6865 3.14 0.0221 0.3365 0.0657 0.5801 4.8377 2.53 0.0559 0.4386 0.1274 0.6622 2.7117 3.15 0.0218 0.3351 0.0650 0.5788 4.8838 2.54 0.0550 0.4366 0.1260 0.6608 2.7372 3.16 0.0215 0.3337 0.0643 0.5776 4.9304 2.55 0.0542 0.4347 0.1246 0.6593 2.7630 3.17 0.0211 0.3323 0.0636 0.5764 4.9774 2.56 0.0533 0.4328 0.1232 0.6578 2.7891 3.18 0.0208 0.3309 0.0630 0.5752 5.0248 2.57 0.0525 0.4309 0.1218 0.6564 2.8154 3.19 0.0205 0.3295 0.0623 0.5740 5.0727 2.58 0.0517 0.4289 0.1205 0.6549 2.8420 3.20 0.0202 0.3281 0.0617 0.5728 5.1210 2.59 0.0509 0.4271 0.1192 0.6535 2.8688 3.21 0.0199 0.3267 0.0610 0.5716 5.1697 2.60 0.0501 0.4252 0.1179 0.6521 2.8960 3.22 0.0196 0.3253 0.0604 0.5704 5.2189 2.61 0.0493 0.4233 0.1166 0.6506 2.9234 3.23 0.0194 0.3240 0.0597 0.5692 5.2685 2.62 0.0486 0.4214 0.1153 0.6492 2.9511 3.24 0.0191 0.3226 0.0591 0.5680 5.3186 2.63 0.0478 0.4196 0.1140 0.6477 2.9791 3.25 0.0188 0.3213 0.0585 0.5668 5.3691 2.64 0.0471 0.4177 0.1128 0.6463 3.0073 3.26 0.0185 0.3199 0.0579 0.5656 5.4201 2.65 0.0464 0.4159 0.1115 0.6449 3.0359 3.27 0.0183 0.3186 0.0573 0.5645 5.4715 2.66 0.0457 0.4141 0.1103 0.6435 3.0647 3.28 0.0180 0.3173 0.0567 0.5633 5.5234 434 Appendix D: Isentropic Table (γ = 1.4)

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 3.29 0.0177 0.3160 0.0561 0.5621 5.5758 3.91 0.0074 0.2464 0.0302 0.4964 9.8877 3.30 0.0175 0.3147 0.0555 0.5609 5.6286 3.92 0.0073 0.2455 0.0299 0.4955 9.9771 3.31 0.0172 0.3134 0.0550 0.5598 5.6820 3.93 0.0072 0.2446 0.0296 0.4945 10.0672 3.32 0.0170 0.3121 0.0544 0.5586 5.7358 3.94 0.0071 0.2436 0.0293 0.4936 10.1581 3.33 0.0167 0.3108 0.0538 0.5575 5.7900 3.95 0.0070 0.2427 0.0290 0.4926 10.2496 3.34 0.0165 0.3095 0.0533 0.5563 5.8448 3.96 0.0069 0.2418 0.0287 0.4917 10.3420 3.35 0.0163 0.3082 0.0527 0.5552 5.9000 3.97 0.0069 0.2408 0.0285 0.4908 10.4350 3.36 0.0160 0.3069 0.0522 0.5540 5.9558 3.98 0.0068 0.2399 0.0282 0.4898 10.5289 3.37 0.0158 0.3057 0.0517 0.5529 6.0120 3.99 0.0067 0.2390 0.0279 0.4889 10.6234 3.38 0.0156 0.3044 0.0511 0.5517 6.0687 4.00 0.0066 0.2381 0.0277 0.4880 10.7188 3.39 0.0153 0.3032 0.0506 0.5506 6.1260 4.01 0.0065 0.2372 0.0274 0.4870 10.8148 3.40 0.0151 0.3019 0.0501 0.5495 6.1837 4.02 0.0064 0.2363 0.0271 0.4861 10.9117 3.41 0.0149 0.3007 0.0496 0.5484 6.2419 4.03 0.0063 0.2354 0.0269 0.4852 11.0093 3.42 0.0147 0.2995 0.0491 0.5472 6.3007 4.04 0.0062 0.2345 0.0266 0.4843 11.1077 3.43 0.0145 0.2982 0.0486 0.5461 6.3600 4.05 0.0062 0.2336 0.0264 0.4833 11.2069 3.44 0.0143 0.2970 0.0481 0.5450 6.4198 4.06 0.0061 0.2327 0.0261 0.4824 11.3068 3.45 0.0141 0.2958 0.0476 0.5439 6.4801 4.07 0.0060 0.2319 0.0259 0.4815 11.4076 3.46 0.0139 0.2946 0.0471 0.5428 6.5409 4.08 0.0059 0.2310 0.0256 0.4806 11.5091 3.47 0.0137 0.2934 0.0466 0.5417 6.6023 4.09 0.0058 0.2301 0.0254 0.4797 11.6115 3.48 0.0135 0.2922 0.0462 0.5406 6.6642 4.10 0.0058 0.2293 0.0252 0.4788 11.7147 3.49 0.0133 0.2910 0.0457 0.5395 6.7266 4.11 0.0057 0.2284 0.0249 0.4779 11.8186 3.50 0.0131 0.2899 0.0452 0.5384 6.7896 4.12 0.0056 0.2275 0.0247 0.4770 11.9234 3.51 0.0129 0.2887 0.0448 0.5373 6.8532 4.13 0.0055 0.2267 0.0245 0.4761 12.0290 3.52 0.0127 0.2875 0.0443 0.5362 6.9172 4.14 0.0055 0.2258 0.0242 0.4752 12.1354 3.53 0.0126 0.2864 0.0439 0.5351 6.9819 4.15 0.0054 0.2250 0.0240 0.4743 12.2427 3.54 0.0124 0.2852 0.0434 0.5340 7.0471 4.16 0.0053 0.2242 0.0238 0.4735 12.3508 3.55 0.0122 0.2841 0.0430 0.5330 7.1128 4.17 0.0053 0.2233 0.0236 0.4726 12.4597 3.56 0.0120 0.2829 0.0426 0.5319 7.1791 4.18 0.0052 0.2225 0.0234 0.4717 12.5695 3.57 0.0119 0.2818 0.0421 0.5308 7.2460 4.19 0.0051 0.2217 0.0231 0.4708 12.6801 3.58 0.0117 0.2806 0.0417 0.5298 7.3135 4.20 0.0051 0.2208 0.0229 0.4699 12.7916 3.59 0.0115 0.2795 0.0413 0.5287 7.3815 4.21 0.0050 0.2200 0.0227 0.4691 12.9040 3.60 0.0114 0.2784 0.0409 0.5276 7.4501 4.22 0.0049 0.2192 0.0225 0.4682 13.0172 3.61 0.0112 0.2773 0.0405 0.5266 7.5193 4.23 0.0049 0.2184 0.0223 0.4673 13.1313 3.62 0.0111 0.2762 0.0401 0.5255 7.5891 4.24 0.0048 0.2176 0.0221 0.4665 13.2463 3.63 0.0109 0.2751 0.0397 0.5245 7.6595 4.25 0.0047 0.2168 0.0219 0.4656 13.3622 3.64 0.0108 0.2740 0.0393 0.5234 7.7305 4.26 0.0047 0.2160 0.0217 0.4648 13.4789 3.65 0.0106 0.2729 0.0389 0.5224 7.8020 4.27 0.0046 0.2152 0.0215 0.4639 13.5965 3.66 0.0105 0.2718 0.0385 0.5213 7.8742 4.28 0.0046 0.2144 0.0213 0.4631 13.7151 3.67 0.0103 0.2707 0.0381 0.5203 7.9470 4.29 0.0045 0.2136 0.0211 0.4622 13.8345 3.68 0.0102 0.2697 0.0378 0.5193 8.0204 4.30 0.0044 0.2129 0.0209 0.4614 13.9549 3.69 0.0100 0.2686 0.0374 0.5183 8.0944 4.31 0.0044 0.2121 0.0207 0.4605 14.0762 3.70 0.0099 0.2675 0.0370 0.5172 8.1691 4.32 0.0043 0.2113 0.0205 0.4597 14.1984 3.71 0.0098 0.2665 0.0367 0.5162 8.2443 4.33 0.0043 0.2105 0.0203 0.4588 14.3215 3.72 0.0096 0.2654 0.0363 0.5152 8.3202 4.34 0.0042 0.2098 0.0202 0.4580 14.4456 3.73 0.0095 0.2644 0.0359 0.5142 8.3968 4.35 0.0042 0.2090 0.0200 0.4572 14.5706 3.74 0.0094 0.2633 0.0356 0.5132 8.4739 4.36 0.0041 0.2083 0.0198 0.4563 14.6965 3.75 0.0092 0.2623 0.0352 0.5121 8.5517 4.37 0.0041 0.2075 0.0196 0.4555 14.8234 3.76 0.0091 0.2613 0.0349 0.5111 8.6302 4.38 0.0040 0.2067 0.0194 0.4547 14.9513 3.77 0.0090 0.2602 0.0345 0.5101 8.7093 4.39 0.0040 0.2060 0.0193 0.4539 15.0801 3.78 0.0089 0.2592 0.0342 0.5091 8.7891 4.40 0.0039 0.2053 0.0191 0.4531 15.2099 3.79 0.0087 0.2582 0.0339 0.5081 8.8695 4.41 0.0039 0.2045 0.0189 0.4522 15.3406 3.80 0.0086 0.2572 0.0335 0.5072 8.9506 4.42 0.0038 0.2038 0.0187 0.4514 15.4724 3.81 0.0085 0.2562 0.0332 0.5062 9.0323 4.43 0.0038 0.2030 0.0186 0.4506 15.6051 3.82 0.0084 0.2552 0.0329 0.5052 9.1148 4.44 0.0037 0.2023 0.0184 0.4498 15.7388 3.83 0.0083 0.2542 0.0326 0.5042 9.1979 4.45 0.0037 0.2016 0.0182 0.4490 15.8735 3.84 0.0082 0.2532 0.0323 0.5032 9.2817 4.46 0.0036 0.2009 0.0181 0.4482 16.0092 3.85 0.0081 0.2522 0.0320 0.5022 9.3661 4.47 0.0036 0.2002 0.0179 0.4474 16.1459 3.86 0.0080 0.2513 0.0316 0.5013 9.4513 4.48 0.0035 0.1994 0.0178 0.4466 16.2837 3.87 0.0078 0.2503 0.0313 0.5003 9.5372 4.49 0.0035 0.1987 0.0176 0.4458 16.4224 3.88 0.0077 0.2493 0.0310 0.4993 9.6237 4.50 0.0035 0.1980 0.0174 0.4450 16.5622 3.89 0.0076 0.2484 0.0307 0.4984 9.7110 4.51 0.0034 0.1973 0.0173 0.4442 16.7030 3.90 0.0075 0.2474 0.0304 0.4974 9.7990 Appendix D: Isentropic Table (γ = 1.4) 435

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 4.52 0.0034 0.1966 0.0171 0.4434 16.8449 5.14 0.0016 0.1591 0.0101 0.3989 27.9373 4.53 0.0033 0.1959 0.0170 0.4426 16.9878 5.15 0.0016 0.1586 0.0100 0.3983 28.1579 4.54 0.0033 0.1952 0.0168 0.4418 17.1317 5.16 0.0016 0.1581 0.0099 0.3976 28.3800 4.55 0.0032 0.1945 0.0167 0.4411 17.2767 5.17 0.0016 0.1576 0.0099 0.3970 28.6036 4.56 0.0032 0.1938 0.0165 0.4403 17.4228 5.18 0.0015 0.1571 0.0098 0.3963 28.8287 4.57 0.0032 0.1932 0.0164 0.4395 17.5699 5.19 0.0015 0.1566 0.0097 0.3957 29.0552 4.58 0.0031 0.1925 0.0163 0.4387 17.7181 5.20 0.0015 0.1561 0.0096 0.3950 29.2833 4.59 0.0031 0.1918 0.0161 0.4380 17.8674 5.21 0.0015 0.1555 0.0095 0.3944 29.5129 4.60 0.0031 0.1911 0.0160 0.4372 18.0178 5.22 0.0015 0.1550 0.0095 0.3938 29.7441 4.61 0.0030 0.1905 0.0158 0.4364 18.1693 5.23 0.0015 0.1545 0.0094 0.3931 29.9767 4.62 0.0030 0.1898 0.0157 0.4357 18.3218 5.24 0.0014 0.1540 0.0093 0.3925 30.2109 4.63 0.0029 0.1891 0.0156 0.4349 18.4755 5.25 0.0014 0.1536 0.0092 0.3919 30.4467 4.64 0.0029 0.1885 0.0154 0.4341 18.6303 5.26 0.0014 0.1531 0.0092 0.3912 30.6840 4.65 0.0029 0.1878 0.0153 0.4334 18.7862 5.27 0.0014 0.1526 0.0091 0.3906 30.9229 4.66 0.0028 0.1872 0.0152 0.4326 18.9433 5.28 0.0014 0.1521 0.0090 0.3900 31.1634 4.67 0.0028 0.1865 0.0150 0.4319 19.1015 5.29 0.0014 0.1516 0.0089 0.3893 31.4054 4.68 0.0028 0.1859 0.0149 0.4311 19.2608 5.30 0.0013 0.1511 0.0089 0.3887 31.6491 4.69 0.0027 0.1852 0.0148 0.4304 19.4212 5.31 0.0013 0.1506 0.0088 0.3881 31.8943 4.70 0.0027 0.1846 0.0146 0.4296 19.5828 5.32 0.0013 0.1501 0.0087 0.3875 32.1411 4.71 0.0027 0.1839 0.0145 0.4289 19.7456 5.33 0.0013 0.1497 0.0087 0.3869 32.3896 4.72 0.0026 0.1833 0.0144 0.4281 19.9095 5.34 0.0013 0.1492 0.0086 0.3862 32.6397 4.73 0.0026 0.1827 0.0143 0.4274 20.0746 5.35 0.0013 0.1487 0.0085 0.3856 32.8914 4.74 0.0026 0.1820 0.0141 0.4267 20.2409 5.36 0.0013 0.1482 0.0085 0.3850 33.1448 4.75 0.0025 0.1814 0.0140 0.4259 20.4084 5.37 0.0012 0.1478 0.0084 0.3844 33.3998 4.76 0.0025 0.1808 0.0139 0.4252 20.5770 5.38 0.0012 0.1473 0.0083 0.3838 33.6565 4.77 0.0025 0.1802 0.0138 0.4245 20.7469 5.39 0.0012 0.1468 0.0083 0.3832 33.9148 4.78 0.0025 0.1795 0.0137 0.4237 20.9179 5.40 0.0012 0.1464 0.0082 0.3826 34.1748 4.79 0.0024 0.1789 0.0135 0.4230 21.0902 5.41 0.0012 0.1459 0.0081 0.3820 34.4365 4.80 0.0024 0.1783 0.0134 0.4223 21.2637 5.42 0.0012 0.1454 0.0081 0.3814 34.6999 4.81 0.0024 0.1777 0.0133 0.4216 21.4384 5.43 0.0012 0.1450 0.0080 0.3808 34.9650 4.82 0.0023 0.1771 0.0132 0.4208 21.6144 5.44 0.0011 0.1445 0.0079 0.3802 35.2318 4.83 0.0023 0.1765 0.0131 0.4201 21.7916 5.45 0.0011 0.1441 0.0079 0.3796 35.5003 4.84 0.0023 0.1759 0.0130 0.4194 21.9700 5.46 0.0011 0.1436 0.0078 0.3790 35.7705 4.85 0.0023 0.1753 0.0129 0.4187 22.1497 5.47 0.0011 0.1432 0.0078 0.3784 36.0425 4.86 0.0022 0.1747 0.0128 0.4180 22.3306 5.48 0.0011 0.1427 0.0077 0.3778 36.3162 4.87 0.0022 0.1741 0.0126 0.4173 22.5128 5.49 0.0011 0.1423 0.0076 0.3772 36.5917 4.88 0.0022 0.1735 0.0125 0.4166 22.6963 5.50 0.0011 0.1418 0.0076 0.3766 36.8690 4.89 0.0022 0.1729 0.0124 0.4159 22.8811 5.51 0.0011 0.1414 0.0075 0.3760 37.1480 4.90 0.0021 0.1724 0.0123 0.4152 23.0671 5.52 0.0011 0.1410 0.0075 0.3754 37.4288 4.91 0.0021 0.1718 0.0122 0.4145 23.2545 5.53 0.0010 0.1405 0.0074 0.3749 37.7113 4.92 0.0021 0.1712 0.0121 0.4138 23.4431 5.54 0.0010 0.1401 0.0073 0.3743 37.9957 4.93 0.0021 0.1706 0.0120 0.4131 23.6331 5.55 0.0010 0.1397 0.0073 0.3737 38.2819 4.94 0.0020 0.1700 0.0119 0.4124 23.8243 5.56 0.0010 0.1392 0.0072 0.3731 38.5699 4.95 0.0020 0.1695 0.0118 0.4117 24.0169 5.57 0.0010 0.1388 0.0072 0.3725 38.8597 4.96 0.0020 0.1689 0.0117 0.4110 24.2109 5.58 0.0010 0.1384 0.0071 0.3720 39.1513 4.97 0.0020 0.1683 0.0116 0.4103 24.4061 5.59 0.0010 0.1379 0.0071 0.3714 39.4448 4.98 0.0019 0.1678 0.0115 0.4096 24.6027 5.60 0.0010 0.1375 0.0070 0.3708 39.7402 4.99 0.0019 0.1672 0.0114 0.4089 24.8007 5.61 0.0010 0.1371 0.0070 0.3703 40.0374 5.00 0.0019 0.1667 0.0113 0.4082 25.0000 5.62 0.0009 0.1367 0.0069 0.3697 40.3365 5.01 0.0019 0.1661 0.0112 0.4076 25.2007 5.63 0.0009 0.1363 0.0069 0.3691 40.6374 5.02 0.0018 0.1656 0.0112 0.4069 25.4027 5.64 0.0009 0.1358 0.0068 0.3686 40.9402 5.03 0.0018 0.1650 0.0111 0.4062 25.6062 5.65 0.0009 0.1354 0.0067 0.3680 41.2450 5.04 0.0018 0.1645 0.0110 0.4055 25.8110 5.66 0.0009 0.1350 0.0067 0.3674 41.5516 5.05 0.0018 0.1639 0.0109 0.4049 26.0172 5.67 0.0009 0.1346 0.0066 0.3669 41.8602 5.06 0.0018 0.1634 0.0108 0.4042 26.2249 5.68 0.0009 0.1342 0.0066 0.3663 42.1707 5.07 0.0017 0.1628 0.0107 0.4035 26.4339 5.69 0.0009 0.1338 0.0065 0.3658 42.4831 5.08 0.0017 0.1623 0.0106 0.4029 26.6444 5.70 0.0009 0.1334 0.0065 0.3652 42.7974 5.09 0.0017 0.1618 0.0105 0.4022 26.8563 5.71 0.0009 0.1330 0.0064 0.3646 43.1137 5.10 0.0017 0.1612 0.0104 0.4015 27.0696 5.72 0.0008 0.1326 0.0064 0.3641 43.4320 5.11 0.0017 0.1607 0.0104 0.4009 27.2843 5.73 0.0008 0.1322 0.0063 0.3635 43.7523 5.12 0.0016 0.1602 0.0103 0.4002 27.5005 5.74 0.0008 0.1318 0.0063 0.3630 44.0745 5.13 0.0016 0.1597 0.0102 0.3996 27.7182 436 Appendix D: Isentropic Table (γ = 1.4)

p T ρ a A p T ρ a A M ∗ M ∗ p0 T0 ρ0 a0 A p0 T0 ρ0 a0 A 5.75 0.0008 0.1314 0.0063 0.3624 44.3987 5.87 0.0007 0.1267 0.0057 0.3560 48.4481 5.76 0.0008 0.1310 0.0062 0.3619 44.7249 5.88 0.0007 0.1263 0.0057 0.3554 48.7991 5.77 0.0008 0.1306 0.0062 0.3613 45.0532 5.89 0.0007 0.1260 0.0056 0.3549 49.1522 5.78 0.0008 0.1302 0.0061 0.3608 45.3834 5.90 0.0007 0.1256 0.0056 0.3544 49.5075 5.79 0.0008 0.1298 0.0061 0.3603 45.7157 5.91 0.0007 0.1252 0.0055 0.3539 49.8649 5.80 0.0008 0.1294 0.0060 0.3597 46.0500 5.92 0.0007 0.1249 0.0055 0.3533 50.2244 5.81 0.0008 0.1290 0.0060 0.3592 46.3864 5.93 0.0007 0.1245 0.0055 0.3528 50.5861 5.82 0.0008 0.1286 0.0059 0.3586 46.7248 5.94 0.0007 0.1241 0.0054 0.3523 50.9501 5.83 0.0008 0.1282 0.0059 0.3581 47.0653 5.95 0.0007 0.1238 0.0054 0.3518 51.3161 5.84 0.0007 0.1279 0.0058 0.3576 47.4079 5.96 0.0007 0.1234 0.0053 0.3513 51.6844 5.85 0.0007 0.1275 0.0058 0.3570 47.7525 5.97 0.0007 0.1230 0.0053 0.3508 52.0549 5.86 0.0007 0.1271 0.0058 0.3565 48.0993 5.98 0.0006 0.1227 0.0053 0.3502 52.4276 5.99 0.0006 0.1223 0.0052 0.3497 52.8026 Multiple Choice Questions in Aerospace Engineering E

1. High wing position gives (a) remain constant. (b) increase isentropically to the static pressure at the noz- (a) the same lateral stability as a low wing. zle exit. (b) more lateral stability than a low wing. (c) decrease isentropically to the static pressure at the noz- (c) less lateral stability than a low wing. zle exit. (d) no stability change. (d) increase or decrease, depending upon the static pressure at the nozzle exit. 2. The Mach number range of hypersonic flow (until the continuum hypothesis holds for air), is 6. For a flow across Normal shock wave, (a) 5 ≤ M ≤ 25 (a) stagnation pressure remains constant. (b) 5 ≤ M ≤ 40 (b) Mach number increases. (c) 5 ≤ M ≤ 55 (c) stagnation temperature remains constant. (d) 5 ≤ M ≤ 75 (d) both static pressure and density decreases. 3. What is the purpose of Elevons in Light Combat Aircraft? 7. The absolute ceiling is determined by (a) rolling (b) pitching (a) aircraft weight, altitude, and speed. (c) both a & b (b) aircraft weight, speed, and cg position. (d) none of the above (c) aircraft speed, altitude, and cg position. (d) aircraft weight and cg position. 4. Which of the following statement is TRUE with respect to International Standard Atmosphere? 8. The Stagnation or total pressure at a point is defined as the pressure when the flow is brought to rest (a) Cruising phase of civil aviation flights takes place in TROPOSPHERE. (a) isothermally (b) Cruising phase of civil aviation flights takes place in (b) isobarically TROPOPAUSE. (c) isentropically (c) Cruising phase of civil aviation flights takes place in (d) adiabatically STRATOSPHERE. (d) Cruising phase of civil aviation flights takes place in 9. How does CL vary with altitude? MESOSPHERE. (a) It increases with increasing altitude. 5. Considering a steady and inviscid flow in a convergent– (b) It decreases with increasing altitude. divergent nozzle, with a normal shock placed in the diver- (c) It decreases with decreasing altitude. gent portion. The static pressure along the nozzle, down- (d) It remains constant with increasing altitude. stream of the normal shock will

© Springer Nature Singapore Pte Ltd. 2019 437 M. Kaushik, Theoretical and Experimental Aerodynamics, https://doi.org/10.1007/978-981-13-1678-4 438 Appendix E: Multiple Choice Questions in Aerospace Engineering

10. For a ﬂow across Prandtl–Meyer expansion wave, (b) 0.04 (c) 0.24 (a) Density remains constant. (d) 0.12 (b) Temperature remains constant. (c) Entropy remains constant. 17. For any two-dimensional, irrotational, and incompress- (d) Mach number remains constant. ible ﬂow

11. Among the choices given below, the specific impulse is (a) Both velocity potential and stream function satisfies maximum for a Laplace’s equation. (b) Velocity potential satisfies but stream function does (a) solid rocket not satisfy Laplace’s equation. (b) liquid rocket (c) Stream function satisfies but velocity potential does (c) ramjet not satisfy Laplace’s equation. (d) cryogenic rocket (d) Both velocity potential and stream function do not satisfy Laplace’s equation. 12. For a flow across an oblique shock wave, which of the statement is TRUE? 18. The induced drag coefficient for a finite wing with general lift distribution is (a) Component of velocity normal to shock wave decreases while tangential component increases. (a) directly proportional to aspect ratio (b) Component of velocity normal to shock wave (b) inversely proportional to aspect ratio increases while tangential component decreases. (c) directly proportional to (aspect ratio)1/2 (c) Component of velocity normal to shock wave (d) inversely proportional to (aspect ratio)1/2 decreases while tangential component remains unchanged. 19. The pressure distribution on the surface of the sphere is (d) Component of velocity normal to shock wave is given by unchanged while tangential component decreases. = − 5 2θ (a) Cp 1 4 sin = ˆ− ˆ . = − 4 2θ 13. A flow has a velocity field given by v 2xi 2yj The (b) Cp 1 9 sin = − 2θ potential function, φ(x, y) for the flow is (c) Cp 1 4sin 2 (d) Cp = 2sin θ (a) 2x–2y + constant (b) 2xy + constant 20. Combustion efficiency of a rocket engine is generally in (c) x2 + y2 + constant the range of (d) x2 − y2 + constant (a) 80–89% dCl = π (b) 70–79% 14. Thin airfoil theory predicts that lift slope is dα 2 for (c) 40–49% (a) any airfoil shape. (d) 90–99% (b) symmetric airfoils only (c) cambered airfoils only 21. In hot-wire anemometry, the hot-wire sensor is generally (d) Joukowski airfoils only made of

15. The conventional altimeter is the instrument used for (a) stainless steel (b) nickel (a) pressure measurement (c) tungsten (b) temperature measurement (d) copper (c) density measurement (d) velocity measurement 22. The Shadowgraph is an optical diagnostic technique which is sensitive to changes of the 16. The maximum thickness-to-chord ratio for NACA 2412 airfoil is (a) fluid density. (b) first derivative of the fluid density. (a) 0.02 (c) second derivative of the fluid density. (d) third derivative of the fluid density. Appendix E: Multiple Choice Questions in Aerospace Engineering 439

23. “Washout” is (a) increase with increasing altitude. (b) are independent of outside air temperature. (a) a decrease in chord from root to tip. (c) increase in proportion to the airspeed. (b) an increase in incidence from root to tip. (d) decrease in proportion to the ambient pressure at (c) a decrease in incidence from root to tip. constant temperature. (d) a decrease and then increase in angle of chord from root to tip. 31. The effect of a tailwind on the time to climb to a given altitude is 24. If KE is the mean molecular kinetic energy, T is the temperature in Kelvin, and κ is the Boltzmann constant (a) none then (b) increases (c) decreases (a) KE = 52κT (d) depends on the airplane type. (b) KE = 32κT = κ (c) KE 12 T 32. Apart from lift, the forces that determine the angle of = κ (d) KE 72 T climb are

25. The Air deviates from the perfect gas behavior when (a) weight and drag (b) thrust and drag (a) pressure decreases and temperature increases. (c) weight and thrust (b) pressure increases and temperature decreases. (d) weight, drag, and thrust (c) when both pressure and temperature decreases. (d) when both pressure and temperature increases. 33. Which of the following statements are correct?

