That's a Drag: the Effects of Drag Forces
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Glossary Physics (I-Introduction)
1 Glossary Physics (I-introduction) - Efficiency: The percent of the work put into a machine that is converted into useful work output; = work done / energy used [-]. = eta In machines: The work output of any machine cannot exceed the work input (<=100%); in an ideal machine, where no energy is transformed into heat: work(input) = work(output), =100%. Energy: The property of a system that enables it to do work. Conservation o. E.: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Equilibrium: The state of an object when not acted upon by a net force or net torque; an object in equilibrium may be at rest or moving at uniform velocity - not accelerating. Mechanical E.: The state of an object or system of objects for which any impressed forces cancels to zero and no acceleration occurs. Dynamic E.: Object is moving without experiencing acceleration. Static E.: Object is at rest.F Force: The influence that can cause an object to be accelerated or retarded; is always in the direction of the net force, hence a vector quantity; the four elementary forces are: Electromagnetic F.: Is an attraction or repulsion G, gravit. const.6.672E-11[Nm2/kg2] between electric charges: d, distance [m] 2 2 2 2 F = 1/(40) (q1q2/d ) [(CC/m )(Nm /C )] = [N] m,M, mass [kg] Gravitational F.: Is a mutual attraction between all masses: q, charge [As] [C] 2 2 2 2 F = GmM/d [Nm /kg kg 1/m ] = [N] 0, dielectric constant Strong F.: (nuclear force) Acts within the nuclei of atoms: 8.854E-12 [C2/Nm2] [F/m] 2 2 2 2 2 F = 1/(40) (e /d ) [(CC/m )(Nm /C )] = [N] , 3.14 [-] Weak F.: Manifests itself in special reactions among elementary e, 1.60210 E-19 [As] [C] particles, such as the reaction that occur in radioactive decay. -
Drag Force Calculation
DRAG FORCE CALCULATION “Drag is the component of force on a body acting parallel to the direction of relative motion.” [1] This can occur between two differing fluids or between a fluid and a solid. In this lab, the drag force will be explored between a fluid, air, and a solid shape. Drag force is a function of shape geometry, velocity of the moving fluid over a stationary shape, and the fluid properties density and viscosity. It can be calculated using the following equation, ퟏ 푭 = 흆푨푪 푽ퟐ 푫 ퟐ 푫 Equation 1: Drag force equation using total profile where ρ is density determined from Table A.9 or A.10 in your textbook A is the frontal area of the submerged object CD is the drag coefficient determined from Table 1 V is the free-stream velocity measured during the lab Table 1: Known drag coefficients for various shapes Body Status Shape CD Square Rod Sharp Corner 2.2 Circular Rod 0.3 Concave Face 1.2 Semicircular Rod Flat Face 1.7 The drag force of an object can also be calculated by applying the conservation of momentum equation for your stationary object. 휕 퐹⃗ = ∫ 푉⃗⃗ 휌푑∀ + ∫ 푉⃗⃗휌푉⃗⃗ ∙ 푑퐴⃗ 휕푡 퐶푉 퐶푆 Assuming steady flow, the equation reduces to 퐹⃗ = ∫ 푉⃗⃗휌푉⃗⃗ ∙ 푑퐴⃗ 퐶푆 The following frontal view of the duct is shown below. Integrating the velocity profile after the shape will allow calculation of drag force per unit span. Figure 1: Velocity profile after an inserted shape. Combining the previous equation with Figure 1, the following equation is obtained: 푊 퐷푓 = ∫ 휌푈푖(푈∞ − 푈푖)퐿푑푦 0 Simplifying the equation, you get: 20 퐷푓 = 휌퐿 ∑ 푈푖(푈∞ − 푈푖)훥푦 푖=1 Equation 2: Drag force equation using wake profile The pressure measurements can be converted into velocity using the Bernoulli’s equation as follows: 2Δ푃푖 푈푖 = √ 휌퐴푖푟 Be sure to remember that the manometers used are in W.C. -
Chapter 4: Immersed Body Flow [Pp
MECH 3492 Fluid Mechanics and Applications Univ. of Manitoba Fall Term, 2017 Chapter 4: Immersed Body Flow [pp. 445-459 (8e), or 374-386 (9e)] Dr. Bing-Chen Wang Dept. of Mechanical Engineering Univ. of Manitoba, Winnipeg, MB, R3T 5V6 When a viscous fluid flow passes a solid body (fully-immersed in the fluid), the body experiences a net force, F, which can be decomposed into two components: a drag force F , which is parallel to the flow direction, and • D a lift force F , which is perpendicular to the flow direction. • L The drag coefficient CD and lift coefficient CL are defined as follows: FD FL CD = 1 2 and CL = 1 2 , (112) 2 ρU A 2 ρU Ap respectively. Here, U is the free-stream velocity, A is the “wetted area” (total surface area in contact with fluid), and Ap is the “planform area” (maximum projected area of an object such as a wing). In the remainder of this section, we focus our attention on the drag forces. As discussed previously, there are two types of drag forces acting on a solid body immersed in a viscous flow: friction drag (also called “viscous drag”), due to the wall friction shear stress exerted on the • surface of a solid body; pressure drag (also called “form drag”), due to the difference in the pressure exerted on the front • and rear surfaces of a solid body. The friction drag and pressure drag on a finite immersed body are defined as FD,vis = τwdA and FD, pres = pdA , (113) ZA ZA Streamwise component respectively. -