26. With increasing the aircraft weight, it will (a) Induced drag is independent of speed. (b) Induced drag decreases with increasing angle of (a) increase the stalling speed. attack. (b) not affect the stalling speed. (c) Induced drag decreases with increasing speed. (c) decrease the stalling speed. (d) Induced drag increases with increasing speed. (d) stalling speed becomes zero. 34. The Bernoulli equation for compressible flow is 27. In level flight Maximum horizontal speed occurs when 1 2 (a) p + ρv = p0 (a) thrust = minimum drag. γ 2 γ p + 1 ρ 2 = p0 (b) thrust does not increase with increasing speed. (b) γ+1 ρ 2 v γ+1 ρ γ γ 0 (c) maximum thrust = total drag. (c) p + 1 ρv2 = p0 γ−1 ρ 2 γ−1 ρ0 (d) thrust = maximum drag. (d) γ p + 1 v2 = γ p0 ρ 2 ρ0 28. In a level flight, at a constant mass and Mach number, a 35. The speed to attain the minimum power required for a higher altitude requires a turbojet aircraft is

(a) higher angle of attack (a) less than the speed for minimum drag. (b) lower CL (b) higher than the speed for minimum drag. (c) lower CD (c) slower in a climb and faster in a descent. (d) lower angle of attack (d) the same as minimum drag speed.

29. The maximum operating altitude for an aircraft with a 36. Which of the following is CORRECT? pressurized cabin (a) With increase of temperature, the viscosity of air (a) is dependent on the aerodynamic ceiling. decreases and viscosity of water increases. (b) is dependent on the outside air temperature. (b) With increase of temperature, the viscosity of air (c) is only certified for four engine aircraft. increases and viscosity of water decreases. (d) is the highest pressure altitude certified for normal (c) With increase of temperature, the viscosity of BOTH operation. air and water increases. (d) With increase of temperature, the viscosity of BOTH 30. At a constant Mach number, the thrust and fuel flow of air and water decreases. a jet engine 440 Appendix E: Multiple Choice Questions in Aerospace Engineering

37. The thrust of a jet engine at constant RPM (a) diesel (b) petrol (a) is inversely proportional to the airspeed. (c) liquid hydrogen (b) increases in proportion to the airspeed. (d) kerosene (c) does not change with changing altitude. (d) is independent of airspeed. 45. In a straight and level ﬂight of an aircraft

38. If the thrust available exceeds the thrust required in level (a) Lift equals aircraft weight. flight, the aircraft (b) Lift is more than weight. (c) Lift is less than weight. (a) will accelerate. (d) Lift depends upon the size of aircraft and its (b) will descend if the airspeed remains constant. loading. (c) decelerates if it is in the region of reversed command. (d) will decelerate. 46. In propulsion engines, generally the combustion takes place at 39. Which force compensates the mass in unaccelerated straight and level flight (a) constant volume (b) constant pressure (a) lift (c) constant entropy (b) thrust (d) constant temperature (c) drag (d) resultant from lift and drag 47. For a flow across Normal shock wave, when M1 →∞ then which of the following is CORRECT? 40. Increased mass will cause the climb performance to ρ 2 = (a) limM1→∞ ρ 2 ρ1 (a) improve. (b) lim →∞ 2 = 4 M1 ρ1 (b) be unchanged. ρ2 (c) limM →∞ ρ = 6 (c) be unchanged if the short-field technique is used. 1 1 ρ2 (d) limM →∞ =∞ (d) degrade. 1 ρ1

41. Modern transport aircraft use which of the following 48. The speciﬁc impulse of a solid rocket motor is of the engine for propulsion? order of

(a) turbojet (a) 650 seconds (b) turbofan (b) 250 seconds (c) rocket (c) 550 seconds (d) turboshaft (d) 750 seconds 2 2 42. In a glide the lift force is 49. A ﬂow ﬁeld has the stream function, ψ = x −y and velocity potential, φ = x3 + y3 . Which of the follow- (a) greater than the weight . ing statements are correct? (b) to the weight. (c) less than the weight. (a) Flow is incompressible and irrotational. (d) equal to drag. (b) Flow is incompressible and rotational. (c) Flow is compressible and irrotational. 43. When a Rocket climbs up, the thrust (d) Flow is compressible and rotational.

(a) increases. 50. In straight and level ﬂight the following forces act on the (b) decreases. a/c (c) remains constant. (d) decreases and then increases. (a) thrust, lift, and drag only. (b) lift and drag only. 44. Which of the following is a potential fuel in a supersonic (c) thrust, lift, and weight only. combustion ramjet (SCRAMJET), which can also serve (d) all thrust, lift, drag, and weight. as a coolant Appendix E: Multiple Choice Questions in Aerospace Engineering 441

51. A Ramjet engine does not have the following 58. In an irrotational, incompressible and two-dimensional flow, the velocity potential (φ), satisfies which of the (a) nozzle following relation (u and v are velocity components in (b) combustion chamber Cartesian coordinates)? (c) compressor (d) flame holder = ∂φ =−∂φ (a) u ∂x and v ∂y ∂φ ∂φ (b) u =− and v = 52. In a climb the lift force is ∂x ∂y ∂φ ∂φ (c) u = ∂ and v =−∂ (a) greater than the weight. x y =−∂φ =−∂φ (b) equal to the weight. (d) u ∂x and v ∂y (c) than the weight. (d) greater than trust. 59. If an aircraft maintains a constant radius of turn but the speed is increased then 53. To maintain steady level flight, as the angle of attack is increased, the airspeed must (a) The bank angle must be increased. (b) The bank angle must be decreased. (a) be increased. (c) The bank angle will remain constant. (b) be decreased. (d) The bank angle is equal to zero. (c) remain constant. (d) no affect by airspeed. 60. Maximum range for a jet occurs when the airplane is flying at 54. For International Standard Atmosphere, the relation / between geopotential and geometric altitude is C1 2 (a) L CD + max = r hG / (a) h r hG C3 2 (b) L r CD (b) h = + hG max h hG CL r−hG (c) (c) h = h CD r G max 5/2 r C (d) h = + hG (d) L r hG CD max 55. Power available at absolute ceiling is 61. For maximum aerodynamic efficiency the wing plan (a) more than the power required. shape would be (b) less than the power required. (c) zero. (a) elliptical (d) equal to the power required. (b) triangular (c) rectangular 56. Which statement is true as far as a rocket vehicle is con- (d) circular cerned 62. Stall speed is affected by (a) The vehicle velocity can exceed the exhaust velocity. (b) The vehicle velocity cannot exceed the exhaust (a) weight, load factor, and power. velocity. (b) load factor, angle of attack, and power. (c) The vehicle velocity is always equal to the exhaust (c) angle of attack, weight, and air density. velocity. (d) only load factor and power. (d) The vehicle velocity can exceed exhaust velocity in vacuum only. 63. Which of the following is true due the expansion of the gas through a nozzle 57. Lift on a wing (a) Mach number increases. (a) acts through center of gravity. (b) Pressure decreases. (b) acts vertically upward. (c) Temperature decreases. (c) is perpendiculars to chord line. (d) All of the above. (d) acts vertically upward through center of pressure. 442 Appendix E: Multiple Choice Questions in Aerospace Engineering

64. To improve the frequency of a structure, you will (c) rudder (d) vertical tail (a) increase stiffness. (b) decrease mass. 72. For the flow past a “Golf Ball” kept in a uniform flow, (c) both (a) & (b). which of the following statement is correct? (d) increase mass. (a) Skin friction drag is greater when boundary layer is 65. Spiral divergence is a form of laminar. (b) Skin friction drag is greater when boundary layer is (a) longitudinal dynamic instability. turbulent. (b) lateral dynamic instability. (c) Form drag is greater when boundary layer is turbu- (c) lateral static stability. lent. (d) all are correct. (d) Both Skin friction drag and form drag are higher when boundary layer is laminar. 66. The function of the horizontal stabilizer is to assist 73. If the angle of attack of an airfoil is increased, then the (a) lateral stability center of pressure will (b) directional stability (c) longitudinal stability (a) moved forward (d) none (b) moved backward (c) stay the same 67. Anhedral is defined as (d) none

(a) the upward inclination of the aircraft wings in the 74. Dutch roll is tip. (b) neutrally stable. (a) a type of slow roll. (c) the downward inclination of the aircraft wings in the (b) primarily a pitching instability. tip. (c) a combined rolling and yawing motion. (d) none. (d) a combined pitching and yawing motion.

68. Sweep-back wing provides 75. The viscosity of air at very high temperature is (a) directly proportional to T1/2 (a) increased lateral stability (b) inversely proportional to T1/2 (b) reduced drag at all speed (c) directly proportional to T3/2 (c) less wing weight (d) inversely proportional to T3/2 (d) all are correct 76. When the horizontal control surface is deflected, then 69. In aircraft design, it is usual to position the center of lift the slope of C versus α curve is relative to the center of gravity in the following location m (a) proportional to deflection (a) forward of CG (b) inversely proportional to deflection (b) aft of CG (c) depending on position (c) to the side of CG (d) the same throughout (d) below CG 77. Aircraft load factor is found from the relationship 70. Control of yaw is mainly influenced by (a) lift/drag (a) the vertical fin (b) lift/weight (b) the tail-plane (c) weight/drag (c) the ailerons (d) drag/lift (d) the rudder 78. Which of the following statements are FALSE? 71. Differential control of an aircraft is associated with (a) Local jump in radial velocity across the vortex sheet (a) aileron is equal to the local sheet strength. (b) trim tab Appendix E: Multiple Choice Questions in Aerospace Engineering 443

(b) Circulation around an airfoil takes a value so that the 85. Natural frequency of a structure depends upon ﬂow leaves the trailing edge smoothly. (c) Time rate of change of circulation in a ﬂow domain (a) mass and stiffness is zero. (b) mass and damping (d) Quarter-chord point is both the center of pressure (c) stiffness and damping and aerodynamic center of the symmetric airfoil. (d) none of the above

79. In the airfoil, NACA 23015, what do the second and third 86. The Young’s Modulus of most of the metallic materials digits signify? used in aerospace applications varies with temperature. With increase in temperature it 3 (a) Multiply by 2 to get design lift coefficient in hundredths. (a) increases. (b) Maximum thickness in hundredths of chord. (b) decreases. (c) Divide by 2 to get location of maximum camber in (c) first increases up to critical temperature and then tenths of chord. decreases. (d) Location of minimum pressure in hundredths of (d) remains constant. chord. 87. During supersonic isentropic expansion, total tempera- 80. Consider a non-lifting flow over a circular cylinder. At ture along the length of the nozzle which of the following angular positions will have the (a) increases. value of pressure coefficient, Cp to be zero? (b) decreases. (a) 90o (c) first decreases, then increases. (b) 30o (d) remains the same. (c) 0o 88. For stability point recommended position of CG of a (d) 45o control surface

81. Which of the following statements are FALSE? (a) ahead or on the hinge line (a) For an incompressible flow, ∇2φ = 0. (b) after the hinge line (b) For an incompressible flow, ∇2ψ = 0. (c) anywhere (c) Principle of superposition does not hold good for (d) none incompressible, irrotational flows. 89. Solid rocket motors nozzles have a thermal protection (d) Laplace equation is a linear PDE. system based on

82. Name the angle between the reference line of an aircraft (a) regenerative cooling and the projection of the wind vector on the yaw plane. (b) ﬁlm cooling (a) angle of attack (c) ablative cooling (b) angle of side-slip (d) radiation cooling (c) angle of incidence 90. If a disturbing force is removed from a body and the body (d) ﬂight path angle immediately tends to return toward the equilibrium, then 83. PHUGOID motion is a form of it is

(a) longitudinal dynamic stability (a) statically stable (b) directional dynamic stability (b) dynamically stable (c) lateral dynamic stability (c) dynamically unstable (d) all are correct (d) none of the above 91. What are the four typical loads are on the aircraft? 84. For a given area ratio Ae , thrust can be maximized by At (a) tension, torsion, creep, elongation. (a) maximizing combustion chamber pressure. (b) elasticity, shear, compression, torsion. (b) ensuring optimum expansion at nozzle exit. (c) tension, compression, torsion, shear. (c) increasing altitude. (d) compression, buckling, elasticity, shear. (d) all of the above. 444 Appendix E: Multiple Choice Questions in Aerospace Engineering

92. In vacuum, the maximum exit velocity (ve)max depends (a) increases. on which of the following? (b) decreases. (c) first increases then decreases. (a) area ratio Ae (d) none of the above. At (b) pressure ratio pe p0 99. Which of the following fuel/oxidizer combinations is (c) mass flow rate m˚ hypergolic? (d) combustion chamber temperature (Tc) (a) hydrazine (N2H4) and di–nitrogen tetraoxide 93. A convergent–divergent nozzle is said to be choked when (N2O4) (b) RP–1 and LOX (a) Pressure at the exit is equal to ambient pressure (c) hydrazine (N2H4) and LOX = (pe pa). (d) none of the above (b) Area Ratio is maximized for optimum expansion. (c) Pressure at some point in the nozzle equals Critical 100. Consider the following statements: Pressure (p = p∗). I. Frozen flow in nozzle is isentropic. (d) Nozzle operates shock-free. II. Equilibrium flow in nozzle is isentropic.

94. The famous TACHOMA suspension bridge failed due to (a) Only I is TRUE. (b)OnlyIIisTRUE. (a) divergence (c) Both I and II are TRUE. (b) ﬂutter (d) Both I and II are FALSE. (c) vibration (d) fatigue 101. For overexpanded nozzle, pressure equalization takes place through 95. Total temperature across a Normal shock wave (a) normal shock wave (a) increases. (b) subsonic diffusion (b) decreases. (c) both (a) and (b) (c) remains the same. (d) when exit pressure is equal to the ambient pressure (d) ﬁrst decreases, then increases. (pe = pa)

96. Mass ﬂow rate is dependent on which of the following? 102. Which of the following factor affects Creep? (a) pressure ratio pe (a) the duration of the load applied p0 (b) combustion chamber temperature (Tc) (b) buckling of the material (c) molecular weight of combustion gases (c) shear (d) all of the above (d) strength of the material

97. Consider the following statements: 103. The construction of an aircraft wing is centered on a I. Aerodynamic heating can take place in space. main member. The member is II. Design of airframes at room temperature is adequate for development of missiles. (a) skin III. Infrared heating using IR lamps are commonly used (b) rib for thermo-structural testing. (c) frame Which of the above statements is/are true? (d) spar ( ) (a) only I 104. The torsion constant J of a thin-walled closed tube of ( ) ( ) (b) I and II thickness t and mean radius r is given by (c) only III (a) J = 2πrt3 (d) all of the above (b) J = 2πr3t = π 2 2 98. As ﬂight Mach number increases, TSFC of Ramjet (c) J 2 r t = π 4 Engine (d) J 2 r Appendix E: Multiple Choice Questions in Aerospace Engineering 445

105. The number of independent elastic constants in the con- I. At this Mach number, the aerodynamics drag on an stitutive equations of a generalized anisotropic solid is airfoil begins to increase rapidly.

(a) 2 II. At this Mach number, the aerodynamics drag on an (b) 9 airfoil begins to decrease rapidly. (c) 21 (d) 36 III. This is always greater than critical Mach number.

106. In an impulse turbine, the degree of reaction is IV.The large increase in drag is caused by the formation of a shock wave on the upper surface of the airfoil. (a) 1 (b) 0.75 Which of the above is/are CORRECT? (c) 0 (d) 0.5 (a) I and IV (b) II and IV 107. A column of length l and ﬂexural rigidity EI has both (c) II, III, and IV ends ﬁxed. The critical buckling load for the column is (d) I, III, and IV π2 (a) EI (0.7l)2 111. Consider the following statements: π2 (b) EI (0.5l)2 π2 I. The velocity of a satellite in a circular orbit depends (c) EI (l)2 on altitude of the satellite from Earth’s surface. π2 (d) EI (2l)2 II. In an elliptical orbit, the velocity of a satellite at 108. Consider the following statements: apogee is lesser than that at perigee.

I. Airy stress function can be used only for two- III. Eccentricity of an elliptical orbit determines the dimensional problems. shape of the ellipse.

II. Euler’s equations can be applied for viscous ﬂows IV. Geosynchronous satellite has an orbital time period as well. of 24 hrs.

III. In Schlieren flow visualization, the optical refrac- Choose correct answer from the following: tive index is sensitive to the second-order derivative of the flow density. (a) I and II (b) I, II, and III Which of the above is/are CORRECT? (c) I, III, and IV (d) all (a) I only (b) I and II only 112. Steady flow occurs when (c) all (d) none (a) Pressure does not change along the flow. (b) Velocity does not change. 109. Which is the point on the airfoil about which pitching (c) Conditions change gradually with time. moment coefficient is not a function of angle of attack? (d) Conditions do not change with time at any point.

(a) aerodynamic center 113. The ﬂuid forces considered in the Navier Stokes equa- (b) center of pressure tion are (c) center of gravity (d) leading edge of airfoil (a) gravity, pressure, and viscous. (b) gravity, pressure, and turbulent. 110. Consider the following statements about Drag diver- (c) pressure, viscous, and turbulent. gence Mach number: (d) gravity, viscous, and turbulent. 446 Appendix E: Multiple Choice Questions in Aerospace Engineering

114. Which one of the following statements is FALSE for a (a) 5 × 105 supersonic flow? (b) 2300 (c) 1.66 × 105 (a) Over agradual expansion, entropyremains constant. (d) 200 (b) Over asharpexpansioncorner, entropycanincrease. (c) Over a gradual compression, entropy may remain 121. In a low-speed wind tunnel, the honeycomb and wire- constant. gauze structures are used because (d) Over asharpcompressioncorner, entropyincreases. (a) Honeycomb reduces more lateral turbulence, while 115. The existence of a boundary layer near a solid surface wire-gauze reduces more axial turbulence. was first proposed by (b) Honeycomb reduces more axial turbulence, while wire-gauze reduces more lateral turbulence. (a) Ludwig Prandtl (c) Both honeycomb and wire-gauze reduces mostly (b) Theodore von Karman axial turbulence. (c) Albert Einstein (d) Both honeycomb and wire-gauze reduces mostly (d) Isaac Newton lateral turbulence. 116. According to the boundary layer theory, the flow field 122. The continuity equation outside a boundary layer is

(a) viscous (a) Expresses relationship between hydraulic parame- (b) inviscid ters of flow. (c) can be inviscid or viscous (b) Expresses the relationship, between work and (d) none of the above energy. (c) Is based on Bernoulli’s theorem. 117. For a flow around a stagnation point, the boundary layer (d) Relates the mass rate of flow along a streamline. thickness perpendicular to the flow direction 123. Which of the following is true? (a) grows. (a) Induced drag ∝ 1 (b) decreases. (EAS)2 (c) remains constant. (b) Induced drag ∝ (EAS)2 (d) first increases and then decreases. (c) Induced drag ∝ √ 1 √EAS (d) Induced drag ∝ EAS 118. If n is the degree of freedom of the gas molecules, then the ratio of specific heats will be 124. Consider the following statements: γ = n+4 I. A perfect gas must be both thermally and calorically (a) n γ = n−2 perfect. (b) n + II. A calorically perfect gas must be thermally perfect. (c) γ = n 2 n III. A thermal perfect gas must be calorically perfect. (d) γ = n n+2 Which of the following is true? 119. Consider the following: (a) I only I. concept of pathline (b) I and II II. concept of streakline (c) I and III III. concept of streamline (d) all Which of the above concepts are REAL in nature? 125. The region of speed instability is (a) I only (b) I and II (a) The same as the region of reverse command. (c) II and III (b) The region in which manual control is not possible. (d) I and III (c) At speeds below the low buffet speed. (d) The region above the thrust available and drag curve 120. In a cross-flow situation for a pipe flow, based on intersection. cylinder diameter, what is the typical value of critical Reynolds number? Appendix E: Multiple Choice Questions in Aerospace Engineering 447

p02 126. Choose the CORRECT relation between flow Mach (b) p ∗ 01− number (M) and characteristics Mach number (M ), p2 p1 (c) p defined as ratio of local flow speed and critical speed of −1 (d) p2 p1 sound: p2 133. Which of the following does not fall under solid rocket (a) If M →∞then M∗ →∞ ∗ propellant group? (b) If M →∞then M → 0 γ+ (c) If M →∞then M∗ −→ 1 γ−1 (a) double base ∗ γ− (b) cast modified double base (d) If M →∞then M −→ 1 γ+1 (c) bipropellant 127. At a constant mass and altitude a decreased airspeed (d) composite propellant requires: 134. A constant headwind component: (a) a higher C . L (a) increases the angle of climb path (b) less thrust and a lower C . L (b) increases the maximum rate of climb (c) more thrust and a lower C . L (c) decreases the angle of climb path (d) more thrust and a lower C . D (d) increases the maximum endurance 128. The temperature of a gas is produced due to 135. If an aircraft is put into a 2g turn from level flight, main- (a) kinetic energy of molecules taining a constant speed: (b) the heating value of gas (a) C will be increased by four times and C will be (c) cohesive and adhesive forces among the gas L D doubled. molecules (b) C will be doubled C will be increased by four (d) surface tension of molecules L D times. 129. The most efficient methods of compressing the gas (c) CL will be doubled and C√D will be doubled. and maximum work done on the gas are ______, (d) CL will be increased by 2 times, and CD will be respectively. increased by four times.

(a) adiabatic and isothermal 136. Which of the following will increase the takeoff dis- (b) isentropic and polytropic tance? (c) isothermal and adiabatic (a) Downhill slope because of decreased angle of (d) isothermal and polytropic attack. 130. Which of the following compressors are used in air- (b) Slush. craft? (c) Headwind due to increased drag. (d) Decreased takeoff mass. (a) radial flow compressors (b) centrifugal 137. For a light engine airplane the carriage of an additional (c) axial flow passenger will cause the climb performance to be: (d) combination of above (a) degraded 131. The buckling load for a given material depends on (b) improved (c) unchanged (a) Slenderness ratio and area of cross section. (d) unchanged if a short-field takeoff technique is used (b) Poisson’s ratio and modulus of elasticity. ( > ) (c) Slenderness ratio and modulus of elasticity. 138. In a Hypersonic flow M 5 past a wedge (ver- θ (d) Slenderness ratio, area of cross section, and modu- tex angle, 2 ), the hypersonic similarity parameter is lus of elasticity. defined as: 2θ 132. The strength of a normal shock is defined as (a) M M2 (b) θ (a) p01 (c) Mθ p02 M (d) θ 448 Appendix E: Multiple Choice Questions in Aerospace Engineering

139. For a perfect gas, the supersonic flow becomes a sub- 144. If Mcr is critical Mach number and, MDD is drag diver- sonic flow across a normal shock wave. This is, in accor- gence Mach number then which of the following is dance with which of the following law of thermodynam- TRUE for an airfoil kept in a subsonic flow? ics? (a) MDD < Mcr < 1.0 (a) zeroth law (b) Mcr < MDD < 1.0 (b) first law (c) 1.0 < Mcr < MDD (c) second law (d) MDD < 1.0 < Mcr (d) third law 145. For a propeller-driven airplane, choose the CORRECT 140. The free molecular flow is the regime in which the from the following: fluid molecules are so widely dispersed that the inter- R molecular forces can be neglected. This situation is best (a) At absolute ceiling the maximum rate of climb C described by which of the following range of Knudsen of airplane is maximum. R number (Kn)? (b) At service ceiling the maximum rate of climb C of airplane is maximum. < . R (a) Kn 0 01 (c) At absolute ceiling the maximum rate of climb C (b) 0.01 < Kn < 0.1 of airplane is zero. . < < R (c) 0 1 Kn 5 (d) At service ceiling the maximum rate of climb C (d) Kn > 5 of airplane is 0.05 ms−1.

141. Consider the following statements with respect to vis- 146. A low pressure altitude at an airport causes cous flow past a full length aircraft and its model: I. The geometrically similar flows must be dynamically (a) improved takeoff and degraded climb characteris- similar. tics. II. The dynamically similar flows must be geometrically (b) degraded takeoff and climb characteristics. similar. (c) degraded takeoff and improved climb characteris- Which of the above is true? tics. (d) improved takeoff and climb characteristics. (a) I (b) II 147. If T represents thrust and v represents the velocity, and (c) I and II (d) none I. Trequired − Tavailable = 0 ∂( − ) Trequired Tavailable = 142. For the flow over a flat plate, the turbulent boundary II. ∂v 0 layer thickness can be expressed as Which of the following is true? δ 5 (a) = / x Re1 2 x (a) I δ = 5 (b) x 1/2 Rex (b) II δ = 0.16 (c) I and II (c) x 1/7 Rex (d) none δ = 0.16 (d) x 1/2 Rex 148. If the drag polar of a propeller aircraft is = + 2 < γ < π 143. “The circulation of a vortex tube remains constant in CD CD0 KCL, for a given climb angle 0 2 time”. Which of the following Helmholtz’s theorem and with shallow climb approximation, the maximum describes this? climb rate represents (a) first vortex theorem 2CD0 (a) CL = (b) second vortex theorem K 3C = D0 (c) third vortex theorem (b) CL K (d) fourth vortex theorem = (c) CL 3CD0 K = (d) CL 2CD0 K Appendix E: Multiple Choice Questions in Aerospace Engineering 449 2 149. With reference to gliding flight, considering the exact u (a) Cp =−2 form of dynamical equations the flattest glide occurs Ua (b) C =−2 Ua when p u 2 Ua (c) Cp =−2 2 u = 4 Emax (a) u 2 + u Emax 1 (d) C =−2 p Ua 2 + = 4 Emax 1 (b) u 2 Emax 155. In the wind tunnel operation, which of the following is 2 = 4 Emax FALSE? (c) u 2 − Emax 1 2 + (a) The normal shock in the test section owes to about = 4 Emax 1 (d) u 2 − Emax 1 80% of the total power requirements in supersonic wind tunnels. 150. If ρ is the measured density around the airplane, and (b) Pitot probe does not measure the actual freestream ρSL is the standard sea level density then which of the stagnation pressure in the test section of supersonic following is TRUE for airspeeds of an airplane? wind tunnels. (c) The starting load is less than the Running load in ρ (a) Vtrue = Vequivalent ρ supersonic wind tunnels. SL ρ (d) In the subsonic wind tunnel the test-section walls (b) Vequivalent = Vtrue ρ √SL √ should not be made parallel but divergent. = ρ × ρ (c) Vequivalent Vtrue SL ρ (d) Vtrue = Vequivalent ρ 156. A low wing and a high wing configuration aircraft are SL identical to each other in all respects except the loca- 151. Generally for closed throat wind tunnels the energy ratio tion of the wing. The longitudinal static stability of the (ER) will be airplane with high wing configuration will be:

(a) ER < 3 (a) More than the airplane with low wing configuration. (b) 2 < ER < 5 (b) Less than the airplane with low wing configuration. (c) 3< ER <7 (c) Same as the airplane with low wing configuration. (d) always greater than 5 (d) More if the elevator is deflected.

152. In the wind tunnel operation, if Re is the effective 157. Let an airplane in a steady level flight be trimmed at a Reynolds number and Rec is the measured Reynolds certain speed. A level and steady flight at higher speed number then Turbulence Factor is defined as could be achieved by changing

(a) Re (a) engine throttle only Rec Rec (b) elevator only (b) Re 2 (c) throttle and elevator together (c) Re × Rec × 2 (d) rudder only (d) Re Rec

153. In both intermittent and blowdown supersonic wind 158. The effect of propeller on the longitudinal static stability tunnel operations, the axial flow compressors is used of the aircraft is to because of (a) increase longitudinal static stability. (a) High pressure ratio and large mass flow rate. (b) decrease longitudinal static stability. (b) High pressure ratio and small mass flow rate. (c) longitudinal static stability remains same. (c) Low pressure ratio and small mass flow rate. (d) longitudinal static stability is minimum. (d) It has small power requirements. 159. If the center of gravity of an airplane is moved forward toward the nose of the airplane, the CL,max (maximum 154. If u is perturbation velocity and Ua is freestream velocity. Using small perturbation theory the pressure coef- value of the lift coefficient) value for which the aircraft ( = ) ficient in two-dimensional planar flows will be can be trimmed Cm 0 will be 450 Appendix E: Multiple Choice Questions in Aerospace Engineering

(a) decreased. (b) Isentropic flows only. (b) increased. (c) Adiabatic flows whether reversible or irreversible. (c) remains the same. (d) Defined only for Mach numbers greater than one. (d) depend upon the rudder deflection. 166. For a given gas, the maximum mass flow rate per unit m˚ max 160. If the contribution of only the horizontal tail of an air- area A is directly proportional to ∂Cm plane was considered for estimating ∂α , and if the tail moment arm lt was doubled, then how many times the √T0 ∂ (a) original value would the new Cm , become P0 ∂α (b) √P0 √T0 (a) 1.414 times (c) T0 P2 (b) 1.732 times (d) √ 0 (c) 2 times T0 (d) 3 times 167. The flow across a non-isentropic compression front can be made isentropic flow by optimizing the entropy gen- 161. If the vertical tail of an airplane is inverted and put below eration (S) and flow deflection angle (θ) across the horizontal tail, the contribution to roll derivative, the compression front. The approximate linear relation ∂CL ∂β will be holds for this is

(a) negative (a) S ∝ θ (b) positive (b) S ∝ (θ)3 (c) zero ∝ 1 (c) S 3 (d) imaginary (θ) ∝ 1 (d) S (θ)4 162. PHUGOID motion can be excited by giving an initial disturbance in 168. The Joukowski airfoil is studied in aerodynamics because (a) Speed only. (b) By any one or both of the Elevator deflection and (a) It has a simple geometry. Speed. (b) It is used in many aircraft during World War II. (c) By any one or both of the Elevator deflection and (c) It is easily transformed into circle, mathematically. Angle of attack. (d) It has highest lift curve slope among all airfoils. (d) By any one or all of the Speed, Elevator deflection, 169. Consider a pin supported rod of length L, with E as and Angle of attack. Young’s modulus and I is the area moment of inertia 163. Spiral divergence arises because of then the critical load at which the rod buckles is π3 (a) EI (a) high directional and low roll stability. 2L2 π2 (b) high roll and low directional stability. (b) EI L3 π2 (c) high roll and high yaw stability. (c) EI L2 (d) low roll and low yaw stability. π3 (d) EI L2 164. If the aircraft wing has an Anhedral of then the local 170. A supercritical airfoil has angle of attack (αl) on the starboard side and the port side are given by (a) higher wave drag. (b) higher critical Reynolds number. (a) αl = α ± β (c) higher critical Mach number. (b) αl = α ∓ β β (d) higher drag divergence Mach number. (c) αl = α ± α = α ± (d) l β 171. A uniform beam of length L, is simply supported at its ends and carries a uniformly distributed load of w 165. The ratio of stagnation and static temperature is defined (γ− ) per unit length between mid-span and a point from the as T0 = 1 + 1 M2 this relation holds for T 2 right hand end. An expression for the deflection at the (a) Adiabatic flows only. mid-span is Appendix E: Multiple Choice Questions in Aerospace Engineering 451

= 19wL4 (a) y 4096EI (d) It cannot be predicted. 4 (b) y = 29wL 384EI 177. In a steady state, the Bernoulli’s equation is applicable = 19wL4 (c) y 384EI in which of the following situation? 4 (d) y = wL 4096EI (a) Between any two points in both inviscid and potential flows. 172. Consider the following statements: (b) Between any two points in inviscid flow and only I. A geostationary orbit can be geosynchronous, but along a streamline in potential flow. not all geosynchronous orbits are geostationary. (c) Only along a streamline in both inviscid and poten- II. An orbit can be both in a Sun-synchronous orbit and tial flows. in a repeat orbit at the same time. (d) Only along a streamline in inviscid flow and between any two points in potential flow. Choose the CORRECT from the following: 178. For the maximum propulsive efficiency, the ratio of (a) I flight speed to the nozzle exhaust velocity is (b) II (c) I and II (a) 0.5 (d) none (b) 1.0 (c) 2.0 173. Which of the following criteria leads to maximum turn (d) 4.0 rate and minimum radius in a level turn flight? 179. The skin and spar-webs are used in semimonocoque (a) Highest possible load factor and highest possible wing configurations because they are the primary car- velocity. riers of: (b) Lowest possible load factor and lowest possible velocity. (a) Shear stresses due to an aerodynamics moment (c) Highest possible load factor and lowest possible component alone. velocity. (b) Normal stresses due aerodynamics forces alone. (d) Lowest possible load factor and highest possible (c) Shear stresses due aerodynamics forces alone. velocity. (d) Shear stresses due aerodynamics forces and a moment component. 174. Which of the following input is required to produce constant roll rate using ailerons in an aircraft? 180. In the closed-circuit supersonic wind tunnel, the convergent–divergent nozzle and test section are (a) a step input attached with convergent–divergent diffuser to swal- (b) an impulse input low the stalling normal shock. The condition which (c) a ramp input must be met is (d) a sinusoidal input (a) The diffuser throat area must be larger than nozzle 175. The Hohmann ellipse used as Earth–Mars transfer orbit throat area and shock must be standing downstream has of diffuser throat. (a) apogee at Earth and perigee at Mars. (b) The diffuser throat area must be smaller than nozzle (b) both apogee and perigee at Earth. throat area and shock must be standing downstream (c) apogee at Mars and Perigee at Earth. of diffuser throat. (d) both apogee and perigee at Mars. (c) The diffuser throat area must be same as the nozzle throat area and shock must be standing upstream of 176. An aircraft in a steady climb suddenly experiences a diffuser throat. 10% drop in thrust. After a new equilibrium is reached (d) The diffuser throat area must be smaller than nozzle at the same speed, the new rate of climb is? throat area and shock must be standing upstream of diffuser throat. (a) Lower by exactly by 10%. (b) Lower by more than 10%. 181. The effect of increasing the internal pressure on the (c) Lower by less than 10%. buckling of the fuselage skin is 452 Appendix E: Multiple Choice Questions in Aerospace Engineering

(a) It is delayed. 187. In the combustion chamber an efficient fuel injection (b) It is advanced. system is required because (c) It remains the same. (d) Insufficient data to predict. (a) It increases the fuel flow rate in the combustion chamber. 182. The process in which there is only work interaction (b) It increases the airflow rate in the combustion cham- between the system and its surroundings is ber. (c) It sprays the fuel in the form of small droplets. (a) iIsothermal process (d) It acts as an igniter in initiating the combustion. (b) diabatic process (c) quasi-static process 188. An aircraft is flying at Mach 2, where the ambient tem- (d) adiabatic process perature is found to be 200K. What is the stagnation temperature on the surface of the aircraft? (Assume the 183. An oblique shock wave with a wave angle β is generated specific heat ratio of air to be 1.4) from a wedge angle of θ. The ratio of the Mach number downstream of the shock to its normal component is (a) 300 (b) 360 (a) sin (β − θ) (c) 375 (b) cos (β − θ) (d) 400 (c) sin (θ − β) (d) cos (θ − β) 189. In choosing materials for structural members of an aircraft, there is most often a trade-off between which of 184. According to Euler–Bernoulli beam theory, the nature the following characteristics? of the governing equation for the static transverse deflection of a beam under a uniformly distributed load (a) strength and weight is (b) plasticity and weight (c) strength and elasticity (a) Second-order linear homogeneous partial differen- (d) plasticity and elasticity tial equation. (b) Fourth-order linear nonhomogeneous ordinary dif- 190. In the cantilever shown in Fig.E.1, what type of force ferential equation. is being applied to the wall at point A? (c) Second-order linear nonhomogeneous ordinary differential equation. (a) compression (d) Fourth-order nonlinear homogeneous ordinary dif- (b) tension ferential equation. (c) shear (d) torsion 185. Consider a spring–mass system. If a mass of 1 kg is attached the spring elongates by 16 mm. The mass 191. Sometimes wrinkles are formed on webs. The reason is pulled by 10 mm and then released from rest. of wrinkle formation is The response of the mass in mm is given by. g = 9.81ms−2 (a) tensile principal stress. (b) compressive principal stress. (a) x = 10 cos (24.76t) (c) buckling of thin sheet of web. (b) x = 10 cos (16t) (d) fatigue in the webs. (c) x = 10 sin (24.76t) (d) x = 10 sin (16t) 192. Consider Fig. E.2. Assuming the same wedge angles (θ),ifM1 > M2 then for shock angles β1 and β2, which 186. If an axial flow turbine is operating at high temperature of the following is true? then which of the following material is suitable for its construction? (a) β1 > β2 (b) β1 < β2 (a) nickel alloy (c) β1 = β2 (b) steel alloy (d) cannot say (c) titanium alloy (d) aluminum alloy Appendix E: Multiple Choice Questions in Aerospace Engineering 453

Fig. E.1 Cantilever beam

β M >> 1β M >> 1 1 1 2 2

Fig. E.2 Oblique shocks on diamond airfoil

r r

t t

Fig. E.3 Thin-walled tubes

193. The presence of carbon monoxide in the combustion The ratio of torsional rigidity of thin-walled closed tube products means to thin-walled open tube is (a) high excess air (a) 2 r 2 t (b) poor combustion (b) 3 r 2 (c) high thermal efﬁciency t (c) r 2 (d) all of the above t r 3 (d) 4 t 194. Consider the following thin-walled tubes shown in Fig. E.3. 195. Consider a simply supported beam of length L, shown in Fig. E.4. 454 Appendix E: Multiple Choice Questions in Aerospace Engineering

M L/2

Fig. E.4 Simply supported beam

A counterclockwise concentrated bending moment M, 199. In scramjet, the ﬂow at entry to the combustion cham- is applied at mid-span of the beam. The shear force ber is diagram of the beam is (a) stagnant (M = 0)

(a) (b) 1 2 1 2

(d) (c) 12 12

196. Under uniformly distributed load, the shape of a can- (b) low subsonic (M < 0.3) tilever beam will be: (c) supersonic (d) hypersonic (a) straight line (b) hyperbolic 200. In a centrifugal compressor, the stagnation pressure rise (c) parabolic takes place (d) elliptical (a) in the diffuser only. 197. The overall efficiency of a rocket will be maximum, (b) in the impeller only. when aircraft velocity is the exhaust jet velocity. (c) in the inlet guide vanes only. (d) in the diffuser and impeller. (a) equal to (b) one-half 201. In the wind tunnel experiments, a pitot-static probe (c) double measures (d) four times (a) static pressure (λ) 198. Let the slenderness ratio of a column is defined (b) stagnation pressure in terms of effective length and minimum radius of (c) both static and stagnation pressures λ gyration. The range of , for Euler’s crippling load for- (d) absolute pressure mula is 202. The benefits of thin wing design are (a) λ ≤ 12 λ ≤ (b) 30 (a) Reduced shock stall effect. < λ ≤ (c) 30 80 (b) Reduced low-speed stall effects. (d) λ > 80 Appendix E: Multiple Choice Questions in Aerospace Engineering 455

(d) Reduced Mach angle. coefficient Cd1 . The circular cylinder is then mounted on a device called external balance which holds it from 203. An aircraft moving at supersonic Mach numbers dis- outside the test section and can measure all the forces turbs the airstream acting on it when the tunnel is running. From the read- ing of the balance the drag coefficient is obtained as (a) behind the Mach lines. Cd2 . The two drag coefficient values obtained from the (b) on both sides of the Mach lines. two separate measurements can be compared as follows (c) ahead of the Mach lines. (d) beyond the ends of the Mach lines. = (a) Cd1 Cd2 > (b) Cd1 Cd2 204. The pressure gradient normal to the body surface of a (c) Cd1 2Cd2 boundary layer flow is (d) Cd2 2Cd1

(a) negative 208. Which of the following statement is TRUE about the (b) positive steady flow of a fluid in a streamtube? (c) zero (d) constant (a) Mass flow is conserved. (b) The speed increases if the cross-sectional area 205. Under adverse pressure gradient a viscous flow can be increases. assisted to remain attached to the boundary by (c) The density must be constant. (d) The pressure must be constant. (a) Moving the boundary tangential to the flow and along flow direction. 209. Spoilers can also be used to assist (b) Vibrating the boundary normal to the flow direction. (c) Moving the boundary tangential to the flow and (a) flaps opposite to the flow direction. (b) ailerons (d) Injecting high momentum fluid into the flow tan- (c) slats gentially. (d) rudder

206. If is Young’s modulus of elasticity (E) is the shear 210. The difference between air-breathing engine and rocket modulus (G) is the bulk modulus of elasticity (K) and engine are is the Poisson’s ratio (ν) then for isotropic materials consider the following: (a) There is altitude limit. (b) There is temperature limit. = E I. G 2(1+ν) (c) Atmospheric air is used for formation of the jet. (d) All of the above. = E II. G 3(1−ν) 211. It is better to operate a centrifugal compressor with = E respect to mass ﬂow rate III. K 3(1−2ν)

E (a) Close to the surge line. IV. K = ( − ν) 1 2 (b) Left side of the surge line. Which of the above are CORRECT? (c) Right side of the surge line. (d) Both at left and right side of the surge line. (a) I and IV (b) I and III 212. Which of the following propellants has highest speciﬁc (c) II and III impulse? (d) II and IV (a) Powdered Al + Ammonium Perchlorate. ( ) + 207. A circular cylinder is mounted in the test section of (b) Monomethyl Hydrazine MMH Nitrogen ( ) a low-speed wind tunnel. The pressure distribution Tetroxide N2O4 . ( ) + ( ) around it is measured when the tunnel is running. (c) Liquid Hydrogen LH2 Liquid Oxygen LOX . (d) Kerosene + Liquid Oxygen (LOX). 456 Appendix E: Multiple Choice Questions in Aerospace Engineering

213. Which of the following tend to increase the Dutch roll 219. The rocket travels upward from the launch pad, it gets tendency? continually easier to accelerate mainly because

(a) wings placed well above the center of mass. (a) the jet stream helps to push it. (b) sweep-back wings. (b) the rocket continually loses mass as fuel is burned. (c) dihedral wings. (c) the engines are more efﬁcient at higher altitude. (d) all of the above. (d) there is little gravity at higher altitude.

214. When the particles of a body or system move approxi- 220. If a hollow, circular torsion bar has a wall thickness (t) mately perpendicular to the axis of the body the vibra- and a mean radius of (r) then its polar moment of inertia tionissaidtobe (J) will be (a) longitudinal vibrations. (a) 2πr3t 1 + t 2r 2 (b) undamped vibrations. (b) 2πr3t 1 + t (c) torsional vibrations. 2r 3 t 2 (d) lateral or transverse vibrations. (c) 2πr t 1 − 2r 4 (d) 2πr3t 1 + t 215. If the Airy’s stress function φ = Ay2 + Bxy, the normal 2r stress σ is yy 221. The conditions that determine aerodynamic ceiling are (a) 0 (a) When thrust available is equal to the thrust required. (b) 2A (b) When power available is equal to the power (c) −2A required. (d) B (c) When the high-speed buffet and low-speed buffet 216. The ratio of maximum shear stress to average shear are equal. stress of a circular beam is (d) All three of the above.

2 222. In the following list, identify the monopropellant (a) 3 3 (b) 2 (a) Hydrogen peroxide 3 (b) Hydrazine (c) 4 (c) Mono methyl Hydrazine (d) 4 3 (d) Dimethyl Hydrazine

217. Due to downwash, the nature of the lift distribution over 223. The ratio of maximum adiabatic ﬂame temperature in wings of an aircraft is air to the maximum adiabatic temperature in pure oxygen, is always (a) equal throughout (b) parabolic (a) equal to one (c) elliptical (b) much less than one (d) hyperbolic (c) much greater than one (d) uncertain 218. Consider the following statements: I. A geostationary orbit can be geosynchronous, but not 224. In a shock tube, the driver gas should have all geosynchronous orbits are geostationary. II. An orbit can be both in a Sun-synchronous orbit and (a) Low molecular weight at low temperature. in a repeat orbit at the same time. (b) High molecular weight at low temperature. Choose the CORRECT from the following: (c) High molecular weight at high temperature. (d) Low molecular weight at high temperature. (a) I 225. The hypersonic reentry capsules have a blunt leading (b) II edge because of (c) I and II (d) none (a) aerodynamic heating. Appendix E: Multiple Choice Questions in Aerospace Engineering 457

1 (b) aerobraking. (c) √T (c) payload consideration. (d) T (d) more structural strength as compared to aerodynamic shape. 231. When compared to turboprop, turbojet engines are characterized by handling 226. Flow across a curved shock wave is (a) high mass of air at low velocity. (a) irrotational (b) high mass of air at high velocity. (b) incompressible (c) low mass of air at high velocity. (c) one-dimensional (d) low mass of air at low velocity. (d) none of the above 232. Modern ﬁghter class engines belong to which of the 227. Time history is required for the analysis of following category?

(a) lateral stability (a) turbojet engines. (b) longitudinal stability (b) low bypass turbofan engines. (c) static stability (c) high-bypass turbofan engines. (d) dynamic stability (d) turboshaft engines.

228. Consider the following statements for a chocked nozzle 233. A typical propeller aircraft is performing a climb in the flow: international standard atmosphere at constant equiva- I. The nozzle must be a supersonic one lent airspeed and with the maximum power setting. The II. Critical condition exists at the nozzle throat power available of this aircraft can be assumed indepen- III. Flow inside the nozzle must be isentropic dent of airspeed and decreases with altitude according IV. There is no heat transfer from the hot flowing gases to the following relation to the wall Which of the above is/are TRUE? ρ 0.72 Pa,max= Pa,max(sealevel) ρ0 (a) I (b) II It can be said that the aircraft is performing a flight. (c) I, II, and III (d) I, II, and IV (a) straight (quasi-rectilinear) and steady (b) straight (quasi-rectilinear) and unsteady 229. Consider the following two statements: (c) curved and steady I. Separation system is a part of Liquid Propellant (d) curved and unsteady Rocket Propulsion system. II. In solid propellant “grain” contains all the chemical 234. To describe the motion of an airplane, four coordinate elements for complete burning. systems are used. In order to describe the attitude of an Which of the above is/are CORRECT? airplane (body axes), with respect to the moving Earth axis system, three Euler angles are used. The sequence (a) I in which these angles are used is very important. The (b) II correct sequence of these angles to obtain the orienta- (c) Both I and II tion of the body axes, starting from the moving Earth (d) none axes is

230. With all other things remaining constant and with T (a) angle of pitch (θ), angle of roll (φ), angle of yaw the outside static air temperature expressed in Kelvin, (ψ). the speciﬁc fuel consumption of a turbojet powered air- (b) angle of pitch (θ), angle of yaw (ψ), angle of roll plane in a constant Mach number cruise in still air is (φ). proportional to (c) angle of yaw (ψ), angle of roll (φ), angle of pitch (θ). (a) T (d) angle of yaw (ψ), angle of pitch (θ), angle of roll (b) 1 T2 (φ). 458 Appendix E: Multiple Choice Questions in Aerospace Engineering

235. A pilot wants to perform a steady coordinated turn. The 240. Which of the following statement related to the “snow- pilot initiates the turn by banking the aircraft. After ball effect” with respect to an aircraft is correct? banking the aircraft the pilot must (a) By reducing the empty weight of the aircraft more (a) increase the pitch attitude. payloads can be transported or the range can be (b) increase the thrust. increased. (c) decrease the thrust. (b) Reducing the structural weight of an aircraft, (d) increase the pitch attitude and the thrust. additional weight reductions due to the “snowball effect” are also structural. 236. The decision airspeed is an important speed during take- (c) Once an initial weight reduction is achieved, all off. For a given multi-engine aircraft, this airspeed is other systems of the aircraft can be reduced in weight as well. (a) independent of the balanced field length. (d) Given a combination of fuel and payload, an initial (b) a function of weight, altitude, and temperature. weight reduction induces extra weight reductions. (c) a function of aircraft weight. (d) generally much higher than the rotation speed. 241. To limit the wing bending, which of the following solution should be applied? 237. Lift dumpers are used to reduce the landing ground run distance (a) A high strength material as the skin material of the wing. (a) By decreasing lift on the wing, this makes it easier (b) A high strength material as the web plate material for the pilot to put the aircraft on the ground. for the spars. (b) By decreasing lift on the wing, this creates a larger (c) A high stiffness material as the skin material of the normal force on the wheels and thus a larger ground wing. drag when applying brakes. (d) A high stiffness material as the web material for the (c) By disturbing the airflow on the wing, this creates ribs. a lot of turbulence and thus aerodynamic drag. (d) By increasing lift on the wing, this makes it easier 242. The efficiency of a jet engine is higher at for the pilot to put the aircraft on the ground. (a) low altitudes 238. Which of the following statements about material and (b) high altitudes structural properties are true? (c) high speeds (d) low speeds (a) The material properties and structural properties are identical. 243. Only rocket engines can be propelled to space because (b) The material properties and structural properties are complementary. (a) They can generate very high thrust. (c) Structural properties depend on material properties (b) They have high propulsion efficiency. and geometrical features. (c) These engines can work on many fuels. (d) Material properties are much more important than (d) They are not air-breathing engines. structural properties. 244. The thrust of a jet propulsion power unit can be 239. Even though the first metal aircraft appeared in early increased by 1930s, the real problems with metal fatigue showed up about 20 years later. What is the reason for this time (a) injecting ammonia into the combustion chamber. difference? (b) burning fuel after gas turbine. (c) injecting water into the compressor. (a) It takes quite some time to initiate and grow a (d) all of the above. fatigue crack to a detectable size. (b) In the early 1950s aircraft flew at higher altitudes 245. A turboprop is preferred to turbojet because and had pressure cabins. (c) In the early 1950s the aircraft were much bigger (a) it can fly at supersonic Mach numbers. and much faster. (b) it can fly at high altitudes. (d) The metal alloys of the 1930s were not fatigue- (c) it has high power for takeoff. sensitive like the later ones. Appendix E: Multiple Choice Questions in Aerospace Engineering 459

(d) it has high propulsive efﬁciency at high Mach num- (c) III. The highest possible velocity. bers. (d) IV. The lowest possible velocity.