Aerodynamic Characteristics of Naca 0012 Airfoil Section at Different Angles of Attack
AERODYNAMIC CHARACTERISTICS OF NACA 0012 AIRFOIL SECTION AT DIFFERENT ANGLES OF ATTACK SUPREETH NARASIMHAMURTHY GRADUATE STUDENT 1327291 Table of Contents 1) Introduction………………………………………………………………………………………………………………………………………...1 2) Methodology……………………………………………………………………………………………………………………………………….3 3) Results……………………………………………………………………………………………………………………………………………......5 4) Conclusion …………………………………………………………………………………………………………………………………………..9 5) References…………………………………………………………………………………………………………………………………………10 List of Figures Figure 1: Basic nomenclature of an airfoil………………………………………………………………………………………………...1 Figure 2: Computational domain………………………………………………………………………………………………………………4 Figure 3: Static Pressure Contours for different angles of attack……………………………………………………………..5 Figure 4: Velocity Magnitude Contours for different angles of attack………………………………………………………………………7 Fig 5: Variation of Cl and Cd with alpha……………………………………………………………………………………………………8 Figure 6: Lift Coefficient and Drag Coefficient Ratio for Re = 50000…………………………………………………………8 List of Tables Table 1: Lift and Drag coefficients as calculated from lift and drag forces from formulae given above……7 Introduction It is a fact of common experience that a body in motion through a fluid experience a resultant force which, in most cases is mainly a resistance to the motion. A class of body exists, However for which the component of the resultant force normal to the direction to the motion is many time greater than the component resisting the motion, and the possibility of the flight of an airplane depends on the use of the body of this class for wing structure. Airfoil is such an aerodynamic shape that when it moves through air, the air is split and passes above and below the wing. The wing’s upper surface is shaped so the air rushing over the top speeds up and stretches out. This decreases the air pressure above the wing. The air flowing below the wing moves in a comparatively straighter line, so its speed and air pressure remain the same. -
UNIT – 4 FORCES on IMMERSED BODIES Lecture-01
1 UNIT – 4 FORCES ON IMMERSED BODIES Lecture-01 Forces on immersed bodies When a body is immersed in a real fluid, which is flowing at a uniform velocity U, the fluid will exert a force on the body. The total force (FR) can be resolved in two components: 1. Drag (FD): Component of the total force in the direction of motion of fluid. 2. Lift (FL): Component of the total force in the perpendicular direction of the motion of fluid. It occurs only when the axis of the body is inclined to the direction of fluid flow. If the axis of the body is parallel to the fluid flow, lift force will be zero. Expression for Drag & Lift Forces acting on the small elemental area dA are: i. Pressure force acting perpendicular to the surface i.e. p dA ii. Shear force acting along the tangential direction to the surface i.e. τ0dA (a) Drag force (FD) : Drag force on elemental area = p dAcosθ + τ0 dAcos(90 – θ = p dAosθ + τ0dAsinθ Hence Total drag (or profile drag) is given by, Where �� = ∫ � cos � �� + ∫�0 sin � �� = pressure drag or form drag, and ∫ � cos � �� = shear drag or friction drag or skin drag (b) Lift0 force (F ) : ∫ � sin � ��L Lift force on the elemental area = − p dAsinθ + τ0 dA sin(90 – θ = − p dAsiθ + τ0dAcosθ Hence, total lift is given by http://www.rgpvonline.com �� = ∫�0 cos � �� − ∫ p sin � �� 2 The drag & lift for a body moving in a fluid of density at a uniform velocity U are calculated mathematically as 2 � And �� = � � � 2 � Where A = projected area of the body or�� largest= � project� � area of the immersed body. -
Chapter 4: Immersed Body Flow [Pp
MECH 3492 Fluid Mechanics and Applications Univ. of Manitoba Fall Term, 2017 Chapter 4: Immersed Body Flow [pp. 445-459 (8e), or 374-386 (9e)] Dr. Bing-Chen Wang Dept. of Mechanical Engineering Univ. of Manitoba, Winnipeg, MB, R3T 5V6 When a viscous fluid flow passes a solid body (fully-immersed in the fluid), the body experiences a net force, F, which can be decomposed into two components: a drag force F , which is parallel to the flow direction, and • D a lift force F , which is perpendicular to the flow direction. • L The drag coefficient CD and lift coefficient CL are defined as follows: FD FL CD = 1 2 and CL = 1 2 , (112) 2 ρU A 2 ρU Ap respectively. Here, U is the free-stream velocity, A is the “wetted area” (total surface area in contact with fluid), and Ap is the “planform area” (maximum projected area of an object such as a wing). In the remainder of this section, we focus our attention on the drag forces. As discussed previously, there are two types of drag forces acting on a solid body immersed in a viscous flow: friction drag (also called “viscous drag”), due to the wall friction shear stress exerted on the • surface of a solid body; pressure drag (also called “form drag”), due to the difference in the pressure exerted on the front • and rear surfaces of a solid body. The friction drag and pressure drag on a finite immersed body are defined as FD,vis = τwdA and FD, pres = pdA , (113) ZA ZA Streamwise component respectively. -