246. The degree of reaction is usually kept for all types Which of the following combination is TRUE? of axial flow compressors. (a) I and III (a) 0.4 (b) II and III (b) 0.3 (c) I and IV (c) 0.5 (d) II and IV (d) 0.2 252. For pull-up maneuvers, if n stands for load factor and Ua 247. Adding dihedral to a glider can improve its is the freestream velocity then, which of the following relation holds for turn radius R? (a) pitch stability 2 = Ua (b) roll stability (a) R g(n+1) (c) yaw stability U2 (b) R = a (d) static Stability g(n−1) (c) R = Ua g(n+1)2 3 248. At apogee, the centrifugal force is = Ua (d) R g(n−1) (a) less than the gravitational force. 253. For a given airfoil, which of the following relationship (b) more than the gravitational force. is BEST suited to represent the lift coefficient (CL)? (c) equal to the gravitational force. (d) not dependent on the gravitational force. (a) CL =(α) (b) C =(α, M , Re) 249. For the flow past a NACA 2315 airfoil, which of the L a (c) C =(M , Re) following relation is TRUE? L a (d) CL =(α, Re) 2 (a) Cd ∝ M∞ − 1 (where α is angle of attack, Ma is Mach number, Re is √ 1 (b) Cd ∝ the Reynolds number, and stands for function) (M∞2 −1) (c) C ∝ M2 − 1 254. For a given aircraft, consider the following statements: d ∞ ( ) 2 2 I. For a given lift coefficient CL , the drag coefficient (d) Cd ∝ M∞ − 1 (CD) is much larger at supersonic speeds than at sub- 250. For the maximum endurance of a jet-propelled airplane sonic speeds. ( ) consider the following statements? II. For a given lift coefficient CL , the drag coefficient ( ) I. Flying with maximum aerodynamic efficiency. CD is much smaller at supersonic speeds than at sub- II. Having the lowest possible thrust-specific fuel con- sonic speeds. III. The values of L at supersonic speeds are sumption. D max III. Having the highest possible thrust-specific fuel con- smaller than at subsonic speeds. IV.The values of L at supersonic speeds are larger sumption. D max IV. Carry a lot of fuel. than at subsonic speeds, Which one of the following is true? Which of the following is/are TRUE?

(a) I and II (a) I and III (b) I, II, and IV (b) I and IV (c) I, III, and IV (c) II and III (d) II and IV (d) II and IV

251. For an aircraft, to obtain the largest possible turn rate 255. Under which of the following condition, the free vibra- consider the following statements. tion of a linear spring–mass–dashpot system undergoes a non-oscillatory motion? (a) I. The highest possible load factor. (b) II. The lowest possible load factor. (a) undamped (b) underdamped 460 Appendix E: Multiple Choice Questions in Aerospace Engineering

(c) overdamped (a) vr = 4ve (d) critically damped (b) vr = ve = ve (c) vr 4 256. Which of the following airfoil will be appropriate in (d) vr = 2ve constructing the vertical tail of an aircraft?

262. In the flow across a normal shock, if M1 and M2 repre- (a) NACA 2-series positively cambered airfoil sent the Mach number upstream and downstream of the (b) symmetric airfoil shock, what is the asymptotic value of the downstream (c) negatively cambered airfoil Mach number for an ideal gas having γ = 1.4. (d) supercritical airfoil √ (a) √0.5 257. Compared to the monoplane, the biplane wing experi- (b) 0.14 ences a in the lift and a in the drag. 1 (c) √7 (d) 7 (a) increase, decrease (b) decrease, increase 263. Which of the following is not a characteristic of a NACA (c) increase, increase 5-digit airfoil? (d) decrease, decrease (a) Roughness has less effect. 258. If an elliptical wing has an aspect ratio (AR →∞), (b) Higher maximum lift coefficient. the value of lift curve slope will be approximately (c) Low pitching moment. equal to (d) High pitching moment. (a) ∞ 264. For a solid object subjected to the arbitrary loading, (b) 8 which of the following material properties will be con- (c) 5 stant irrespective of the loading? (d) 6 (a) specific volume only 259. Which of the following inequalities are true for an air- (b) density and elasticity craft engine cruising at subsonic velocity? (Intake, com- (c) mass only pressor, turbine, and nozzle efficiencies are denoted by (d) volume, mass, and density ηi, ηc, ηt, and ηn, respectively) 265. For a solid rod of circular cross section under torsional (a) η < η < η < η t c i n vibration, the boundary conditions are changed from (b) η < η < η < η c t i n fixed-free to fixed-fixed. The fundamental natural fre- (c) η < η < η < η i c t n quency is changed by a factor of (d) ηt < ηc < ηn < ηi (a) 2.0 260. At an altitude a 35,000 feet, a supersonic nozzle is π (b) designed to produce maximum thrust. At which alti- 2 (c) π tude, the nozzle will operate in underexpanded condi- (d) 1 tion? 2 266. For an axial compressor stage having the degree of reac- (a) 40,000 feet tion 0.5. Which of the following is NOT true? (b) near service ceiling (c) 35,000 feet (a) Velocity triangles at the entry and exit of the rotor (d) 34,000 feet are symmetrical. (b) The pressure drop is equally shared by the rotor and 261. Through a single impulse out-of-plane maneuver, a the stator. satellite is transferred from its geostationary orbit to a (c) The stator has a larger contribution to the total work circular polar orbit of same radius. The relation between extracted or work done. the magnitude of required velocity (v ) for orbit transfer r (d) The whirl components are same at the inlet of rotor in terms of magnitude of escape velocity (v ) is e and diffuser. Appendix E: Multiple Choice Questions in Aerospace Engineering 461

267. To obtain maximum sink rate, the glider must be oper- (c) I and IV are true. ated at (d) II and IV are true.

(a) maximum CL condition 273. The CREEP in a turbine blade is CD (b) minimum CL condition CD (a) pronounced more at increased heats near melting CL (c) minimum 3/2 condition CD point. CL (d) minimum / condition (b) independent of exposure time to thermal stresses. C1 2 D (c) a temporary deformation. 268. In airplanes, a step input at the rudder excites which (d) a sudden plastic deformation. dynamic mode of instability? 274. The construction of a fuselage in the modern aircrafts (a) phugoid are based on (b) dutch roll (a) monocoque design (c) spiral divergence (b) semimonocoque design (d) roll Subsidence (c) truss structure 269. Bernoulli’s equation is based on the assumption that (d) geodesic construction

(a) There is no loss of energy of the liquid flowing. 275. The negative Poisson ratio in a circular rod shows that (b) The velocity of flow is uniform across any cross the section of the pipe. (a) longitudinal strain increases when the lateral strain (c) No force except gravity acts on the fluid. decreases. (d) All of the above. (b) lateral and longitudinal strains are equal. 270. Which of the following is the necessary criterion for (c) lateral strain increases when the longitudinal strain stick fixed longitudinal balance and static stability? increases. (d) longitudinal strain decreases when the lateral strain (a) CM,cq at zero lift must be positive. increases. ∂CM,cq (b) ∂α must be positive (αa is absolute angle of a 276. The relation between Bulk modulus and Young’s mod- attack). ulus is (c) CM,cq at zero lift must be negative. α (d) Slope of CL versus a must be negative. = K (a) E (1−2ν) = K 271. The design characteristic that cannot improve the sta- (b) K (2+ν) = K bility of the roll subsidence is (c) E (2−ν) E (d) K = ( − ν) (a) high and dihedral angles. 1 2 (b) swept wing. 277. In a canard wing configuration, the position of the C.G. (c) low wing. is (d) high and anhedral wings. (a) far aft the wing and before the neutral point. 272. Which of the following are TRUE regarding service and (b) at 1 of the chord. 3rd absolute ceilings? (c) at 1 of the chord. 4th I. The rate of climb drops below a prescribed value in (d) at the neutral point. absolute ceiling. II. The rate of climb drops below a prescribed value in 278. The headwind or tailwind does not affect the service ceiling. III. The rate of climb drops to zero in absolute ceiling. (a) range of the aircraft. IV. The rate of climb drops to zero in service ceiling. (b) the takeoff distance. (c) endurance of the aircraft. (a) I and II are true. (d) the angle of glide. (b) II and III are true. 462 Appendix E: Multiple Choice Questions in Aerospace Engineering

279. The area under the flight envelope of an aircraft is 285. Euler’s equation in the differential form for the motion of liquids is given by (a) larger for general aviation aircraft. ∂p (b) larger for fighter aircraft. (a) ρ − gdz + vdv = 0 (c) same for all the aircraft types. (b) ρ∂p + gdz + vdv = 0 ∂p (d) not dependent on the load factor of the aircraft. (c) ρ + gdz + vdv = 0 (d) ρ∂p − gdz + vdv = 0 280. The value of bulk modulus of a fluid is required to determine 286. The square root of the ratio of inertia force to gravity force is called (a) Reynolds number (b) Mach number (a) Reynolds number (c) Froude number (b) Froude number (d) Prandtl number (c) Mach number (d) Euler number 281. For the maximum power transmission, what should be the diameter of the nozzle (d)? (where D = Diameter 287. Which of the following statement holds correct? of pipe, f = Darcy’s coefficient of friction for pipe, and L = Length of pipe). (a) In laminar flow, Newton’s law of viscosity does not apply. / 5 1 2 (a) d = D (b) A forced vortex occurs when fluid particles rotates 8fL 1/3 about its own axis. = D5 (b) d 8fL (c) In turbulent flow, there are neither crosscurrents nor / 5 1 4 eddies. (c) d = D 8fL (d) A free vortex occurs, when fluid particles rotates 1/5 = D5 about its own axis. (d) d 8fL 288. Consider the following statements: 282. The velocity profile of a turbulent flow through a closed I. Cruising phase of civil aviation flights takes place in conduit is TROPOSPHERE. (a) parabolic II. Cruising phase of civil aviation flights takes place in (b) hyperbolic STRATOSPHERE. (c) linear III. Entropy remains constant across Prandtl–Meyer (d) logarithmic expansion wave. IV. Static temperature increases across Prandtl–Meyer 283. At high Reynolds number, expansion wave. Which of the following is/are TRUE? (a) the inertial forces control and viscous forces are unimportant. (a) I, III, and IV (b) viscous forces are predominant. (b) II, III, and IV (c) inertial forces are unimportant and viscous forces (c) II and III control. (d) II and IV (d) both the inertial and viscous forces are predominant. 289. The Schlieren optical flow visualization technique is sensitive to changes in 284. The power loss in the flow through an orifice is the flow through a venturi tube having the same throat (a) fluid density. diameter. (b) first derivative of the fluid density. (c) second derivative of the fluid density. (a) same as (d) third derivative of the fluid density. (b) more than (c) less than 290. An ideal Ramjet is based upon which of the following (d) Insufficient data cycle? Appendix E: Multiple Choice Questions in Aerospace Engineering 463

(a) Brayton cycle (a) feed system (b) Carnot cycle (b) conversion system (c) Otto cycle (c) acceleration system (d) Rankine cycle (d) separation system

291. High critical Mach number as a design criteria, the high- 297. Identify the monopropellant speed subsonic aircraft are made of (a) hydrogen peroxide (a) thin airfoils (b) hydrazine (b) thick airfoils (c) mono methyl hydrazine (c) laminar airfoils (d) dimethyl hydrazine (d) diamond airfoils 298. Eccentricity of an elliptical orbit determines 292. Consider the following statements about subsonic compressible flow over an airfoil: (a) shape of the ellipse I. Thick airfoils at small angle of attack. (b) size of the ellipse II. Mach numbers do not approach too close to one. (c) both of these III. Mach numbers should always be greater than one. (d) none of these IV. Inviscid and irrotational flow. The statements which are applicable to Prandtl–Glauert 299. A particle moving at uniform velocity in sea level stan- rule? dard air creates two disturbance spheres at two different times. If the later sphere is outside the initial sphere, the (a) I, II, and IV particle Mach number is (b) I, III, and IV (c) II and IV (a) subsonic (d) III and IV (b) transonic (c) sonic 293. In the limit of a high Mach number flow across a shock (d) supersonic wave, which of the following is TRUE? 300. Boundary layer thickness depends on p2 2γ (a) = γ− M1 sin β p1 1 (a) wall roughness p2 2γ 2 (b) = γ− (M1 sin β) (b) freestream velocity p1 1 ρ2 γ+1 (c) Reynolds number (c) ρ = γ− 1 1 (d) all of the above ρ γ 2 = (d) ρ γ−1 1 301. Ramjet and Scramjet engine differentiates themselves 294. In steady, level turning flight of an aircraft at a load in the concept of factor n, the ratio of the horizontal component of lift and aircraft weight is (a) compression √ (b) combustion (a) √n − 1 (c) expansion (b) √n + 1 (d) afterburner (c) √n2 − 1 (d) n2 + 1 302. When the freestream velocity in a subsonic wind tunnel test section is increased by 3 times, the power require- 295. Which of the following is NOT a Duct jet engine? ments to run the tunnel will be

(a) turbojet (a) increased by 3 times (b) turbofan (b) increased by 9 times (c) pulse jet (c) increased by 27 times (d) turboprop (d) increased by 81 times

296. Which of the following is NOT a part of the liquid pro- 303. In designing the Cryogenic wind tunnel, which of the pellant rocket propulsion? following nondimensional parameters must match? 464 Appendix E: Multiple Choice Questions in Aerospace Engineering

(a) Prandtl number and Mach number. 310. The maximum operating flow rate through a centrifugal (b) Mach number and Strouhal number. compressor at a given RPM is limited by (c) Reynolds number and Prandtl number. (d) Reynolds number and Mach number. (a) impeller stall (b) surge 304. A turbofan engine has a bypass ratio of 4 and a total mass (c) choking of diffuser throat flow rate of 100 kgs−1. The mass flow rate through the (d) inlet flow distortion bypass duct is 311. For subsonic axial compressors, the inlet guide vanes (a) 25 kgs−1 have been used to (b) 80 kgs−1 (a) give the incoming air a TANGENTIAL velocity (c) 100 kgs−1 component in the direction NORMAL to the blade (d) 400 kgs−1 velocity. 305. An aircraft of mass 2500 kg in straight and level flight (b) reduce the relative Mach number of the flow. at a constant speed of 100 ms−1 has available excess (c) increase the stage work, for the same rotor exit power of W. The steady rate of climb it can attain at velocity. that speed is (d) operate with a lower mass flow rate for a given relative Mach number of the flow. (a) 100 ms−1 (b) 60 ms−1 312. Using 2-dimensional approximations in subsonic axial (c) 40 ms−1 compressors, for the calculations of blade passage flow (d) 20 ms−1 fields, which of the following methods can be used? I. streamline curvature method 306. What are the four typical loads on an aircraft? II. stream function method III. potential function method (a) tension, torsion, creep, elongation. IV. Euler equation solvers (b) elasticity, shear, compression, torsion. Select the best answer(s) given below. (c) tension, compression, torsion, shear. (d) compression, buckling, elasticity, shear. (a) I and II (b) I, III, and IV 307. is where the materials natural inbuilt elasticity (c) II, III, and IV enables it to stretch when under load. (d) all

(a) elasticity 313. A wing of taper ratio 0.2 has a planform area of 48 m2. (b) buckling If the total wing span is 16 m, the root and tip chords (c) shear of the wing will be , respectively. (d) creep (a) 4 m, 0.8 m 308. Select one of the factors affecting CREEP? (b) 7.0 m, 1.4 m (c) 3.0 m, 0.6 m (a) strength of the material (d) 5.0 m, 1.0 m (b) shear (c) buckling of the material 314. The ideal static pressure coefﬁcient of a diffuser with (d) the duration of the load applied an area ratio of is

309. A model aircraft in a wind tunnel that is operating at (a) 0.25 50 ms−1 develops a minimum pressure coefﬁcient of at (b) 0.5 some point on its upper surface. The local airspeed at (c) 0.75 that point is (d) 1.0

(a) 16.67 ms−1 315. An airfoil has following characteristics. (b) 50 ms−1 I. Design lift coefﬁcient of 0.3. (c) 150 ms−1 II. Maximum camber located at 15 chord length from (d) 200 ms−1 leading edge. Appendix E: Multiple Choice Questions in Aerospace Engineering 465

III. Maximum thickness of 12 chord length. 321. When the pressure drop across a converging–diverging Which of the following airfoil is best represented by the nozzle is different from the design value for isentropic above characteristics? ﬂow, which of the following is possible?

(a) NACA 0012 (a) There is one normal shock in converging part and (b) NACA 23012 one normal shock in diverging part. (c) NACA 4412 (b) There is only one normal shock in converging part (d) NACA 4512 and none in diverging part. (c) There is only one normal shock in diverging part 316. Isentropic flow is and none in converging part. (d) There are two or more normal shocks in diverging (a) irreversible adiabatic flow. part, depending upon the pressure drop and none in (b) reversible adiabatic flow. converging part. (c) ideal fluid flow. (d) frictionless reversible flow. 322. A spring used to absorb shocks and vibrations is

317. If the flow conditions satisfy Laplace equation, then (a) conical spring flow (b) torsion spring (c) disk spring (a) is rotational. (d) leaf spring (b) does not satisfy continuity equation. (c) is irrotational but does not satisfy continuity equa- 323. Modulus of rigidity is defined as the ratio of tion. (d) is irrotational and satisfies continuity equation. (a) longitudinal stress and longitudinal strain. (b) volumetric stress and volumetric strain. 318. A thin flat plate has been placed parallel to the flow (c) lateral stress and lateral strain. direction. The relative magnitudes of skin friction and (d) shear stress and shear strain. pressure drags will be 324. A concentrated mass m is attached at the center of a rod (a) negligible skin friction as well as pressure drags. of length 2L as shown in Fig. E.5. The rod is kept in a (b) negligible pressure drag and maximum skin friction horizontal equilibrium position by a spring of stiffness drag. k. For very small amplitude of vibration, neglecting the (c) maximum pressure drag and negligible skin friction weights of the rod and spring, the undamped natural drag. frequency of the system is (d) pressure drag equals skin friction drag. (a) k m 319. An isentropic nozzle is discharging air through critical (b) 4k pressure ratio. If the back pressure is further decreased m the discharge will (c) 2k m k (a) decrease (d) 2m (b) increase (c) remain unaffected 325. The natural frequency of the system shown in Fig. E.6 (d) come to a dead stop due to shock waves is 320. The thickness of boundary layer in a turbulent flow is (a) k 2m 5x k (a) √ (b) m Rex . (b) 5√835x (c) 2k Rex m 0.377x (c) 1/5 3k (Rex) (d) m 5.377x (d) 1/5 (Rex) 466 Appendix E: Multiple Choice Questions in Aerospace Engineering

k m

Fig. E.5 Spring–mass system

K/2 K

K/2

Fig. E.6 Spring–mass system

326. Velocity potential for an incompressible fluid flow is (c) Uwδ φ = 2 + − 2 2 δ given as: 2 x 2y y Assume the value of (d) 3 Uw stream function at the origin to be zero. The value of stream function at the point (2, 2) is 328. For the given values of pressures and densities, upstream and downstream of a normal shock as shown (a) 8 in Fig. E.8, the velocity upstream of the normal shock (b) 16 will be? (c) 4 − (d) 2 (a) 4 ms 1 (b) 5 ms−1 327. Consider a laminar flow over a flat plate of width w. At (c) 10 ms−1 section ‘1–1’, the velocity profile is uniform as shown (d) 15 ms−1 in Fig. E.7.Thex−direction velocity profile at section ‘2-2’isgivenby 329. Which of the following type of viscous damping will give periodic motion to the vibrating body? u y y 2 I. underdamping = 2 − U δ δ II. critical damping III. overdamping δ where is the boundary layer thickness. Select the answer among the following:

The volume ﬂow rate through section ‘2-2’ is given by (a) I (b) II 1 δ (a) 2 Uw (c) III 1 δ (b) 3 Uw (d) I and II Appendix E: Multiple Choice Questions in Aerospace Engineering 467

UU 1 2 y

δ u(y) x

1 2

Fig. E.7 Laminar ﬂow over a ﬂat plate

Upstream Downstream

5 P =1 x 10 5 Pa P =21 x 10 Pa 1 2 ρ 3 ρ = 1 kg/m3 = 5 kg/m 1 2 v 1 v2

Normal shock

Fig. E.8 Flow across a normal shock

330. The aircraft structural materials which show direction (c) steel dependent properties are called (d) concrete

(a) homogeneous 333. Which of the following stress–strain response curve (b) viscoelastic best represents linear elastic – perfectly plastic behav- (c) isotropic ior? (d) anisotropic σ 331. Modulus of rigidity and bulk modulus of a material are found to be 60 GPa and 140 GPa, respectively. Then consider the following: I. Elasticity modulus is nearly 200 GPa. II. Poisson’s ratio is nearly 0.3. III. Elasticity modulus is nearly 158 GPa. IV. Poisson’s ratio is nearly 0.25. Which of the above is/are CORRECT? (a) ε (a) I and II (b) I and IV σ (c) II and III (d) III and IV

332. Which of the following material has NEGATIVE value of Poisson’s ratio?

(a) rubber (b) novel Foam (b) ε 468 Appendix E: Multiple Choice Questions in Aerospace Engineering

σ 337. In a hypersonic ﬂow (M = 8) past a wedge (total vertex angle, 30o), the hypersonic similarity parameter (H) is

4π (a) 3 2π (b) 3 96 (c) π 48 (d) π

(c) ε 338. In the pitot-static probe (as shown in Fig. E.9) the static pressure holes are generally kept at a distance σ (a) D = 2d (b) D = 8d (c) D = 25d (d) D = 50d 339. If the Airy’s stresses function is φ = 3y2 + 2xy ,the σ σ (d) ε normal stresses xx and yy are , respectively. (a) 6, 0 334. Two identical circular rods of same diameter and same (b) 0, 6 length are subjected to same magnitude of the axial (c) 0, 0 tensile force. One of the rods is made out of mild steel (d) 6, 6 having the modulus of elasticity 206 GPa. The other rod is made out of cast iron having the modulus of elasticity 340. The spacecraft reentry into the atmosphere takes place of 100 GPa. Assume both the materials to be homoge- in the Mach number range, M 28–32. At such a high neous and isotropic and axial force causes same amount Mach numbers, the gases present near the spacecraft of uniform stress in both the rods. The stresses devel- nose are subjected to high temperature. To visualize this oped are within the proportional limit of the respective phenomenon in the wind tunnel, which of the following materials. Which of the following is correct? technique is best suited?

(a) Both rods elongate by the same amount. (a) oil flow visualization with color dyes (b) Mild steel rod elongates more than the cast iron rod. (b) shadowgraph technique (c) Cast iron rod elongates more than the mild steel (c) schlieren technique rod. (d) interferometry technique (d) As the stresses are equal strains are also equal in both the rods. 341. In the wind tunnel testing of, the maximum lift coefficient is found to be 1.5. If the aircraft has an elliptical 335. In a Mohr’s circle, the radius of the circle is represented wing planform of gross area 25m2 and wing tip span of as 10 m, then the maximum induced drag coefficient will be? σ −σ 2 x y + τ 2 (a) 2 xy (a) 9 (σ −σ )2 16π x y + τ 2 16 (b) xy (b) π 2 9 2 (c) 1.5 σx−σy (c) − τ 2 ∞ 2 xy (d) (σ − σ )2 + τ 2 (d) x y xy 342. A subsonic wind tunnel contains a circular Effuser (con- 336. Which of the following is a valid potential function (φ)? traction cone) with entry and exit diameters of 6 m and 2.5 m, respectively. The contraction ratio of effuser is (a) φ = clnx (a) 0.17 (b) φ = c cos x (b) 5.76 (c) φ = 3xy (c) 2.4 (d) φ = c x2 + y2 (d) 0.42 Appendix E: Multiple Choice Questions in Aerospace Engineering 469

Static pressure holes

Probe diameter = d

Fig. E.9 Pitot-static probe

343. The equation of free vibration of a system is 347. If p is the internal pressure in a thin-walled cylinder of 2 d x + 16π2x = 0. Its natural frequency would be diameter d and thickness t, the correct expression of dt2 Hoop stress is (a) 2π Hz pd (b) 4π Hz (a) t (c) 16π2 Hz pd (b) 2t (d) 2 Hz pd (c) 4t pd 344. Consider an incompressible laminar boundary layer (d) 8t flow past a flat plate at zero degree angle of attack. If the direction velocity profile is given by 348. Consider the following statements. The efficiency of a nozzle depends on u y y 2 = 2 − I. Size and shape of the nozzle. U δ δ II. Flow Mach number. III. Flow Reynolds number. where δ is the boundary layer thickness, then the bound- IV. Material of the nozzle. ary layer shape factor will be Which of the following is/are correct? (a) 5 (a) I, II, and III (b) 2.5 (b) I, III, and IV (c) 0.4 (c) I and IV (d) 1.0 (d) II and IV 345. The shape factor of a typical turbulent boundary layer 349. If v is the exhaust jet velocity and v is the rocket veloc- lies in the range j r ity, then the propulsive efficiency of the Rocket is given (a) 0.1 - 0.2 by (b) 0.2 - 0.5 v 2 j η = vr (c) 1.3 - 1.4 (a) p v 2 1+ j (d) 5.5 - 5.6 vr v 2 j η = vr 346. The velocity potential function in a two-dimensional (b) p v 2 1− j flow field is given by φ = 2x + y2. The magnitude of vr 2 the velocity at a point (1, 3) is (c) ηp = v 1+ j vr (d) η = 2 (a) 0 p − vj 1 v (b) 4√ r (c) 2 10 350. Consider the beam with pointed and distributed loads (d) 40 shown in Fig. E.10. 470 Appendix E: Multiple Choice Questions in Aerospace Engineering

400 N 800 N

1 m 2 m

w=50 N/m

Ra Ra

Fig. E.10 Beam with pointed and distributed loads

352. The impulse response of an initially relaxed linear system is u (t) exp−2t, where u (t) is a unit step function. To produce a response of tu (t) exp−2t, the input must be equal to

− (a) (a) 2u (t) exp 2t 1 ( ) −2t (b) 2 u t exp (c) u (t) exp−2t (d) u (t) exp−t

353. If M represents the Mach number, t is thickness-to- chord ratio and γ is the ratio of speciﬁc heat. Then the (b) transonic similarity parameter (K) will be √ M2−1 (a) / [t(γ+1)]1 3 M2−1 (b) 2/3 [t(√γ+1)] M2−1 (c) − / (c) [t(γ+1)] 1 3 M2−1 (d) − / [t(γ+1)] 2 3

354. Closed-loop transfer function of a unity-feedback sys- Y(s) = 1 tem is given by R(s) s+1 . Steady-state error to ramp (d) input is

351. Consider the following statements: (a) ∞ I. At the point of contraflexure, shear force is either zero (b) τ or changes its sign. (c) 1 II. For the flow past a circular cylinder, when the bound- 1 (d) τ ary layer transits from laminar to turbulent then skin friction drag increases. 355. If the roots of the characteristic equation are given by III. The number of natural frequencies of an elastic s1,2 =−3 ± 2j the value of damping ξ and damped nat- beam with cantilever boundary conditions is infinite. ural frequency are Which of the above is/are TRUE? √ (a) √3 , 13 (a) I, only 13 1 (b) I & II (b) √ , 2 13 √ (c) I & III (c) √1 , 13 (d) II & III 13 (d) √3 , 2 13 Appendix E: Multiple Choice Questions in Aerospace Engineering 471

356. The condition that all the roots of the polynomial, 361. For the minimum power required for a level unac- = 3 + 2 + + > s a0s a1s a2s a3; (ai 0),havenegative celerated ﬂight, the aerodynamic condition that holds real parts is given by between zero-lift drag CD,0 , and induced drag due to lift CD,i is given by (a) a1a3 > a0a2 (b) a1a0 > a2a3 (a) CD,0 = 3CD,i > = 1 (c) a1a2 a0a3 (b) CD,0 3 CD,i > = 2 (d) a2a0 a1a3 (c) CD,0 CD,i 1 = 2 357. In a centrifugal pump, the liquid enters the pump (d) CD,0 CD,i

(a) at the center 362. The maximum lift-to-drag ratio for the CP-1 aircraft is (b) at the bottom 13.6. In the power-off mode, the minimum glide angle (c) at the top will be (d) from sides o (a) θmin = 4.2 θ = o 358. Which of the following is NOT correct about winglet? (b) min 45 o (c) θmin = 60 θ = (a) increases the lift generated at the wingtip. (d) min 0 (b) increases the lift induced drag caused by wingtip vortices. 363. In the previous question, if the CP-1 aircraft begins to (c) increases the effective aspect ratio of a wing. glide in power-off mode at an altitude of 3048 m, the (d) increases fuel efﬁciency. maximum range covered by the aircraft measured along the ground will be approximately equal to 359. Consider the following statements: I. static pressure (a) 41500 m II. total pressure (b) 20750 m III. dynamic pressure (c) 83000 m Which of the above affects airspeed measurement using (d) 10000 m a pitot probe? 364. In a steady level ﬂight, the difference in the rate of ( / ) (a) I climbs R C between the service and absolute ceilings −1 (b) II will be (in ftmin ) (c) II and III (a) 0 (d) All (b) 50 360. The characteristic equation of a closed-loop system as (c) 100 ∞ shown in the Fig. E.11,is (d) 365. An object will escape from an Earth orbit, if the velocity (a) s2 + 11s + 10 = 0 is: (b) s2 + 11s + 130 = 0 2 + + = (c) s 10s 120 0 (a) equal to 3.95 kmsec−1 2 + + = (d) s 10s 12 0 (b) equal to 7.9 kmsec−1

R(s) + 3 Y(s) 4 s+1 −

10 s+10

Fig. E.11 Closed-loop system 472 Appendix E: Multiple Choice Questions in Aerospace Engineering

(c) more than 7.9 kmsec−1 but must be less than 11.17 (d) I, IV, and V kmsec−1 (d) equal to or more than 11.17 kmsec−1 370. Consider the following propellant combinations: I. liquid O2+ liquid H2 366. On hot summer days, the air density is lesser than that II. H2+ F2 on cool winter days. For a given aircraft the ground III. monomethylhydrazine (MMH)+ N2O4 liftoff distance on a summer day will be Which of the above forms a hypergolic mixture?

(a) shorter than the winter day (a) I (b) equal to the winter day (b) I and II (c) half than that on a winter day (c) II and III (d) longer than the winter day (d) all the above

367. Consider the following statements: 371. Consider the following: I. Static margin should be positive. I. concept of streamline II. Static margin should be zero or negative. II. concept of streakline III. Shorter the static margin implies more stable air- III. concept of pathline craft. Which of the above concept(s) is/are IMAGINARY in IV.Larger the static margin implies more stable aircraft. nature? For static stability, which of the following are true? (a) I only (a) I and III (b) I and II (b) II and III (c) II and III (c) I and IV (d) I and III (d) II and IV 372. Which of the following statement is NOT correct? 368. The heat transfer rate during the ballistic reentry phase is an important parameter for designing a spacecraft. (a) A calorically perfect gas must be thermally perfect. When the velocity of a given spacecraft is increased by (b) A thermal perfect gas must be calorically perfect. 3 times, the associated heat transfer rate will be? (c) A perfect gas must be both thermally and calorically perfect. (a) increased by 3 times (d) A real gas behaves like an ideal gas at higher tem- (b) increased by 9 times perature and lower pressure. (c) decreased by 9 times (d) increased by 27 times 373. A typical rocket consumes fuel in the order of − 369. Consider the following fuel–oxidizer combinations in (a) 8000 kgs 1 − lightweight propellants: (b) 9000 kgs 1 − I. Kerosene–Oxygen combination has the lowest adia- (c) 10000 kgs 1 − batic flame temperature. (d) 11000 kgs 1 II. Kerosene–Oxygen combination has the highest specific impulse. 374. The standard rocket ejects burnt gases at speeds of over III. Hydrogen–Oxygen combination has the highest adi- (a) 2000 ms−1 abatic flame temperature. (b) 3000 ms−1 IV. Hydrogen–Fluorine combination has the highest (c) 3500 ms−1 adiabatic flame temperature. (d) 4000 ms−1 V. Hydrogen–Fluorine combination has the lowest specific impulse. 375. Which of the following represents a turbojet engine? Which of the following combinations are true? (a) Olympus 593 (a) I, II, III, and V (b) Spey (b) I, II, IV, and V (c) Tyne (c) I and IV (d) Pegasus Appendix E: Multiple Choice Questions in Aerospace Engineering 473

376. The efficiency of a jet engine will be higher at 380. For a given aircraft flying level at steady state with symmetric load distribution, the circulation will be given (a) high Altitudes by (Maximum circulation at root chord = 0) (b) low Altitudes (c) high speeds (a) = 0 cos φ = 0 (d) low speeds (b) cos φ (c) = 0 sin φ 377. For atmospheric ozone, which of the following state- = 0 (d) sin φ ments are NOT true? 381. The boundary layer shape factor (H) for a zero-pressure (a) Ozone levels in the stratosphere have been danger- gradient boundary layer (Blasius Profile) is ously reduced, due to release of CFCs containing refrigerants and propellants. (a) 0 (b) Automobile exhaust can help replace ozone in the (b) 0.83 troposphere. (c) 2.59 (c) Ozone in the stratosphere protects the Earth from (d) 100 excessive UV radiation. (d) Ozone in the troposphere has toxic effects on ani- 382. The turbulence number of a uniform horizontal flow at − mals and plants. 25 ms 1 is 6. If the turbulence is isotropic, determine the mean square values of the fluctuations. 378. For an aircraft flying at supersonic speeds, consider the following statements: (a) 3.37 I. The wave drag of wing with sharp leading edge will (b) 6.75 be lower. (c) 13.5 II. The wave drag of wing with rounded leading edge (d) 45.56 will be lower. III. The wing with sharp leading edge will have well- 383. For a wing the root chord, tip chord, and span are 18 m, defined point of boundary layer separation. 3.5 m and 25 m, respectively. The wing area will be IV. The resultant wing loading with rounded leading (a) 450 m2 edge will be steady. (b) 87.5 m2 Choose the correct option among the following: (c) 225 m2 2 (a) I and III (d) 268.75 m (b) I and IV 384. If the velocity of the flow is given by (c) III and IV v = c (x + y) î−c (x + y) ˆj, the vorticity will be (d) II, III, and IV (a) 0 379. For the aircraft which are operational, consider the fol- (b) −c lowing statements: (c) c I. Most of the cargo and transport aircraft use low aspect (d) −2c ratio wings. II. Most of the cargo and transport aircraft use high 385. The elementary circulation at the midpoint of a flat plate aspect ratio wings. kept at 2o to a freestream of speed 30 ms−1 will be III. Fuel economy of low aspect ratio wings is higher approximately equal to than high aspect ratio wings. IV. Fuel economy of low aspect ratio wings is lower (a) 2.1 than high aspect ratio wings. (b) 1.1 Choose the correct option among the following: (c) 0 (d) 8 (a) I and III (b) II and III 386. If the circulation distribution around a wing is given by (c) II and IV k = 16 1 − y 2. The downwash will be (d) I and IV 10 474 Appendix E: Multiple Choice Questions in Aerospace Engineering

(a) 0.2 ms−1 (c) same (b) 0.4 ms−1 (d) unpredictable (c) 1 ms−1 (d) 1.2 ms−1 393. When the camber of an airfoil is increased then the induced lift will 387. A glider of aspect ratio 6 has a drag polar of, = . + . 2 (a) increase CD 0 02 0 06CL. For minimum glide angle, the lift coefficient CL will be approximately equal to (b) decrease (c) remains Same (a) 1 (d) cannot say (b) 0.6 (c) 1.7 394. In an isothermal atmosphere, the pressure (d) data insufficient (a) decreases linearly with elevation. 388. The aerodynamic efficiency of a sail plane of weight (b) increases exponentially with elevation. 2 3600 N and wing area 10 m is 30. If it is in level flight (c) varies in the same as density at sea level ρ = 1.2kgm−3 with a speed of 36 kmh−1, (d) remains constant the drag coefficient will be 395. Consider the following statements: (a) 0.4 I. Viscosity of liquids increases with increase of tem- (b) 0.8 perature. (c) 0.2 II. Viscosity of gases decreases with increase of tem- (d) 0.9 perature. III. Viscosity of liquids increases with increase of pres- 389. Which of the following visualization technique cannot sure. be used in supersonic flow? Which of the above statements is/are correct?

(a) schlieren (a) I (b) shadowgraph (b) II (c) tuft (c) III (d) interferometry (d) all

390. The Bernoulli’s equation can be applied between any 396. In flow fields with rapidly varying density gradient, two points located on two different streamlines, only if which of the following visualization technique is best the flow is suited?

(a) viscous (a) schlieren (b) supersonic (b) shadowgraph (c) steady (c) interferometry (d) irrotational (d) smoke

391. The Bernoulli’s equation is valid for which of the fol- 397. Consider the following statements: lowing Mach number range? I. Fighter bombers use turboprop engine. II. Adding ammonia and water vapor in the compressor (a) 0 ≤ M ≤∞ decreases the effective power output of turbine. (b) 0.8 ≤ M ≤ 1.2 III. The jet velocity in turbofan engine is less than that (c) 0 ≤ M ≤ 0.5 in turbojet engine. (d) 0 ≤ M ≤ 0.3 Which of the above is/are correct?

392. The stall angle in the symmetrical airfoil is than the (a) I cambered airfoil. (b) I and II (c) II and III (a) higher (d) III (b) lower Appendix E: Multiple Choice Questions in Aerospace Engineering 475

Normal shock M = 0.5 1 M 1 = 2.5

p = 100 kpa p = 690 kpa 2 2

Fig. E.12 Flow across normal shock wave

p , T , v 0 0 0 ρ 0 v

Fig. E.13 Air discharge from a large reservoir

398. Choose the correct one among the following statements. (c) 0.85 (d) 5 (a) The pressure and temperature of air at the suction of compressor are slightly more than atmospheric. 401. If the ratio of back pressure (pb) to reservoir stagnation (b) The pressure and temperature of air at the suction pressure (p0) is less than 0.528, then the flow exiting a of compressor are slightly less than atmospheric. convergent nozzle will be (c) The pressure is slightly more than atmospheric but the temperature is slightly less than atmospheric. (a) underexpanded (d) The pressure is slightly less than atmospheric but (b) overexpanded the temperature is slightly more than atmospheric. (c) supersonic (d) subsonic 399. Choose the INCORRECT option among the following: 402. Consider the high pressure air discharge coming out (a) In an elliptical orbit, the velocity of a satellite at of a small opening from a large reservoir with given apogee is more than that at perigee. stagnation conditions as shown in Fig. E.13. (b) The velocity of a satellite in a circular orbit does not depend on the altitude of the satellite from Earth’s The error involved in treating the air as an incompress- surface. ible medium is (c) Eccentricity of an elliptical orbit determines the shape of the ellipse. (a) 20 (d) Geosynchronous satellite has same orbital time (b) 60 period as that of Earth. (c) 90 (d) data insufficient 400. Consider the flow across a normal shock with given flow conditions as shown in Fig. E.12. 403. Consider a hypersonic flow past a wedge (vertex angle, 2θ), which of the following condition holds? The strength of shock will be (a) Mθ ≥ 1 (a) 6.9 (b) Mθ ≥ 5 (b) 5.9 476 Appendix E: Multiple Choice Questions in Aerospace Engineering

(c) Mθ ≤ 1 increase of height. (d) Mθ ≤ 1 III. In mesosphere, the temperature decreases with increase of height. 404. A supersonic flow encounters a normal shock wave and IV. In thermosphere, the temperature increases with brings down to a subsonic flow. Keeping the flow condi- increase of height. tions same as of previous case the flow is reversed across Which of the above is/are correct? the shock (i.e., from subsonic to supersonic). Which of the following remains valid? (a) I I. state equation (b) II and III II. continuity equation (c) I, III, and IV III. first law of thermodynamics (d) all are correct IV. increase of entropy principle Choose the correct option among the following: 409. The Ornithopter is

(a) I, III, and IV (a) ﬁxed wing aircraft. (b) I, II, and III (b) rotary wing aircraft. (c) I, II, and IV (c) ﬂapping wing aircraft. (d) all the above (d) wingless aircraft.

405. Consider the following: 410. If the Young’s modulus, the shear modulus, and the I. Creep bulk modulus have positive values, then the range of II. Elongation Poisson’s ratio (ν) of a stable, isotropic, linear elastic III. Tension material will be IV. torsion − < ν < . Which of the above are typical loads acting over an (a) 1 0 5 − . < ν < aircraft? (b) 1 5 1 (c) 0.5 < ν < 1 (a) I and II (d) 0 < ν < 1.5 (b) I and III (c) III and IV 411. In two-dimensional state of stress and strain, it is given σ − σ = τ (d) all the above that x y 2 xy. The principle angle will be o 406. For inspection and maintenance purposes, which of the (a) 0 o following entire section of an aircraft is called empen- (b) 22.5 o nage? (c) 45 (d) 90o (a) entire wing section (b) entire cockpit section 412. Generally, the aircraft instrument panels are shock (c) entire landing gear section mounted to absorb (d) entire tail section (a) low frequency and high amplitude shocks. 407. Which of the following is used for the same purpose as (b) low frequency and low amplitude shocks. hydraulic actuators? (c) high frequency and high amplitude shocks. (d) all the vibrations. (a) flaps (b) ailerons 413. During flight, sometimes the altitude is measured by a (c) trim tabs radar altimeter. It measures altitude by (d) spring tabs (a) transmitting a signal to the ground and receiving 408. Consider the following statements about standard back the reflected signal. atmosphere: (b) means of transponder interrogation. I. In troposphere, the temperature decreases with (c) receiving signals transmitted from ground radar sta- increase of height. tions. II. In stratosphere, the temperature increases with (d) receiving signals from the satellite. Appendix E: Multiple Choice Questions in Aerospace Engineering 477

414. An aircraft is flying at an altitude where the ambient (c) 4 temperature is found to be 200 K. If the stagnation tem- (d) 0.8 perature on the surface of the aircraft is 360 K, then the aircraft is flying at Mach 420. At supersonic Mach numbers the drag coefficient varies approximately as (a) 1.5 1 (a) CD = (b) 2 (M∞2 −1) (c) 2.5 (b) C = √ 1 D ( 2 − ) (d) 3 M∞ 1 2 (c) CD = (M∞ − 1) = 1 415. Consider the flow past a flat plate. The pressure inside (d) CD 3/2 (M∞2 −1) the boundary layer will be 421. Consider the following statements: (a) less than that of outside inviscid flow. I. The lift coefficient for a finite wing is more than that (b) more than that of outside inviscid flow. for its airfoil section. (c) same as of outside inviscid flow. II. The drag coefficient for a finite wing is greater than (d) cannot be predicted. that for its airfoil section. Which of the above is/are TRUE? 416. The normal stresses σx and σy for the Airy’s stress function φ = Ay2 + Bxy are , respectively. (a) I (b) II (a) 2A, 0 (c) all (b) 0, 2A (d) none (c) 0, −2A (d) −2A, 0 422. For longitudinal static stability of an aircraft, the position of center of gravity must be 417. Moon revolves around the Earth in an elliptical orbit. The velocity of moon at perigee is (a) coinciding with the neutral point (b) behind the neutral point (a) same as the apogee. (c) forward of the neutral point (b) higher than the apogee. (d) close enough to the nose of fuselage (c) lower than the apogee. (d) depends on the center of mass of the system. 423. The ratio of thrust-specific fuel consumption (TSFC) of a typical turbojet to a typical turbofan is approximately 418. In continuity and momentum equations the air is equal to replaced with water as fluid medium. The complete analogy between these two sets of equations (a) 0.06 corresponds to (b) 0.7 (c) 1 γ = (a) 1.33 (d) 1.67 (b) γ = 1.4 (c) γ = 1.67 424. For a cantilever with point load at the free end, the (d) γ = 2 bending moment diagram will be

419. The drag measurement of turbulence sphere in sub- (a) parabola sonic wind tunnel testing, the effective and measured (b) triangle with maximum height under free end Reynolds numbers are found to be 400,000 and 80,000, (c) triangle with maximum height under ﬁxed end respectively. The turbulence factor will be (d) an arc

(a) 5 425. A beam subjected to the loading is shown in Fig. E.14. (b) 0.2 The shear force diagram will look like 478 Appendix E: Multiple Choice Questions in Aerospace Engineering

5 kN 12 kN (a) (b) At smaller sizes, the axial blading at the rear of the compressor is easy to manufacture accurately. (c) A single-stage axial compressor increases the pres- −6 kN sure higher than single-stage, centrifugal compres- −7 kN sor. 7 kN (d) It is easy to link them to obtain multistage compres- 6 kN (b) sor.

429. Which of the following statements concerning centrifu- −5 kN −12 kN gal compressors is/are TRUE? 6 kN 6 kN (a) Centrifugal compressors with vane-less diffusers (c) are compact compared to vaned diffusers. (b) In multistage centrifugal compressors, the width of the blades reduces progressively in the direction of −12kN flow. −7 kN (c) In multistage centrifugal compressors, the width of (d) the blades increases progressively in the direction of flow. (d) The multistage centrifugal compressors are commonly used for high refrigerant capacity applica- −12 kN −6 kN tions. 426. Consider the following statements about centrifugal pumps: 430. If is the Mach number and is the characteristic Mach I. high suction pressure number then which of the following is TRUE? II. low delivery pressure III. reduction of flow rate at pump section = M∗2(γ−1) (a) M + ∗2(γ− ) Which of the above helps in avoiding cavitation in 2 M 1 M∗2(γ−1) (b) M = ∗ pumps? 2+M 2(γ+1) M∗2(γ+1) (c) M = ∗ (a) I 2+M 2(γ−1) 2(γ− ) (b) II and III (d) M∗ = M 1 2+M2(γ−1) (c) III (d) All 431. During the flight in troposphere layer of standard atmosphere, when an aircraft goes to higher altitudes main- 427. The overall efficiency of a centrifugal pump is defined taining same speed its Mach number will be as the ratio of (a) increasing (a) energy available at the impeller to the energy sup- (b) decreasing plied to the pump by the prime mover. (c) same (b) actual work done by the pump to the energy sup- (d) cannot say plied to the pump by the prime mover. (c) energy supplied to the pump to the energy available 432. When the flowing air is heated in a nozzle, which of the at the impeller. following changes will NOT occur? (d) manometric head to the energy supplied by the impeller per Newton of water. (a) Velocity of air will decrease. (b) Pressure increases. 428. The axial compressors are preferred over centrifugal (c) Increase in enthalpy. compressors in gas turbine engines because (d) Increase in entropy.

(a) Because of the axial ﬂow direction, it has high 433. Consider the following statements about propellants: cross-sectional area than the corresponding cen- I. hydrogen peroxide trifugal compressor. II. hydrazine III. nitroglycerin Appendix E: Multiple Choice Questions in Aerospace Engineering 479

2 kN/m 6 kN 12 kN

A D BC

1 m 6 m 1 m

Fig. E.14 A beam subjected to the loading

C A

TSFC

Fig. E.15 Plot between TSFC and the Mach number

IV. nitromethane isotropic material, the Bulk modulus of elasticity will Which of the above is/are the example of monopropel- be lant? (a) 44 GPa (a) I (b) 53 GPa (b) II (c) 89 GPa (c) III and IV (d) 133 GPa (d) All 437. Consider the following graph (Fig. E.15), plotted 434. Dive flaps are used in the aircraft because between thrust-specific fuel consumption (TSFC) and Mach number. (a) It provides extra lift to the aircraft. (b) It controls the flow separation over wings. Which of the above curves represent ideal ramjet (c) It reduces the speed of aircraft. engine? (d) It is used for longitudinal stability of aircraft. (a) A 435. The hot-wire anemometer (HWA) is a device used to (b) B measure flow speed. Which of the following is NOT a (c) C type of HWA? (d) D

(a) constant resistance anemometer 438. Consider a 4-seater Cessna-172 propeller aircraft, with (b) constant voltage anemometer propeller of 2 m in diameter spinning at 1200 RPM. If (c) constant temperature anemometer the aircraft is advancing at a speed of 20 ms−1, then the (d) pulse width modulation anemometer advance ratio will be

436. For steel the Young’s modulus of elasticity is 200 GPa 1 (a) 120 and Shear modulus is 80 GPa. Assuming steel to be an 1 (b) 30 480 Appendix E: Multiple Choice Questions in Aerospace Engineering

1 (c) 2 444. Consider the following statements about Hohmann (d) 2 transfer orbits: I. These trajectories consume the maximum amount of 439. Consider a rocket engine burning hydrogen and oxygen propellant. − mixture at a rate of 125 kgs 1 and generating the thrust II. The orbit to Mars is achieved by accelerating the of 4.75 × 105N. The area of rocket nozzle throat is 0.1 spacecraft in the direction of Earth’s revolution to m2. The area of the exit is designed so that the exit pres- place in the Sun’s orbit with a perihelion equal to the sure exactly equals ambient pressure at flying altitude orbit of Mars. of 30 km. For the gas mixture, assume that γ = 1.4 and III. The orbit to Venus is achieved by accelerating the molecular weight M = 16. At standard altitude of the spacecraft in the direction opposite of Earth’s 30 km, the specific impulse will be revolution to place in the Sun’s orbit with an aphelion equal to the orbit of Venus. (a) data insufficient Which of the above statements is/are TRUE? (b) 388 s (c) 475 s (a) I (d) 125 s (b) II and III (c) I, II and III 440. A body traveling in a hyperbolic orbit around a planet (d) none will have 445. Assume that a planet is revolving around the Sun in an (a) will always be at finite distance from planet. elliptical orbit, with a speed of 25 kms−1 at its average (b) zero speed at infinite distance from planet. distance from the Sun. What could be the most likely (c) infinite speed at infinite distance from planet. speed of the planet when it is closer to the Sun? (d) finite speed at infinite distance from planet. (a) 15 kms−1 − 441. Consider the following x momentum Eulerian equa- (b) 20 kms−1 tion, (c) 25 kms−1 −1 ∂ ∂ ∂ ∂ ∂ (d) 30 kms u + u + u + u=−1 p ∂ u∂ v∂ w ∂ ρ ∂ t x y z x 446. Which of the following should be applied to limit the wing bending? The above equation is valid if and only if the flow is (a) High strength material as skin material of the wing. (a) laminar (b) High strength material as web plate material for the (b) inviscid spars. (c) steady (c) High stiffness material as skin material of the wing. (d) unsteady (d) High stiffness material as web material for the ribs. 442. The necessary and sufficient condition to define the 447. A total temperature probe measures the temperature of potential function for a flow is: a Mach 2 air flow as 520 K. If the probe has a recovery (a) laminar factor of 0.9, then the stream static temperature will be (b) incompressible (approximately)? (c) steady (d) irrotational (a) 520 K (b) 350 K 443. Consider the flow past a flat plate as shown in Fig.E.16. (c) 300 K At the point of separation which of the following con- (d) 250 K dition is TRUE? 448. The oblique shock diffuser is more frequently used ∂u (a) ∂x than the normal shock one in a supersonic wind tun- ∂u nel, because it (b) ∂y ∂2 (c) u ∂x2 (a) rapidly accelerates the flow. ∂2 (d) u ∂y2 (b) increases total pressure loss. Appendix E: Multiple Choice Questions in Aerospace Engineering 481

y Ua

Fig. E.16 Flow past a ﬂat plate

(c) reduces the ﬂow speed more rapidly. 454. Consider an aircraft which has the lift-to-drag ratio of (d) reduces total pressure loss. 7. In PHUGOID mode, the damping ratio will be?

449. Consider a turbojet engine, which is operating with (a) 0.01 afterburner in switched-off mode. When the afterburner (b) 0.04 starts functioning then? (c) 0.1 (d) 0.5 (a) Both thrust and specific fuel consumption increase. (b) The thrust increases but specific fuel consumption 455. In a turbojet engine nozzle, the temperature and Mach decreases. number at a particular cross section are T and M, respec- (c) The thrust decreases but specific fuel consumption tively. If T∗ is the temperature at the throat then increases. T∗ (d) Both thrust and specific fuel consumption decrease. = a + bM2 T 450. Consider a rocket engine with liquid propellant. The The constants a and b are , respectively. exhaust velocity (ve) will vary with molecular weight ( ) M of the propellant as 1 2 (a) (γ+1) and (γ+1) (γ− ) 1 (b) 2 and 1 (a) 0.5 (γ−1) (γ+1) M (γ− ) (b) 1 (c) 2 and 1 M1.5 (γ+1) (γ+1) (c) M1.5 2 (1−γ) (d) (γ+1) and (γ+1) (d) 1 M2 456. The volumetric strain experienced by a body with coef- 451. To achieve minimum time for orbital rendezvous by ficient of elasticity E and Poisson ratio ν = 0.3, when Hohmann transfer, the value of phase error (θ) is . subjected to a uniform hydrostatic pressure of magni- × −4 tude E 10 is (a) 180o 3 o (b) 360 − × −6 o (a) 20 10 (c) 0 − × −6 o (b) 40 10 (d) 90 (c) −25.5 × 10−6 (d) −30 × 10−6 452. In which of the following parts of a turbojet engine the maximum pressure loss will occur? 457. A spring–mass system is shown in Fig. E.17. below. The natural frequency of the system is (a) turbine (b) compressor (a) 3k (c) inlet 5m (d) nozzle (b) 5k 3m (ξ) (c) 8k 453. The damping ratio for a critically damped system 5m will be? 5k (d) 8m (a) 0 458. Consider a rectangular beam. What is the nature of dis- (b) > 1 tribution of shear stress? (c) −2 (d) 1 482 Appendix E: Multiple Choice Questions in Aerospace Engineering

k m k k

Fig. E.17 Spring–mass system

(a) linear (c) 8.75 ms−1 (b) parabolic (d) 140 ms−1 (c) hyperbolic (d) ellipse 463. Consider an aircraft is flying as shown in Fig. E.18. The angle of attack is 459. If the diameter of a long column is reduced by 20%, then the percentage reduction in Euler buckling load is (a) −A (b) −B (a) 4 (c) +B (b) 40 (d) A + B (c) 50 (d) 60 464. Which of the following phenomena, occurs because of vortices? 460. Consider the following statements: I. An aircraft with a propeller mounted on the nose of (a) parasite drag the fuselage will contribute negative to the longitudinal (b) skin friction drag stability. (c) wave drag II. For static stability of an aircraft: Cmα > 0. (d) lift induced drag III. If the elevator size is decreased, keeping the tail area same. The static longitudinal stability will increase. 465. The turbofan engine uses bypass Which of the above is/are TRUE? (a) to increase the mass flow rate through the exhaust (a) I nozzle. (b) II (b) to increase the inlet mass flow rate. (c) II and III (c) to increase turbine inlet temperature. (d) III (d) to increase the overall pressure ratio in the compressor. 461. Consider the following statements about ground roll distance during landing of an aircraft: 466. A thin cylinder of inner radius 250 mm and the thickness I. Ground roll distance can be reduced by decreasing 10 mm is subjected to an internal pressure of 8 MPa. wing loading and by increasing the lift coefficient. The maximum shear stress in the cylinder is II. Ground roll distance will be reduced by increasing thrust-to-weight ratio. (a) 25 MPa Which of the above is/are TRUE? (b) 50 MPa (c) 100 MPa (a) I (d) 200 MPa (b) II (c) I and II 467. A two-dimensional flow field is given by φ = 3xy. The (d) none stream function is represented by − − 2 − 2 462. An aircraft has a stall velocity of 35 ms 1 in the cruise (a) 3x y −3 2 + 2 flight. During a maneuver, the load factor is found to be (b) 2 x y −3 2 − 2 16. For this maneuver, the stall velocity will be? (c) 2 x y (d) −3 x2 + y2 (a) 35 ms−1 (b) 560 ms−1 Appendix E: Multiple Choice Questions in Aerospace Engineering 483

horizon

B Chord line

Fig. E.18 A schematic diagram of a typical ﬂying aircraft

468. In a convergent–divergent nozzle, generally a normal 472. Consider the following statements about layers in the shock can occur Earth’s atmosphere: (I) The troposphere is wider at the equator but narrower (a) in the convergent portion. at the poles. (b) in the divergent portion and throat. (II) The troposphere is narrower at the equator but wider (c) near the inlet. at the poles. (d) anywhere in the nozzle. (III) The ozone layer is predominantly located in the lower segment of the stratosphere. 469. The efficiency of a centrifugal pump will be maximum (IV) The ozone layer is predominantly located in the when it’s blades are upper segment of the stratosphere. Choose the CORRECT options in the following: (a) wave shaped (b) bent forward (a) I and III (c) bent backward (b) II and III (d) straight (c) II and IV (d) I and IV 470. For an orbit of a celestial body, the ratio of radius of ( ) apogee ra to radius of perigee rp is 4. Then the eccen- 473. Consider the velocity field given by u = y and (x2+y2) tricity of the elliptical orbit will be? − v = x . The equation of streamlines passing (x2+y2) (a) 1.67 through the point (0, 5) will be given by (b) 0.6 + = (c) 0.78 (a) x y 5 2 + 2 = (d) 0.36 (b) x y 25 (c) xy = 25 2 2 471. Consider the following statements about Earth’s atmo- (d) x − y = 25 sphere: (I) Longitude and latitude of the location on the Earth. 474. For the flow in a convergent–divergent nozzle, which (II) Altitude above the sea level. of the following statement is CORRECT? (III) Season in the year. (a) The velocity is minimum at the throat. (IV) Time in a day. (b) The pressure is maximum at the throat. (V) Sun-spot activities. (c) The pressure is minimum at the throat. The temperature and pressure in the Earth’s atmosphere (d) When the throat is choked, the throat pressure depends on should be higher than the exit pressure to obtain (a) I, II, and III subsonic flow in the divergent section. (b) I, III, and IV 475. Consider an airfoil kept in a flow with a freestream (c) II, III, and IV velocity of 20 ms−1. The velocity at a given point on (d) all the airfoil is 40 ms−1. The pressure coefficient at this point will be 484 Appendix E: Multiple Choice Questions in Aerospace Engineering

(a) 2 481. Consider the following statements about Hohmann (b) −3 Transfer: (c) 3 (I) It is a two-impulse elliptical transfer between two − 1 (d) 3 coplanar circular orbits. (II) The transfer itself consists of an elliptical orbit 476. For a doublet flow, the stream function in cylindrical with a perigee at the outer orbit and an apogee at the coordinates will be given by inner orbit. (III) The fundamental assumption behind it is that −κ sin θ (a) 2π r there is only one body which exerts a gravitational −κ cos θ (b) 2π r force on the body of interest, such as a satellite. κ θ (c) sin 2π r2 (IV) Additional bodies can share the orbit which could κ θ (d) cos induce a gravitational attraction on the body of interest. 2π r2 Which of the above is/are CORRECT? 477. The purpose of fins on a rocket is to (a) II and III (a) reduce drag (b) I and III (b) generate lift (c) II, III, and IV (c) provide stability (d) I, II, and IV (d) streamline shape 482. The force exerted by a jet impinging on a fixed plate 478. What is the main purpose of wing flaps? inclined at an angle θ with the jet is

(a) Decrease the angle of descent without increasing (ρAv sin 2θ) (a) 4 the airspeed. (b) ρAv sin θ (b) Increase the angle of descent without increasing the ρAv2 sin 2θ (c) 2 airspeed. (d) ρAv2 sin 2θ (c) Decreases the angle of descent by increasing the airspeed. 483. Multistage centrifugal pumps are used to (d) Decrease the drag. (a) give high discharge 479. Consider the following statements about ground effect: (b) produce high heads (I) It is the result of the interference of the surface of (c) pump viscous fluids the Earth with the airflow patterns about an airplane. (d) all the above (II) It decreases the induced drag, and therefore, any −→ excess speed at the point of flare may cause considerable 484. Consider the velocity field v = xî floating. (III) Becoming airborne before reaching recommended (a) For an incompressible fluid this field satisfies con- takeoff speed. servation of mass. Which of the above is/are CORRECT? (b) The acceleration of the particle in this field decreases with x. (a) I (c) The acceleration of the particle in this field (b) I and II increases with x. (c) II and III (d) The pressure of an incompressible and inviscid fluid (d) all increase with x.

480. For an elliptical lift distribution over wing span, the 485. What is the primary control surface located on the wings downwash that control the roll of the glider clockwise or counterclockwise? (a) increases with angle of attack. (b) decreases with angle of attack. (a) stabilizer (c) is a constant. (b) rudder (d) is equal to zero. (c) elevator (d) aileron Appendix E: Multiple Choice Questions in Aerospace Engineering 485

C L Plane 1

Plane 2

Fig. E.19 CL versus α curve

486. With the increase of camber of an airfoil, the induced (a) Plane 1. lift will? (b) Plane 2. (c) Both have same aspect ratio. (a) increase. (d) Can’t be determined. (b) decrease. (c) no effect on induced lift. 491. The plot between powers required and true airspeed an (d) no relationship between the camber and induced aircraft at two different altitudes is shown in Fig.E.20. lift. What is the correct order of altitude? 487. The aspect ratio shows the relationship between the

span and chord of a wing. Which of the following wing (a) H1 = H2 would create the maximum lift? (b) H1 < H2 (c) H1 > H2 (a) span = 10, chord = 5 (d) insufﬁcient data (b) span = 10, chord = 2 (c) span = 15, chord = 5 492. If the airfoil thickness increases, the critical Mach num- (d) span = 15, chord = 2 ber will

488. The induced drag for airfoil is (a) Decrease. (b) Increase. (a) inﬁnite (c) Remains constant. (b) zero (d) Can’t be determined. (c) half of ﬁnite wing. (d) depends upon airfoil. 493. At half chord length from the leading edge, which of the following airfoil will have location of the maximum ( ) 489. Consider the following combinations of area S and camber? velocity (v): (I) √v , S (a) NACA 5212 2 (II) v , 2S (b) NACA 2512 2 (c) NACA 1225 (III) (v, 2S) , S (d) NACA 2215 (IV) 2v 2 For a certain angle of attack, at a given altitude the lift 494. A structural member supports loads, which produce at will be doubled for which of the above combinations? a particular point, a state of pure shear stress of 50 −2 (a) I, II, and IV Nmm . At what angles are the principal planes ori- (b) II and III ented with respect to the plane of pure shear? (c) I, III, and IV π 2π (a) 6 and 3 (d) II, III, and IV π π (b) and 3 π4 π4 490. Consider the CL versus α curve as shown in Fig. E.19. (c) 4 and 2 π π Which plane has higher aspect ratio? (d) 2 and 486 Appendix E: Multiple Choice Questions in Aerospace Engineering

H 2 Power required

True air speed

Fig. E.20 Power required versus true airspeeds

495. Consider the following statements: (d) Heat and work are path functions. (I) The combustion in gas turbine engines is an ideal isochoric process. 499. Match the following criteria of material failure, under (II) For a given chamber pressure, the thrust of a rocket biaxial stresses σ1 and σ2 and yield stress σy, with their engine is highest when the rocket is operating at sea corresponding graphic representations (Fig. E.21). level. Which of the above statements is/are CORRECT? (a) P-M, Q-L, R-N (b) P-N, Q-M, R-L (a) I (c) P-M, Q-N, R-L (b) II (d) P-N, Q-L, R-M (c) I and II (d) none 500. Consider Fig. E.22.

496. If the load factor of an aircraft turning at a constant If the surface is frictionless, the natural frequency will altitude is 2, keeping the speed constant the required be lift coefficient will be (a) 32 Hz (a) Same for turning as well as level flights. (b) 13 Hz (b) Half for the turning flight as compared to level (c) 76 Hz flight. (d) 51 Hz (c) Double for the turning flight as compared to level flight. 501. Consider the following statements: (d) Four times for the turning flight as compared to (I) As compared to turboprop, the turbojet engine han- level flight. dles low mass of air at high velocity. (II) The modern fighter class engines are high-bypass 497. In a quasi-steady process, assuming the entropy turbofan engines. increases for a substance. Then the rise in temperature Which of the above is/are CORRECT? will be maximum for (a) I (a) process with constant enthalpy. (b) II (b) isobaric process (c) I and II (c) isothermal process (d) none (d) isochoric process 502. Which of the following statements are NOT correct? 498. Which of the following statement is CORRECT? (a) An airplane which has negative aerodynamic damp- (a) Heat and work are intensive properties. ing will be dynamically unstable. (b) Heat is intensive property but work is extensive (b) Forces and moments arising over the airplane due to property. its motion provide negative aerodynamic damping. (c) Heat is a point function and work is an extensive (c) Forces and moments arising over the airplane due to property. its motion provide positive aerodynamic damping. Appendix E: Multiple Choice Questions in Aerospace Engineering 487

σ 2 σ2 σγ σγ

σ σ1 1 −σ −σ σ γ σ γ γ γ

−σγ −σγ P. Maximum−normal−stress criterion Q. Maximum−distortion−energy criterion

σ 2

σ γ

σ1 −σ γ σ γ

−σ γ

R. Maximum−shear−stress criterion

Fig. E.21 Schematic diagram of stresses and their graphical representation

1 Kg

Fig. E.22 Schematic diagram of spring–mass system

(d) Dynamic stability is usually specified by the time (a) flaps it takes a disturbance to be damped to half of its (b) winglets initial amplitude. (c) trim tabs (d) high-lift devices 503. In order to have static longitudinal stability, through the equilibrium point the aircraft pitching moment curve 505. A typical turbofan engines have the bypass ratio of must have (a) 2:1 (a) zero slope (b) 4:1 (b) negative slope (c) 8:1 (c) positive slope (d) 16:1 (d) can’t say 506. For the steady, fully developed flow inside a straight 504. The devices or modifications to the wing that increase pipe of diameter D, neglecting gravity effects, the pres- the stall angle of attack are 488 Appendix E: Multiple Choice Questions in Aerospace Engineering

Fig. E.23 Schematic diagram of spring–mass system

sure drop p over a length L and the wall shear stress 510. Consider a disk of mass (m), which is attached to a τw are related by spring of stiffness (k) as shown in the Fig. E.23.The disk rolls without slipping on a horizontal surface. The 2 (a) τ = pD natural frequency of vibration of the system will be w 4L2 τ = pD (b) w 2L 1 k τ = pD (a) π (c) w 4L 2 m 4pD 1 2k (d) τw = (b) L 2π m (c) 1 2k 507. Consider the following statements for the turbulent flow 2π 3m of a fluid through a circular pipe of diameter (D): 1 3k (d) π (I) The fluid is well mixed. 2 2m (II) The fluid is unmixed. 511. In an aircraft, constant roll rate can be produced using > (III) Reynolds number, ReD 2300. ailerons by applying (IV) Reynolds number, ReD < 2300. Which of the above is/are TRUE? (a) a step input (b) a ramp input (a) I (c) a sinusoidal input (b) I and III (d) an impulse input (c) II and III (d) I and IV 512. The Shadowgraph optical flow visualization technique depends on the 508. Consider a simply supported beam of length, 50h, with a rectangular cross section of depth h and width 2h. The (a) First derivative of density with respect to spatial beam carries a vertical point load P, at its midpoint. coordinate. Ratio of the maximum shear stress to the maximum (b) Second derivative of density with respect to spatial bending stress in the beam will be coordinate. (c) Third derivative of density with respect to spatial (a) 0.02 coordinate. (b) 0.1 (d) Fourth derivative of density with respect to spatial (c) 0.05 coordinate. (d) 0.01 513. A rocket is to be launched from the bottom of a very 509. The damping ratio of a single degree of freedom spring– deep crater on Mars for Earth return. The specific mass–damper system with mass of 2 kg, stiffness 200 impulse of the rocket, measured in seconds, is to be −1 −1 Nm and viscous damping coefficient of 40 m Ns is normalized by the acceleration due to gravity at

(a) 0.5 (a) The bottom of the crater on Mars. (b) 1.0 (b) Mars standard sea level. (c) 1.25 (c) Earth’s standard sea level. (d) 2.0 (d) The same depth of the crater on Earth. Appendix E: Multiple Choice Questions in Aerospace Engineering 489

514. Which of the following is the CORRECT combination (a) I of greenhouse gases? (b) I and II (c) III and IV (a) water vapor, oxygen, methane, nitrous oxide, and (d) all ozone. (b) water vapor, carbon dioxide, methane, nitrous 520. The cast iron has the Poisson’s ratio (ν) in the range of oxide, and ozone. (c) water vapor, carbon dioxide, hydrogen, nitrous (a) 0.1 < ν < 0.2 oxide, and ozone. (b) 0.23 < ν < 0.27 (d) water vapor, carbon dioxide, methane, sulfur diox- (c) 0.25 < ν < 0.33 ide, and ozone. (d) 0.4 < ν < 0.6

515. The minimum period that any free flight object can 521. Consider a cross-sectional area over which the velocity have in orbit around the Earth (also known as Schuler is zero in one-half and uniform over the rest half. The period) is momentum correction factor will be (a) 84.4 minutes (a) 1 (b) 104.4 minutes 4 (c) 60 minutes (b) 3 (d) 12 hours (c) 2 (d) 4 516. When the freestream velocity in a subsonic wind tunnel test section is decreased by 2 times, the power require- 522. Consider a two-dimensional, steady, and incompressible flow over an airfoil. The freestream velocity suffi- ments to run the tunnel will be − ciently far away from the airfoil is found to be 30 ms 1 (a) decreased by 2 times where the distances between streamlines are 2 cm. The (b) decreased by 4 times velocity near the airfoil where the streamlines are 1.5 (c) decreased by 8 times cm apart, will be (d) increased by 4 times − (a) 11.25 ms 1 − 517. If ratio of specific heats is γ, the Prandtl–Meyer super- (b) 22.5 ms 1 − sonic expansion function (ν) can be written as (c) 33 ms 1 −1 ν = γ (d) 40 ms (a) γ−1 ν = γ−1 (b) γ+1 523. Which of the following statements are CORRECT for γ−1 (c) ν = γ turbulent flows? γ+1 (d) ν = γ− 1 (a) The eddy viscosity is a function of temperature 518. Assume that a planet is revolving around the Sun in an only. elliptical orbit with eccentricity (e = 0.4). The ratio of (b) The eddy viscosity is a physical property of the its velocities at perigee to apogee will be fluid. (c) The eddy viscosity depends on the flow. (a) 0.4 (d) The eddy viscosity is independent of the flow. (b) 0.43 − (c) 2.3 524. If the perturbation velocity is 2 ms 1 and freestream − (d) 2.5 velocity is 8 ms 1. Using small perturbation theory the pressure coefficient in two-dimensional planar flows 519. Consider the following statements: will be (I) The volumetric change of the fluid caused by a resistance is known as compressibility. − 1 (a) 8 (II) The density of water is maximum at 4oC. (b) − 1 (III) The bulk modulus of elasticity decreases with 4 − increase in pressure. (c) 8 − 1 (IV) Viscosity of liquids is appreciably affected by (d) 2 change in pressure. Which of the above statements is/are TRUE? 490 Appendix E: Multiple Choice Questions in Aerospace Engineering

525. Consider the following statements: (d) II and IV (I) An orbit can be both in a Sun-synchronous orbit and in a repeat orbit at the same time. 530. Consider the following statements: (II) A geostationary orbit is geosynchronous and all (I) Airy stress function can be used only for two- geosynchronous orbits are geostationary. dimensional problems. Choose the CORRECT from following: (II) The duration of the load applied affects CREEP. (III) In the constitutive equations of a generalized (a) I anisotropic solid, the numbers of independent elastic (b) II constants are 21. (c) I and II Which of the above is/are CORRECT? (d) none (a) I only 526. An oblique shock wave with a wave angle of β = 60o (b) I and III is generated from a wedge angle of θ = 30o. The ratio (c) II and III of Mach number downstream of the shock to its normal (d) all component will be 531. The roll stability of a glider can be improved if the wing (a) √2 has mainly 3 (b) 0.87 (c) 0.5 (a) sweep angle (d) 2 (b) anhedral (c) dihedral 527. If an aircraft is in cruise motion at Mach 3, where the (d) winglets outside air temperature is found to be 350 K. The stagnation temperature at the nose of the aircraft will be? 532. Consider a steady, level turning flight of an aircraft with ( = ) (For air, the specific heat ratio, γ = 1.4) the load factor n 3 . The ratio of the horizontal component of lift to the weight of aircraft will be (a) 980 K √ (b) 1610 K (a) 2 (b) √1 (c) 350 K √2 (d) insufficient data (c) 2 2 (d) √1 528. Consider a thin-walled-closed and a thin-walled open 2 2 tubes with the radius, r = 10 mm and thickness, t = 1 533. Consider the fluid flow past a wooden wedge (semi- mm in both cases. The ratio of torsional rigidity of thin- vertex angle, θ = 20o) at Mach 10. The similarity walled closed tube to thin-walled open tube will be? parameter for this flow will be?

(a) 100 10π (a) 9 (b) 200 20π (b) 9 (c) 300 90 (c) π (d) 400 45 (d) π 529. Consider the jet exhaust through an underexpanded noz- 534. If an open-loop unstable linear system is represented by zle. 1 . Its closed-loop characteristic equation will (I) normal shock wave (s−1)(s+2) be? (II) expansion fans (III) subsonic diffusion (a) s2 + s − 1 = 0 (IV) supersonic diffusion (b) s2 + 2s − 1 = 0 The pressure equalization takes place through which of (c) s2 + s + 1 = 0 the following combinations? (d) s2 + s − 2 = 0

(a) I and III 535. Consider the following statements about the control (b) I and IV system: (c) II and III Appendix E: Multiple Choice Questions in Aerospace Engineering 491

(I) The nature of bandwidth for a good control system 540. The classiﬁcation of composite materials are based should be small. upon (II) The steady-state error is zero in closed-loop control systems. (a) matrix type (III) Gauss meter controls the speed of D.C. motor. (b) size and shape of reinforcement (IV) A good control system should be sensitive to input (c) both (a) and (b) signals (except noise). (d) none Which of the above statements is/are TRUE? 541. Which of the following is not an example of laminar (a) I and II composite? (b) II and III (c) II and IV (a) wood (d) IV only (b) bimetallic (c) coatings/paints 536. Which of the following statement is WRONG? (d) claddings

(a) In an open-loop control system the output is inde- 542. The oxidizing power is generally determined in terms pendent of control input whereas in closed-loop of electronegativity. Which of the following substances system, the control action is somehow dependent has the highest electronegativity? on the output. (a) hydrogen (b) In a closed-loop control system the output is inde- (b) fluorine pendent of control input, whereas in an open-loop (c) oxygen system, the control action is somehow dependent (d) chlorine on the output. (c) The positive value of feedback gain in a closed-loop 543. Consider the following beams: control system will decrease the overall gain. (I) simply supported beams (d) The closed-loop system has a tendency to oscillate. (II) cantilever beams (III) overhanging beams 537. The satellite orbits are elliptical with a constantly vary- (IV) fixed beams ing radius. Since the satellite’s velocity depends on this (V) continuous beams varying radius, it changes as well. To resolve this prob- Which of the above are statically determinate beams? lem, an eccentric anomaly (E) is defined as: ( Take, ν = True Anomaly) (a) I, II, and IV (b) I, II, and III = ecosν (a) E 1+ecosν (c) II, III and IV = e−2cosν (b) E 1+ecosν (d) III, IV and V = 2e+cos ν (c) E 1−ecosν = e+cos ν 544. Consider a cantilever beam with uniformly distributed (d) E 1+ecosν load starting from zero. The shear force diagram will be 538. Altimeter works on (a) horizontal line parallel to x−axis (a) differential pressure sensing. (b) line inclined to x−axis (b) no air pressure sensing. (c) parabolic curve (c) mono pressure sensing. (d) cubic curve (d) radar sensing. 545. Consider an automobile axle with the loads as shown 539. The airspeed indicator (ASI) is the instrument that in Fig. E.24. The maximum bending moment will be (a) has both pitot and static ports. (b) utilizes pitot port only. (a) Wl ( − ) (c) utilizes static port only. (b) W l a ( + ) (d) does not operate on differential pressure sensing. (c) W l a (d) Wa 492 Appendix E: Multiple Choice Questions in Aerospace Engineering

W W

a a

Fig. E.24 Schematic diagram of axle under pointed loads

5 kN 10 kN

A B C

2 m 2 m

Fig. E.25 Schematic diagram of a beam under loads

546. Consider the beam with loads as shown in Fig.E.25. (c) III (d) I and III The slope of the bending moment diagram between B and C will be 550. Consider the following statements: (I) The conventional vertical tail of an aircraft con- (a) 15 kN tributes toward longitudinal stability. (b) 10 kN (II) The conventional vertical tail of an aircraft con- (c) Zero tributes toward both lateral and directional stability. (d) 20 kN (III) If the C.G. of an aircraft moves forward, the efforts required trimming the aircraft will be increased. 547. The Bernoulli’s equation is valid for which of the fol- (IV) Keeping the tail area same, if the elevator size lowing Mach number ranges? is decreased the static longitudinal stability will also decrease. ≤ . (a) M 0 5 Which of the above statements is/are TRUE? (b) 0.5 ≤ M ≤ 1.0 (c) M ≤ 0.3 (a) I (d) 0.7 ≤ M ≤ 1.2 (b) II and III (c) I and IV 548. As compared to symmetrical airfoil, the angle of stall (d) none for a cambered airfoil is 551. The local skin friction coefficient for a compressible (a) less fluid in laminar boundary layer will be (b) more ( ) (c) same = f Ma (a) Cfx 1 ( ) (d) can’t say Rex 5 f√(Ma) (b) Cfx = Rex ( ) 549. Consider the following statements: = f Ma (c) Cfx 1 (I) Lift induced drag is caused by vortices. (Rex) 7 (II) Aileron is primarily used for pitch. (d) independent of freestream Mach number (III) Slots in flaps decrease the stall angle. 552. Which of the following statements about swept wings Which of the above statements is/are TRUE? in subsonic aircraft are INCORRECT? (a) I (a) Using swept wings the effective critical Mach num- (b) II and III ber is increased. Appendix E: Multiple Choice Questions in Aerospace Engineering 493

(b) By sweeping the wing, the drag divergence is 557. Consider a turbulent boundary layer over a flat plate. delayed to higher Mach numbers. The approximate value of shape factor at which the (c) Keeping all other parameters constant, the increase separation of boundary layer takes place, is of the wing sweep reduces the lift coefficient. (a) 1.4 (d) None. (b) 2.4 553. Consider an airplane in level turn. (c) 0 (I) The highest possible load factor. (d) 3.5 (II) The lowest possible velocity. 558. Based on freestream velocity and momentum thick- (III) The highest possible velocity. To obtain both a small turn radius and a large turn rate, ness of a boundary layer, the typical value of critical which of the above is/are TRUE? Reynolds number is (a) 2300 (a) II (b) 5 × 105 (b) I and III (c) 350 (c) I and II (d) 200 (d) III −→ 559. If a two-dimensional velocity field is given by v = 554. Consider the following statements for Blasius Bound- 2x3yî−3x2y2ˆj ary Layers: (I) For laminar flows the typical value of shape factor (a) rotational ( ) H is approximately 2.6. (b) incompressible (II) For turbulent flows, the shape factor falls in the (c) irrotational − range of 3.3 3.4. (d) unsteady and compressible. (III) The high value of shape factor reflects, weaker adverse pressure gradient. 560. The circulation at the midpoint of a flat plate, at 6o to a − (IV) Higher adverse pressure gradient increases the freestream of speed 40 ms 1,is Reynolds number at which transition into turbulence π may occur. (a) π6 Which of the above statements is/are CORRECT? (b) 3 8π (c) 3 π (a) I (d) 4 (b) I and II 3 (c) II, III, and IV 561. Consider a square ring vortex of side 2a. If each sides (d) III and IV has the strength , the velocity induced at the center of the ring is 555. In supersonic flows, which of the following waves can √ 3 2 never be made isentropic? (a) π√a (b) 2 2 (a) mach line √a 2 (b) expansion wave (c) √πa 2 (c) shock wave (d) a (d) none 562. The statement that “The airfoil generates sufficient cir- 556. If M1 and M2 are the upstream and downstream Mach culation to depress the rear stagnation point from its numbers across a normal shock wave, then which of the position, in the absence of circulation downstream to following is CORRECT? the sharp trailing edge” is known as (I) Kutta condition γ+ (a) (M ) = 1 (II) Joukowski postulation 2 minimum γ−1 γ+ (III) Kutta- Joukowski theorem (b) (M ) = 1 2 minimum 2γ Which of the above statements is/are CORRECT? γ+ (c) (M ) = 1 2 minimum 2γ (a) I ( ) = γ−1 (b) I and II (d) M2 minimum 2γ 494 Appendix E: Multiple Choice Questions in Aerospace Engineering

(c) II and III (a) M ≈ 2 (d) I and III (b) M ≈ 2.5 (c) M ≈ 1 563. The semispan of a rectangular wing of planform area (d) M ≈ 1.5 8.4 m2 is 3.5 m. The aspect ratio of the wing is 569. Which of the following statements are CORRECT? (a) 5.83 m2 2 (b) 11.66 m (a) In transonic flow, the density change is faster than 2 (c) 2.92 m the velocity change. 2 (d) 0.17 m (b) The density change in supersonic flow is slower than the velocity change. 564. In comparison to combustion chamber, the temperature (c) Mach number downstream of an oblique shock rise in afterburner is wave is always subsonic. (a) low (d) In hot-wire anemometry, the hot-wire sensor is gen- (b) equal erally made of Tungsten. (c) high (d) can’t say 570. In an aircraft wing if the incidence from root to tip is decreased, it is known as 565. Consider the following statements about afterburners: (I) Afterburners are not equipped with case and liners. (a) downwash (II) Use of afterburners increases the efficiency. (b) washout (III) Engines with afterburners consume lower amounts (c) slush of fuel. (d) slosh Which of the above statements is/are CORRECT? 571. A sailplane with a glide ratio of 12, flying 2400 m above (a) I and II the ground. The greatest distance it can travel in still air (b) II will be (c) II and III (d) none (a) 14,400 m (b) 28,800 m 566. Mixture of liquid hydrogen and liquid oxygen may pro- (c) 200 m duce the thrust up to (d) 100 m − (a) 1.5 kms 1 − 572. If the pitot tube becomes clogged, then which of the (b) 4 kms 1 − following parameters can’t be computed? (c) 4.5 kms 1 −1 (d) 5 Kms (a) airspeed (b) vertical speed 567. Consider the following statements about cryogenic (c) altitude rocket engines: (d) outside air temperature (I) Pyrotechnic initiators are used in cryogenic rocket engines. 573. Which of the following atmospheric conditions will (II) Cryogenic fuels are stored at room temperature lead to longer takeoff and lower rate of climb? and pressure. (III) Cryogenic rocket engines are also called as hybrid (a) high temperature, high relative humidity, and high rocket engines. altitude. Which of the above statements is/are CORRECT? (b) high temperature, low relative humidity, and low (a) I and III altitude. (b) I (c) low temperature, low relative humidity, and low (c) II and III altitude. (d) III (d) high temperature, low relative humidity, and high altitude. 568. In centrifugal compressors, the flow sometimes leaves the impeller at Mach number Appendix E: Multiple Choice Questions in Aerospace Engineering 495

574. For an airfoil, consider the following statements: (c) velocity variation in the flow field. (I) Geometrical incidence is the angle between the chord (d) density gradient variation in the flow field. of the profile and the direction of motion of the airfoil. (II) Absolute incidence is the angle between the axis of 580. If the Reynolds number in a boundary layer flow zero lift of the profile and the direction of motion of the decreases then airfoil. Which of the above statements is/are CORRECT? (a) Mach number increases. (b) Pressure gradient normal to body surface decreases. (a) I (c) Boundary layer thickness increases. (b) II (d) Boundary layer thickness decreases. (c) I and II (d) none 581. For a supercritical airfoil, which of the following statement is CORRECT? 575. For a given lift curve, decrease of aspect ratio increases (a) Has higher wave drag. (a) geometrical incidence only (b) Has higher critical Reynolds number. (b) induced drag coefficient only (c) Greatly reduces shock-induced boundary layer sep- (c) both geometrical incidence and induced drag coef- aration. ficient (d) Has lower drag divergence Mach number. (d) none 582. When a moving fluid is brought to rest adiabatically, 576. In a straight level flight, for a wing of elliptic loading, then which of the following statement is CORRECT? the condition for minimum drag is (a) Both stagnation pressure and stagnation tempera- = 3 ture are conserved. (a) CD0 kCL 2 (b) Stagnation pressure is not conserved but stagnation = 3 (b) CD0 kCL 3 temperature is conserved. = 2 (c) CD0 kCL (c) Stagnation pressure is conserved but stagnation = 2 (d) CD0 kCL temperature is not conserved. (d) Both stagnation pressure and stagnation tempera- 577. Air flows from a reservoir through a convergent– ture are not conserved. divergent nozzle at low subsonic speed and is exhausted into the atmosphere. A pitot tube is mounted 583. Which of the following statements are CORRECT at the midsection of the nozzle and traversed along the about steady flow? length of the nozzle from the exit to the reservoir end. The pressure recorded by the pitot tube will (a) It occurs when pressure does not change along the flow. (a) increase during traverse. (b) It occurs when conditions do not change with time (b) decrease during traverse. at any point. (c) decrease up to the throat and then increase during (c) It occurs when velocity does not change. traverse. (d) It occurs when conditions change gradually with (d) remain constant during traverse. time.

578. For the same test-section speed and flow rate, the effi- 584. The mixing length model was first proposed by ciency of a closed-circuit low-speed wind tunnel is (a) Ludwig Prandtl (a) greater than that of an open circuit wind tunnel. (b) Theodore von Karman (b) less than that of an open circuit wind tunnel. (c) Albert Einstein (c) equal to that of an open circuit wind tunnel. (d) Isaac Newton (d) not comparable with that of an open circuit tunnel because of design differences. 585. Consider the following statements about the boundary layer flow: 579. The Schlieren technique works on the basis of (I) The flow field outside the boundary layer is rotational. (a) density variation in the flow field. (II) The pressure inside the boundary layer is equal to (b) pressure variation in the flow field. 496 Appendix E: Multiple Choice Questions in Aerospace Engineering

that of outside flow. (a) Both heat and work may cross the system boundary. (III) The skin friction coefficient of laminar boundary (b) Both heat and work are path functions. layer is more than the turbulent boundary layer. (c) Both heat and work are property of the system. Which of the above statements is/are CORRECT? (d) Heat flows when the system and surrounding are not in equilibrium which is not necessary for work. (a) I and II (b) II 591. A thin cylinder of inner radius 500 mm and thickness (c) III 10 mm is subjected to an internal pressure of 5 MPa. (d) all The average circumferential (hoop) stress in MPa is

586. Which of the following statements are CORRECT? (a) 100 (b) 250 (a) The jet velocity in turbofan engine is less than that (c) 500 of turbojet engine. (d) 1000 (b) Fighter bombers use turboprop engine. (c) Adding ammonia and water vapor in compressor 592. The maximum gas ﬂow rate that can be handled by decreases the effective power output of turbine. a multistage axial compressors at a given rotational is (d) Trim tabs are used for the same purpose as hydraulic dictated by actuators. (a) compressor surge 587. In centrifugal pumps, to obtain higher ﬂow output the (b) rotating stall impellers can be (c) choking (d) optimum design pressure ratio (a) connected in series (b) connected in parallel 593. For a turbine stage, which one of the following losses (c) connected either in series or in parallel occurs due to the turning of the wall boundary layer (d) cannot be connected through an angle due to curved surface?

588. Consider the following statements: (a) profile loss (I) Perfectly straight column and axial load apply. (b) annulus loss (II) Length of column is large as compared to its cross- (c) tip clearance loss sectional dimensions. (d) secondary flow loss (III) The shortening of column due to direct compression is not neglected. 594. A column has a rectangular cross section of 10 mm × (IV) The failure of column occurs due to buckling alone. 20 mm and a length of 1 m. The slenderness ratio of the Which of the above statements is/are taken as assump- column is close to tion in Euler’s Column Theory? (a) 200 (a) I, II, and III (b) 346 (b) I, II, and IV (c) 477 (c) II, III, and IV (d) 1000 (d) all 595. A streamline and an equipotential line in a flow field 589. Airy stress function satisfies which of the following equation? (a) are parallel to each other. (b) are perpendicular to each other. (a) ∇2φ = 0 (c) intersect at an acute angle. (b) ∇2φ = g(x) (d) are identical. (c) ∇3φ = 0 (d) ∇4φ = 0 596. Consider the following statements: (I) Gases are considered incompressible when Mach 590. Which of the following is an INCORRECT statement? number is less than 0.2. Appendix E: Multiple Choice Questions in Aerospace Engineering 497

(II) A Newtonian fluid is incompressible and nonvis- (a) Potential function must satisfy the Laplace equa- cous. tion, whereas stream function need not. (III) An ideal fluid has negligible surface tension (b) Stream function must satisfy the Laplace Equation, Which of these statements is/are correct? whereas potential function need not. (c) Both stream function and potential function satisfy (a) II and III the Laplace Equation. (b) II (d) Neither the stream function nor the potential func- (c) I tion need to satisfy the Laplace Equation. (d) I and III dCL 602. In thin airfoil theory, the lift curve slope α = 2π 597. Which one of the following statements is correct? Irro- d is valid for tational flow is characterized as the one in which (a) cambered airfoil. (a) The fluid flows along a straight line. (b) symmetric airfoil. (b) The fluid does not rotate as it moves along. (c) Joukowski airfoil. (c) The net rotation of fluid particles about their mass (d) any airfoil shape. centers remains zero. (d) The streamlines of flow are curved and closely 603. Which of the following stays constant for the flow spaced. through a Prandtl–Meyer expansion wave?

598. In a two-dimensional incompressible steady flow, the (a) density = x velocity component u Ae is obtained. What is the (b) temperature other velocity component, v? (c) mach Number (d) entropy (a) v = Aexy = y (b) v Ae 604. Downward deflection of the flap increases the lift coef- =− x + ( ) (c) v Ae y f x ficient of an airfoil by (d) v =−Aeyx + f (y) (a) increasing the local airspeed near the trailing edge. 599. The continuity equation for a steady flow states that (b) increasing the effective camber of the airfoil. (c) delaying the flow separation. (a) Velocityfield is continuous at all points in flow field. (d) controlling the boundary layer growth. (b) The velocity is tangential to the streamlines. (c) The stream function exists for steady flows. 605. The maximum thickness-to-chord ratio for NACA (d) The net efflux rate of mass through the control sur- 24012 airfoil is faces is zero. (a) 0.12 600. For a stream function to exist, which of the following (b) 0.24 conditions should hold? (c) 0.40 (I) The flow should always be irrotational. (d) 0.01 (II) Equation of continuity should be satisfied. (III) The fluid should be incompressible. 606. The maximum possible value of the pressure coefficient (IV) Equation of continuity and momentum should be in an incompressible flow is satisfied. Which of the following is/are CORRECT? (a) 0.25 (b) 0.5 (a) II (c) 0.75 (b) II and III (d) 1 (c) I, III, and IV (d) all 607. An inviscid and irrotational flow becomes rotational on passing through 601. For a two-dimensional incompressible and irrotational flows (a) an oblique shock wave. (b) a normal shock wave. 498 Appendix E: Multiple Choice Questions in Aerospace Engineering

608. Laminar ﬂow airfoil is used to reduce the 614. The geometrical features of a supercritical airfoil are

(a) pressure drag (a) sharp leading edge, flat suction surface, and no cam- (b) induced drag ber at the rear. (c) skin friction drag (b) rounded leading edge, curved suction surface, and (d) wave drag no camber at the rear. (c) sharp leading edge, curved suction surface, and high 609. Consider a steady inviscid flow in a convergent– camber at the rear. divergent nozzle with a normal shock in the divergent (d) rounded leading edge, flat suction surface, and high section. The static pressure downstream of the normal camber at the rear. shock will 615. Which one of the following high-lift devices results in (a) decrease isentropically to the static pressure at the higher stalling angle? nozzle exit. (b) increase isentropically to the static pressure at the (a) plain flap nozzle exit. (b) fowler flap (c) either increase or decrease depending on the mag- (c) split flap nitude of the static pressure at the nozzle exit. (d) leading edge flap (d) remain constant. 616. The total pressure at a point is defined as the pressure 610. If the Mach number in a turbulent boundary layer over a when the flow is brought to rest flat plate is increased by keeping the Reynolds number unchanged, then the skin friction coefficient will (a) isentropically (b) adiabatically (a) increase (c) isobarically (b) decrease (d) isothermally (c) remain constant (d) becomes infinity 617. The drag divergence Mach number of an airfoil is

611. In supersonic wind tunnel design, an oblique shock dif- (a) always higher than the critical Mach number. fuser is preferred over a normal shock diffuser because (b) equal to the critical Mach number at zero angle of attack. (a) it increases the total pressure loss. (c) a fixed value for a given airfoil. (b) it reduces the total pressure loss. (d) the Mach number at which a shock wave first (c) it rapidly accelerates the flow. appears on the airfoil. (d) it rapidly decelerates the flow. 618. The Joukowski airfoil is studied because 612. The variation of downwash along the span of an untwisted wing of elliptic planform is (a) it is used in many aircraft. (b) it has a simple geometry. (a) constant (c) it has the highest lift curve slope. (b) parabolic (d) it is easily transformed into a circle, mathemati- (c) sinusoidal cally. (d) elliptic 619. Two airfoils of the same family are operating at the 613. The flow past an airfoil is modeled using the vortex same angle of attack. The dimensions of one airfoil are sheet. The strength of vortex sheet at the trailing edge thrice as large as the other one. The ratio of the minimum will be pressure coefficient of the larger airfoil to the minimum pressure coefficient of the smaller airfoil is (a) 0.5 (b) 1 (a) 1 (b) 3 Appendix E: Multiple Choice Questions in Aerospace Engineering 499

(c) 5 (d) None of the above. (d) 6 625. Which of the following is not true for a gouge flaps? 620. Wing A has a constant chord c and span b. Wing B is identical to A, but has a span 4b. When both wings are (a) It increases the chord length. operating at same geometric angle of attack at subsonic (b) It affects the trim. speeds, then (c) It increases the wing area. (d) None of the above. (a) wing A produces a smaller lift coefficient than wing B. 626. If the lift coefficient of a wing is increased by two times, (b) wing A produces a greater lift coefficient than the then the induced drag becomes wing B. (c) wing A and B produce the same lift coefficients. (a) two times lower. (d) freestream Mach number decides, which wing pro- (b) two times higher. duces the greater lift coefficient. (c) three times higher. (d) four times higher. 621. In comparison to a laminar boundary layer, the turbulent boundary layer remains attached on the upper surface 627. The critical Mach number for a thick airfoil will be of an airfoil over a longer distance, because (a) lesser than a thin airfoil. (a) the turbulent boundary layer is more energetic and (b) greater than a thin airfoil. hence can overcome the adverse pressure gradient (c) equal to a thin airfoil. better. (d) cannot be related to thin airfoil. (b) the turbulent boundary layer is thicker, hence the 628. Consider the three-dimensional motion of fluid in the velocity gradients in it are smaller, consequently vicinity of a vortex filament. Which one of the following viscous losses are less. statement is not a Helmholtz’s theorem? (c) the laminar boundary layer develops more skin friction and hence slows down more rapidly. (a) The strength of a vortex filament is constant along (d) turbulence causes the effective coefficient of viscos- its length. ity to reduce, resulting in lesser loss of momentum (b) A vortex filament cannot end in a fluid. It may in the boundary layer. extend to the boundaries of the fluid. (c) A vortex filament cannot form a closed path. 622. In a compressible flow over a flat plate, the boundary (d) In the absence of rotational external forces, a fluid layer thickness (δ) is given by that is initially irrotational, remains irrotational . (a) √5 0x Rex . 629. What is the primary reason for an aircraft with delta (b) 5 0x Rex wings having high stall angles? . 2 (c) 5 0x Rex . 2 (a) The wing’s leading edge does not contact the shock (d) √5 0x Rex wave boundary formed at the nose of the fuselage (b) The delta planform maximizes wing area with a 623. For a stream tube, the area–velocity relation is given by very low wing per unit loading. dA = − 2 dv (c) Due to highly robust nature of the delta wings. (a) A 1 M v dA = ( − ) dv (d) Due to vortex formation at the leading edge which (b) A M 1 v dA = 2 − dv energizes the flow. (c) A M 1 v dA = ( − ) dv (d) A 1 M v 630. An aircraft glides a distance of 5000 m, in which the loss of altitude is 1000 m. If the freestream velocity is 624. An increase in the angle of attack has the following 100 ms−1, the aircraft’s glide ratio is effects. (a) 0.5 (a) The center of pressure moves backward. (b) 5 (b) The center of pressure moves forward. (c) 50 (c) Both (a) and (b). (d) 500 500 Appendix E: Multiple Choice Questions in Aerospace Engineering

631. The thrust developed in the jet engine is due to (a) 0.25 (b) 0.5 (a) balanced force (c) 0.75 (b) unbalanced force (d) 1 (c) both (a) and (b) (d) none of the above 639. In an engine, the maximum pressure loss occurs across the 632. The propulsive efﬁciency of the aircraft’s jet engine is given by (a) inlet (b) compressor (a) energy input rate/propulsive power (c) turbine (b) propulsive power/energy input rate (d) nozzle (c) propulsive power/work done by engine (d) work done by engine/propulsive power 640. Speciﬁc impulse will be maximum for

633. Flapper valves are present in the (a) liquid rocket (b) solid rocket (a) pulsejet engine (c) electric rocket (b) ramjet engine (d) jet engine (c) scramjet engine (d) turbojet engine 641. The combustor efﬁciency of an aircraft engine

634. The engine with afterburner is also called as (a) increases slowly with the altitude. (b) decreases with the altitude. (a) augment engine (c) increase rapidly with the altitude. (b) side engine (d) remains constant with change in the altitude. (c) reheat engine (d) additional engine 642. Premixed ﬂame when compared to diffusion ﬂame has a

635. The gas turbine engine was invented by (a) worse control on fuel–air ratio. (b) better control on fuel–air ratio. (a) Brayton (c) no control on fuel–air ratio. (b) Otto (d) none of the above. (c) Atkinson (d) John Barber 643. Which of the following is not true for a Ramjet engine?

636. The compressor used for aircraft’s application must (a) It has a high thrust-to-weight ratio. have (b) It works well at off-design Mach numbers. (c) As compared to other jet engines, its fuel consump- (a) low airflow capacity tion at subsonic speeds is very high. (b) high frontal area (d) It has zero takeoff thrust. (c) high pressure ratio per stage (d) low volume flow rate 644. The relation between polytropic efficiency ηp and the overall efficiency (ηo) of a compressor is 637. In the rotor of an axial flow compressor, the absolute velocity of the fluid will (a) ηp = ηo (b) ηp > ηo (a) decrease. (c) ηp < ηo (b) increase. (d) no relation exists. (c) initially increases and then decrease. (d) remain constant. 645. The relation between polytropic efficiency ηp and the overall efficiency (ηo) of a turbine is 638. In the combustion chamber of a jet engine, the CO2 emission in the diffusion flame is maximum at the (a) ηp = ηo equivalence ratio of (b) ηp > ηo Appendix E: Multiple Choice Questions in Aerospace Engineering 501

(c) ηp < ηo (d) combustion intensity will go down. (d) no relation exists 652. Because of the diffusion in the inlet of a jet engine 646. In the constant area section, across the fan (a) air velocity decreases and the pressure increases. (a) both velocity and the static pressure increase. (b) both air velocity and the pressure decrease. (b) velocity and static pressure are constant. (c) both air velocity and the pressure increase. (c) velocity is constant and the static pressure (d) air velocity increases and the pressure decreases. increases. (d) velocity increases and the static pressure decreases. 653. The exhaust nozzle’s pressure ratio is a strong function of 647. The specific speed of a centrifugal compressor is generally (a) Reynolds number (b) Prandtl number (a) higher than that of an axial compressor. (c) Euler number (b) less than that of a reciprocating compressor. (d) Mach number (c) independent of the type of the compressor but depends only on the size of the compressor. 654. In a turbojet engine, the pressure thrust as compared to (d) more than the specific speed of the reciprocating the momentum thrust is compressor but less than that of axial compressor. (a) almost equal 648. Consider the following statement: (b) quite high (i). Almost all flow losses take place in the divergent (c) quite low section of the nozzle. (d) cannot predict (ii). Normal shocks are likely to occur in the convergent part of the nozzle. 655. Which of the following is the lightest and most volatile (iii). Efficiency of reaction turbines is higher than that liquid fuel? of impulse turbine. (a) kerosene Out of these statements, (b) gasoline (a) All are correct. (c) fuel oil (b) (ii) and (iii) are correct. (d) vegetable oil (c) (i) and (ii) are correct. 656. The compression ratio for petrol engines is (d) (i) and (iii) are correct. (a) 3 to 6 649. An impulse turbine stage is characterized by the expan- (b) 8 to 10 sion of the gases in (c) 10 to 15 (a) stator nozzles. (d) 15 to 20 (b) rotor nozzles. 657. Propellants in the rocket engine should have (c) both stator and rotor nozzles. (d) neither stator nozzle nor rotor nozzle. (a) high calorific value. (b) low calorific value. 650. Multistage reaction turbine are employed to achieve (c) high viscosity. (a) large pressure drop. (d) lower thermal conductivity. (b) large mass flow rate. 658. In an axial flow compressor, the exit flow angle devia- (c) large volume flow rate. tion from the blade angle is a function of (d) large pressure rise. (a) space–chord ratio. 651. The maximum temperature from the combustor is lim- (b) blade camber. ited in jet engines, because (c) blade camber and incidence angle. (a) it is difficult to burn the fuel. (d) blade camber and space–chord ratio. (b) the air–fuel ratio is too lean. 659. A double-throw crankshaft operates at (c) turbine blades cannot accept very high temperature. 502 Appendix E: Multiple Choice Questions in Aerospace Engineering

o = 3E (a) 90 (c) K (1−2ν) (b) 180o = E (d) K 2(1+ν) (c) 270o (d) 360o 666. If Airy’s function is Φ, then which of the following is correct? 660. Engine-speciﬁc weight is deﬁned as the weight of the engine per unit (a) ∇Φ = 0 (b) ∇2Φ = 0 (a) volume (c) ∇3Φ = 0 (b) mass (d) ∇4Φ = 0 (c) density (d) power 667. Consider u is the displacement, x is the coordinate in axial direction, M is the moment and V is shear force. 661. The intensity of stress which causes unit strain is termed In an elastic beam problem, boundary conditions at free as end will be

(a) modulus of rigidity (a) M = 0 and V = 0 (b) bulk modulus = ∂u = (b) u 0 and ∂x 0 (c) young modulus (c) M = 0 and u = 0 (d) modulus of elasticity = ∂u = (d) V 0 and ∂x 0 662. Capability of the material in absorbing the large amount 668. Critical load for a fixed-free column of length l will be of energy before the fracture is π2 (a) P = EI cr l2 (a) resilience π2 (b) P = EI (b) ductility cr 2l2 π2 (c) P = EI (c) stiffness cr 4l2 π2 (d) toughness (d) P = 4 EI cr l2 663. Resilience is considered when the material is subjected 669. For a plane stress problem, the state of stress can be to represented by Mohr’s circle. The equation of Mohr’s circle is (a) shock loading σ +σ 2 σ −σ 2 (b) creep (a) σ − X Y + τ 2 = Y X n 2 2 (c) fatigue σ +σ 2 σ −σ 2 (b) σ + X Y + τ 2 = Y X n 2 2 (d) fracture σ −σ 2 σ +σ 2 (c) σ + X Y + τ 2 = Y X n 2 2 σ −σ 2 σ +σ 2 σ − X Y + τ 2 = Y X 664. The highest load, which a spring can carry without per- (d) n 2 2 manent distortion, is known as 670. Due to presence of taper in the structure of an aircraft (a) proof stress wing, which of the following remains unchanged com- (b) proof load pared to the case with no taper and same applied loads? (c) proof stiffness (d) proof resilience (a) axial stress in longitudinal direction. (b) shear flow due to torsional moment applied. 665. The relation between the Bulk modulus (K), Young (c) shear flow due to applied bending moment. modulus (E) and Poisson’s ratio (ν) of the material is (d) none of the above. given by

= E (a) K 3(1−2ν) E.1 Keys = E(1+ν) (b) K 2 (See Tables E.1 and E.2) Appendix E: Multiple Choice Questions in Aerospace Engineering 503

Table E.1 Questions 1–440

Q A Q A Q A Q A Q A Q A Q A Q A 1. b 56. a 111. c 166. b 221. c 276. d 331. c 386. b 2. b 57. d 112. d 167. b 222. b 277. a 332. b 387. b 3. c 58. c 113. a 168. c 223. b 278. c 333. c 388. c 4. c 59. b 114. b 169. c 224. d 279. b 334. c 389. c 5. b 60. a 115. a 170. d 225. a 280. b 335. a 390. d 6. c 61. a 116. b 171. a 226. d 281. c 336. c 391. d 7. d 62. c 117. c 172. c 227. d 282. d 337. b 392. a 8. c 63. d 118. c 173. c 228. b 283. a 338. b 393. a 9. d 64. c 119. b 174. b 229. b 284. b 339. a 394. c 10. c 65. b 120. c 175. c 230. a 285. c 340. d 395. c 11. d 66. c 121. a 176. b 231. c 286. b 341. a 396. b 12. c 67. c 122. d 177. d 232. b 287. b 342. b 397. d 13. c 68. a 123. a 178. b 233. b 288. c 343. d 398. d 14. a 69. b 124. b 179. d 234. d 289. b 344. b 399. b 15. a 70. d 125. a 180. a 235. d 290. a 345. c 400. b 16. d 71. a 126. c 181. a 236. b 291. a 346. c 401. a 17. a 72. b 127. a 182. d 237. b 292. c 347. b 402. c 18. b 73. a 128. b 183. b 238. c 293. c 348. d 403. a 19. b 74. c 129. c 184. b 239. b 294. c 349. a 404. b 20. d 75. a 130. c 185. c 240. d 295. d 350. a 405. c 21. c 76. d 131. d 186. a 241. c 296. d 351. d 406. d 22. c 77. b 132. c 187. c 242. b 297. b 352. c 407. d 23. c 78. a 133. c 188. b 243. d 298. a 353. b 408. d 24. b 79. c 134. a 189. a 244. d 299. d 354. b 409. c 25. b 80. b 135. b 190. a 245. c 300. d 355. d 410. a 26. a 81. c 136. b 191. c 246. c 301. b 356. c 411. b 27. c 82. b 137. a 192. a 247. b 302. c 357. a 412. a 28. a 83. a 138. c 193. b 248. a 303. d 358. b 413. a 29. d 84. b 139. c 194. b 249. b 304. b 359. d 414. b 30. d 85. a 140. d 195. c 250. b 305. c 360. b 415. c 31. a 86. b 141. b 196. c 251. c 306. c 361. b 416. a 32. d 87. d 142. c 197. b 252. a 307. d 362. a 417. b 33. c 88. a 143. c 198. d 253. b 308. d 363. a 418. d 34. c 89. c 144. b 199. b 254. a 309. c 364. c 419. a 35. a 90. a 145. c 200. d 255. c 310. c 365. d 420. b 36. b 91. c 146. d 201. c 256. b 311. b 366. d 421. b 37. b 92. d 147. a 202. a 257. c 312. d 367. c 422. c 38. a 93. c 148. b 203. a 258. d 313. d 368. d 423. d 39. a 94. b 149. a 204. c 259. b 314. c 369. c 424. c 40. d 95. c 150. b 205. d 260. a 315. b 370. c 425. a 41. b 96. d 151. c 206. b 261. b 316. b 371. a 426. a 42. c 97. c 152. a 207. d 262. b 317. d 372. b 427. c 43. a 98. b 153. a 208. a 263. d 318. b 373. c 428. d 44. c 99. a 154. d 209. b 264. c 319. c 374. d 429. b 45. a 100. c 155. c 210. d 265. a 320. c 375. a 430. d 46. b 101. c 156. b 211. c 266. c 321. c 376. a 431. a 47. c 102. a 157. c 212. c 267. c 322. d 377. b 432. a 48. b 103. d 158. b 213. d 268. b 323. d 378. a 433. d 49. c 104. b 159. a 214. d 269. d 324. b 379. b 434. c 50. d 105. c 160. c 215. a 270. a 325. a 380. c 435. a 51. c 106. c 161. b 216. d 271. d 326. a 381. c 436. d 52. a 107. b 162. d 217. c 272. b 327. d 382. b 437. c 53. b 108. a 163. a 218. c 273. a 328. b 383. d 438. d 54. d 109. a 164. b 219. b 274. b 329. a 384. d 439. b 55. d 110. d 165. c 220. b 275. c 330. d 385. a 440. d 504 Appendix E: Multiple Choice Questions in Aerospace Engineering

Table E.2 Questions 441–670

Q A Q A Q A Q A Q A 441. b 496. c 551. b 606. d 661. d 442. d 497. d 552. d 607. d 662. d 443. b 498. d 553. c 608. c 663. a 444. d 499. c 554. a 609. b 664. b 445. d 500. a 555. d 610. b 665. a 446. c 501. a 556. b 611. b 666. d 447. c 502. b 557. b 612. a 667. a 448. d 503. b 558. c 613. c 668. c 449. a 504. d 559. a 614. d 669. a 450. a 505. c 560. d 615. c 670. b 451. b 506. c 561. c 616. a 452. b 507. b 562. b 617. a 453. d 508. d 563. a 618. d 454. c 509. b 564. c 619. a 455. c 510. c 565. d 620. c 456. b 511. d 566. c 621. a 457. d 512. b 567. a 622. a 458. b 513. c 568. c 623. c 459. d 514. b 569. d 624. b 460. a 515. a 570. b 625. b 461. c 516. c 571. b 626. d 462. d 517. d 572. a 627. a 463. c 518. c 573. a 628. c 464. d 519. b 574. c 629. d 465. a 520. b 575. c 630 b 466. b 521. c 576 d 631. b 467. c 522. d 577. d 632. b 468. b 523. c 578. a 633. a 469. d 524. d 579. d 634. c 470. b 525. a 580. c 635. d 471. d 526. b 581. c 636. c 472. a 527. a 582. b 637. b 473. b 528. c 583. b 638. c 474. c 529. d 584. a 639. b 475. b 530. d 585. b 640. c 476. a 531. c 586. a 641. b 477. c 532. c 587. b 642. b 478. b 533. a 588. b 643. b 479. d 534. a 589. d 644. b 480. c 535. c 590. c 645. c 481. b 536. b 591. b 646. c 482. c 537. d 592. c 647. c 483. b 538. c 593. d 648. d 484. c 539. a 594. b 649. a 485. d 540. c 595. b 650. a 486. a 541. a 596. d 651. c 487. d 542. b 597. c 652. a 488. b 543. b 598. c 653. d 489. c 544. c 599. c 654. c 490. a 545. d 600. a 655. b 491. c 546. d 601. c 656. b 492. a 547. c 602. d 657. a 493. b 548. a 603. d 658. c 494. b 549. a 604. b 659. b 495. a 550. b 605. a 660. d Letter of Acknowledgment F

The acknowledgment letter received from the honorable defense minister for the book “Essentials of Aircraft Armaments” published by Springer (2016).

A Anticyclone, 16 Absolute altitude, 7 Archimedes principle, 28 Absorption, 11 Area–Mach number relation, 211 Acoustic intensity, 347 Area–velocity relation, 207 Acoustic intensity level, 347 Armstrong Line, 7 Acoustic power, 347 Aspect ratio, 35 Acoustics, 347 Atmosphere, 4 Active control, 346 Fédération Aéronautique Internationale, 4 Active flow control, 346 Primary Layers in the Atmosphere, 4 Adiabatic flow ellipse, 213 Exosphere, 6 Adiabatic lapse rate, 14 Mesopause, 6 Adverse pressure gradient, 256 Mesosphere, 6 Aerodynamic center, 141 Stratopause, 6 Aerodynamic forces, 28 Stratosphere, 5 drag, 28 Thermosphere, 6 lift, 28 Tropopause, 4 Aerodynamic mixing enhancement, 344 Troposphere, 4 Aerodynamic moments, 29 Secondary Layers in the Atmosphere, 6 pitching moment, 29 Heterosphere, 6 rolling moment, 29 Homosphere, 6 yawing moment, 29 Ionosphere, 6 Aerodynamics, 3, 27 Ozone Layer, 6 aircraft aerodynamics, 4 Planetary Boundary Layer, 6 industrial aerodynamics, 4 Average kinetic energy, 31 Aerothermodynamics, 4 Axial force coefficient, 39 Ageostrophic wind, 18 Axis-switch, 334 Aileron, 28 Axisymmetric flows, 83 Airbreathing, 4 Air-Breathing Engine Intakes, 393 Aircraft, 27 Airfoil, 34 B Airfoil thickness, 34 Back pressure, 223 Airspeed, 94 Baroclinic torque, 346 Calibrated Airspeed, 95 Barotropic fluid, 130 Equivalent Airspeed, 95 Bernoulli’s equation, 87 Ground Speed, 95 Bernoulli constant, 87 Indicated Airspeed, 95 Biot and Savart law, 154 Altitude, 7 Blackouts, 194 Angle of attack, 35, 37 Blasius solution, 263 Angle of incidence, 35 Boltzmann constant, 31 Angle of inclination, 35 Boundary layers, 48, 251 Angular velocity, 72 Momentum thickness, 252 Anhedral angle, 35 x - Momentum Equation, 259 y - Momentum Equation, 259 Boundary layer separation, 254

no-slip condition, 255 Curl of a vector, 61 Boundary layer thickness, 251 Cyclone, 16 Boussinesq hypothesis, 323 Bricfielder, 20 Broadband shock-associated noise, 352 D Bump, 374 Degree of turbulence, 288 Buoyant jet or forced plume, 321 Degrees of freedom, 193 De Laval nozzle, 222 Density, 31 C Differential analysis, 65 Calorical equation of state, 192, 193 Diffuser effectiveness, 293 Camber, 34 Diffuser efficiency, 292 Camber line, 133 Dihedral angle, 35 Cape Doctor, 20 Dimensional analysis, 41 Carnot cycle, 187 Buckingham pi theorem, 42 Cauchy–Riemann equations, 84 Rayleigh’s method, 42 Cavity covered with porous surface, 378 Dimensionless velocity, 206 Center of pressure, 39 Direct Numerical Simulation, 332 Characteristics decay, 322 Displacement thickness, 251 Characteristic velocity, 212 Divergence angle, 290 Chinook, 20 Divergence of a vector, 61 Choked, 223 Doldrums, 20 Chord, 34 Dot product, 60 Chord length, 34 Doublet, 113 Chord line, 34, 133 Downwash, 145 Circulation, 62, 123, 127 Drag coefficient, 39 clockwise circulation, 132 Dynamic pressure, 88 counterclockwise, 132 Dynamic similarity, 287 Clausius inequality, 188 Dynamic viscosity, 325 Clausius Statement, 186 Closed system, 181 Closed test section, 285 E Closed-throat tunnel, 290 Eddy viscosity, 276, 325 Coefficient of pressure, 92 Edney classification, 365 Coefficient of thermal conductivity, 185 Effuser, 288 Coefficient of viscosity, 33 Ekman layer, 19 Newton’s law of viscosity, 33 Ekman number, 19 Sutherland formula, 33 Emission, 11 Co-flowing jet, 321 Energy equation, 99, 200 Compressibility, 47 Energy equation for an open system, 185 isentropic compressibility, 47 Energy integral equation, 262 isothermal compressibility, 47 Enthalpy, 183 Compressible flows, 199 stagnation enthalpy, 205 Compressible fluids, 181 static enthalpy, 205 Compressible jets, 322 Entropy, 181, 187 Compressible laminar flow over a flat plate, 266 Entropy layer, 238 Compression corner, 226 Entropy mode acoustics, 347 Concept of enthalpy, 183 Environmental lapse rate, 10 Constant pressure, 184 Equations of fluid motion, 57 Constant volume, 184 Equipotential lines, 85 Continuity equation, 64, 67, 200 Equivalent cone angle, 290 Continuum flow, 45 Eulerian or field description, 63 Knudsen number, 45 Euler number, 44, 287 Contraction cone, 288 Euler’s equation, 207 Control surface, 181 Expansion corner, 226 Control volume, 181 Expansion fan, 226 Convective derivative, 64 Convective Mach number, 346 Convective speed, 346 F Convergent–divergent diffuser, 304 Fan efficiency, 293 Convergent–divergent nozzle, 222 Fanno flow, 215 Coriolis force, 14, 130 Favorable pressure gradient, 256 Coromuel, 21 Ffowcs Williams–Hawkings equation, 349 Correction factor, 299 Finite control mass approach, 65 Correctly expanded, 322 Finite control volume approach, 65 Cross product, 58 First law of thermodynamics, 64, 181 Index 509

Flaps, 28 hypersonic similarity parameter, 244 Flow control, 346 Hypersonic wind tunnel, 309 Flow deflection angle, 228, 230, 237 Flow similarity, 43 dynamic similarity, 43 I geometric similarity, 43 Impinging jet, 321 kinematic similarity, 43 Incompressible jets, 322 scale factor, 43 Indraft tunnel, 297 Flow velocity, 31 Induced drag, 147 Flow work, 185 Infinitesimal fluid element approach, 65 Fluidity, 3 Infinite vortex, 155 Fluids, 3 Inlet, 394 Forced vortex, 149 Integral analysis, 65 Fourier’s law, 185 Intensity of turbulence, 288 Fourier’s law heat conduction, 185 Intensity of wave, 10 Free molecular flow, 45 Intermittent-blowdown wind tunnel, 296, 297 Free or submerged jet, 321 Intermittent-indraft wind tunnels, 297 Free vortex, 149 Internal energy, 181 Froude number, 44, 287 Inviscid flow, 48 Frozen, 223 Isentropic efficiency or diffuser effectiveness, 292 Fully developed region, 322 Isentropic process, 205 Fuselage, 28 Isolated system, 181 Isotropic, 325

G Gauss divergence theorem, 63 J Geometric altitude, 7 Jet centerline pitot pressure decay, 341 Geometric similarity, 287 Jet controls, 344 Geostrophic wind, 16 Jet streams, 20 Gibbs free energy, 189 Gliding angle, 28 Gradient of, 60 K directional derivative, 61 Karman Line, 7 Gradient theorem, 63 Karman–Pohlhausen approximate solution method, 270 Green house effect, 4 Kelvin–Helmholtz instability, 344 Gun tunnel, 311 Kelvin–Helmholtz vortex rings, 328 Kelvin–Planck Statement, 186 Kelvin’s circulation theorem, 129 H Khamsin, 21 Haboob, 21 Kinematic similarity, 287 Half-saddle point, 255 Kinematic turbulent viscosity, 325 Harmattan, 21 Kinetic energy flux factor, 292 Hawk, 21 Kinetic energy thickness, 253 Heat sink, 186 Kinetic theory of gases, 30 Heat source, 186 Kronecker delta, 324 Heavier-than-air, 27 Kutta condition, 128 Helmholtz free energy, 189 Kutta–Joukowski theorem, 123 Helmholtz’s theorems, 150 Hess and Smith method, 169 Hiemenz flow, 267 L Hodograph, 49 Lagrange stream function, 80 Homogeneous turbulence, 274 Lagrangian or the particle or the material description, 63 Honeycomb structures, 288 Laminar boundary layers, 263 Hooke’s law, 3 Laminar separation bubble, 257 Horizontal Buoyancy, 290 Laminar sub-layer, 277 Horizontal stabilizer, 28 Laminar–Turbulent transition, 271 Hurricanes, 16, 148 Land breeze, 19 Hydrostatic pressure, 31 Laplace’s equation, 117 Hypersonic, 4 Lapse rate, 9 Hypersonic flow, 49, 237 Large Eddy Simulation, 330 density ratio, 240 Leading edge, 34 θ − β − M relation, 240 L’ Hospital’s rule, 136 Prandtl–Meyer expansion fan, 242 Lift, 28 pressure ratio, 240 Lift coefficient, 39 temperature ratio, 240 Lift-to-drag ratio, 246 Hypersonic similarity, 243 Lighter-than-air, 27 510 Index

Lighthill stress tensor, 349 Static Pressure Ratio, 227 Line integral, 62 Static Temperature Ratio, 227 Line source distribution, 172 Oblique shock wave cancelation, 362 Line vortex, 114 Open system, 181 Local and Material Derivatives, 63 Open test section, 285 Logarithmic buffer layer, 278 Optical ﬂow visualization, 344 Loo, 21 Ornithopter, 27 Losses in subsonic wind tunnels, 293 Orthogonal coordinate system, 58 Low-density tunnels, 286 Oswatitsch Relation, 369 Ludwieg tube, 311 Overexpanded, 322 Ludwig Prandtl, 251

P M Panel method, 169 Mach angle, 203, 228, 230 Passive control, 346 Mach cone, 203 Pathline, 70 Mach number, 44, 203, 254, 287 Perfect gas, 193 Mach Number Independence, 242 Pitch, 28 Mach-disc, 344 Pitch angle, 35 Mass flow rate, 209 Pitching moment, 37 Matter, 3 Pitching moment coefficient, 141 gas, 3 Pitot probe, 340 intermolecular, 3 Pitot-static probe, 92 liquid, 3 Plasma wind tunnel, 311 solid, 3 Point of separation, 255 Maximum lift coefficient, 246 Polarizability, 11 Maxwell’s relations, 189 Poles, 14 Mayer’s relation, 191, 193 Potential flow, 109 Mean camber line, 34 Potential jet core, 322 Mesh factor, 294 Powered airships, 27 Method of characteristics, 223, 300 Prandtl–Glauret transformations, 348 Microscopic Approach, 65 Prandtl–Meyer expansion fan, 230 Microscopic point of view, 31 Prandtl–Meyer function, 231 Micro-Vortex Generators, 381 Prandtl–Meyer relation, 221 Milky Way, 148 Prandtl’s lifting line integro-differential equation, 160 Minimum wave angle, 228 Prandtl’s Mixing Length Hypothesis, 275 Mixing length, 325 Pressure, 10, 30 Mixing of two uniform laminar flows, 269 Pressure coefficient, 119, 241 Models, 43 Pressure mode acoustics, 347 Modified Newtonian theory, 247 Pressure profiles, 342 Moment coefficient, 39 Pressure regulating valve, 340 Momentum equation, 64, 200 Pressure surface, 34 θ − β − M Relation, 228 Prototypes, 43

N R Navier–Stokes equations, 73 Ramjets, 393 Newtonian sine-squared law, 245 Rankine oval, 117, 169 Newton’s law of viscosity, 361 Rankine–Hugoniot equation, 221 Non-simple regions, 362 Rankine’s half-body, 116 Nonuniform flow, 46 Rarefied flow, 45 Normal force coefficient, 39 Rayleigh flow, 215 Normal shock, 216, 226 Rayleigh Pitot probe formula, 222 Density Ratio, 219 Reference area, 39 Entropy Change, 219 Refractive index, 11 Stagnation Pressure Ratio, 218 refractivity of the atmosphere, 11 Static Pressure Ratio, 218 Snell’s law, 11 Static Temperature Ratio, 218 Reichardt’s equation, 327 Nozzle Pressure Ratios, 341 Reichardt’s inductive theory of turbulent flows, 327 Reverse nozzle diffuser, 304 Reynolds Averaged Navier–Stokes, 322 O Reynolds number, 44, 239, 254, 287 Oblique shock, 216, 226 Reynolds Rules of Averaging, 273 Density Ratio, 227 Reynolds stresses, 275 Entropy Change, 227 Reynolds Transport theorem, 95 Stagnation Pressure Ratio, 227 Richardson number, 321 Index 511

Roll, 28 Stokes theorem, 63, 128 Root chord, 35 Straight vortex line segment, 155 Rossby number, 19 Streakline, 70 Streamline, 68 Streamtube, 69, 150 S Strength of shock, 229 Scalar field, 59 Stress, 31 Scalar product, 57 Mohr’s circle, 32 Scattering angle, 11 Subsonic flow, 48 Scattering phenomena, 10 Subsonic inlet, 394 Rayleigh scattering, 10 Subsonic jet noise, 350 Schlieren, 344 Suction surface, 34 Scramjets, 393 Superposition, 115 Screech tone, 351 Supersonic combustion ramjet, 344 Screens, 289 Supersonic flow, 48 Screen solidity, 294 Supersonic jet core, 322 Sea breeze, 19 Supersonic jet noise, 350 Second law of thermodynamics, 64, 186 Surface forces, 31 Second throat, 296 Surface integral, 62 Self-similar region, 322 Surroundings, 181 Semi-infinite body, 116 Symmetric airfoil, 132 Semi-infinite vortex, 155 System, 181 Separation pressure, 226 Settling chamber, 299 Shadowgraph, 344 T Shaft work, 185 Taper Ratio, 35 Shear strain rate, 73 Taylor’s vorticity transport theory, 326 Shear velocity, 277 Temperature, 10, 31 Shock-associated noise, 351 Test rhombus, 304 Shock–boundary layer interactions, 361 Test section, 290 Shock cell, 328 Theodore von Karman, 7 Shock–Shock interference, 364 Thermal equation of state, 192, 193 Shock tube, 309 Thermally perfect gas, 192 Shock tunnel, 311 Thin airfoil theory, 127 Similarity parameters, 254 Timeline, 68 Simple waves, 362 Tip chord, 35 Sink, 110 Tractive force, 28 line sink, 110 Trailing edge, 34, 131 point sink, 110 Trailing vortex, 145 Sir George Cayley, 27 Transformations for panel coordinates, 177 Sirocco, 21 Transition flow, 45 Slip flow, 45 Transonic flow, 48 Sound pressure level, 347 Transonic interactions, 361 Source, 110 Trim tabs, 28 line source, 110 Tropics, 14 point source, 110 True airspeed, 92 Source panels, 169 Turbulence model, 327 Spalart–Allmaras turbulence model, 330 Turbulent boundary layers, 263, 272 Span, 145 Turbulent kinetic energy, 324 semi-span, 147 Turbulent shear stress, 325 Specific heat ratio, 193 Typhoons, 16, 148 Speed of sound, 10, 201 Spinning tunnels, 286 Stability tunnels, 286 U Stagnation point flow, 267 Uncertainty analysis, 407 Stagnation properties, 205 Underexpanded, 322 Starting vortex, 131 Uniform flow, 46, 109 Static pressure coefficient, 293 Universe, 181, 188 Static properties, 205 Unsteady flow, 46 Static stability, 12 neutrally stable, 12 statically stable, 12 V statically unstable, 12 Vector field, 60 Steady flow, 46 Vector product, 60 Stefan–Boltzmann law, 11 Vertical stabilizer, 28 Stewartson Layer, 19 Viscous flows, 48 512 Index

Viscous-inviscid flow interaction, 239 Westerlies, 20 Volume flow rate, 84 Wind, 14 Volume integral, 63 wind shear, 21 Von Karman constant, 276, 326 Wind tunnel, 285 Von Karman momentum integral equation, 260 Air Supply System and Storage Tanks, 299 Von Karman’s rules, 204 energy ratio, 295 Von Karman’s similarity hypothesis, 326 Fleigner’s formula, 295 Vortex filament, 150 Wing area, 35 Vortex flow, 119 Wing root, 145 Vortex line, 149 Wings, 28 Vortex panel methods, 174 port-wing, 28 Vortex panels, 169 starboard wing, 28 Vortex tube, 150 Wing span, 35 Vorticity, 72 Wing sweep, 35 Vorticity mode acoustics, 347 Wing tip, 145 Work done, 183

W Wall temperature, 240 Y Wave angle, 228, 237 Yaw, 28 Weber number, 44 Wein’s-displacement law, 11