Hydraulics Manual Glossary G - 3
Glossary G - 1 GLOSSARY OF HIGHWAY-RELATED DRAINAGE TERMS (Reprinted from the 1999 edition of the American Association of State Highway and Transportation Officials Model Drainage Manual) G.1 Introduction This Glossary is divided into three parts: · Introduction, · Glossary, and · References. It is not intended that all the terms in this Glossary be rigorously accurate or complete. Realistically, this is impossible. Depending on the circumstance, a particular term may have several meanings; this can never change. The primary purpose of this Glossary is to define the terms found in the Highway Drainage Guidelines and Model Drainage Manual in a manner that makes them easier to interpret and understand. A lesser purpose is to provide a compendium of terms that will be useful for both the novice as well as the more experienced hydraulics engineer. This Glossary may also help those who are unfamiliar with highway drainage design to become more understanding and appreciative of this complex science as well as facilitate communication between the highway hydraulics engineer and others. Where readily available, the source of a definition has been referenced. For clarity or format purposes, cited definitions may have some additional verbiage contained in double brackets [ ]. Conversely, three “dots” (...) are used to indicate where some parts of a cited definition were eliminated. Also, as might be expected, different sources were found to use different hyphenation and terminology practices for the same words. Insignificant changes in this regard were made to some cited references and elsewhere to gain uniformity for the terms contained in this Glossary: as an example, “groundwater” vice “ground-water” or “ground water,” and “cross section area” vice “cross-sectional area.” Cited definitions were taken primarily from two sources: W.B. -
Evaluation of Drag and Lift in the Internal Flow Field of a Dual Rotor Spinning Unit Via CFD
MATEC Web of Conferences 104, 02005 (2017) DOI: 10.1051/ matecconf/201710402005 IC4M & ICDES 2017 Evaluation of drag and lift in the internal flow field of a dual rotor spinning unit via CFD Nicholus Tayari Akankwasa1, Huiting Lin and Jun Wang1,2,a 1College of Textile, Donghua University, Shanghai, 201620, China 2The Key Lab of Textile Science and Technology, Ministry of Education, Shanghai 201620, China Abstract. In the present study, we evaluate the drag and lift magnitude in the new dual-feed rotor spinning unit using computational fluid dynamics technique. We adopt theoretical and numerical approach based on FLUENT to investigate the influence of new design on the drag and lift in the rotor interior. Results reveal that the drag and lift inside the rotor of the proposed model are reduced by 60-80% and 50-66% respectively as compared to the conventional unit. The velocity and pressure profiles become evenly distributed in the dual- feed rotor interior as opposed to the conventional rotor spinning unit and this modification is anticipated to improve fiber configurations. This phenomenon can be utilized to further optimize the rotor spinning unit and other wall-bounded engineering problems. 1 Introduction In the fluid dynamics concept, previous studies have focused more on the turbulent viscosity, flocculation, eddies and vortices among other flow properties. Growing interest in drag reduction in flows has increased in the recent years. Principally, the drag and lift phenomenon has been widely applied in solving aerodynamics and aeronautics problems. For wall-bounded flows, it is important to note that drag and lift has a significant impact on the processing of fibers and polymers. -
New Satellite Drag Modeling Capabilities
44th AIAA Aerospace Sciences Meeting and Exhibit AIAA 2006-470 9 - 12 January 2006, Reno, Nevada New Satellite Drag M odeling Capabilities Frank A. Marcos * Air Force Research Laboratory , Hanscom AFB, MA 01731 -3010 This paper reviews the operational impacts of satellite drag, the historical and current capabilities, and requirements to deal with evo lving higher accuracy requirements. Modeling of satellite drag variations showed little improvement from the 1960’s to the late 1990’s. After three decades of essentially no quantitative progress, the problem is being vigorously and fruitfully attacked on several fronts. This century has already shown significant advances in measurements, models, solar and geomagnetic proxies and the application of data assimilation techniques to operational applications. While thermospheric measurements have been historica lly extremely sparse, new data sets are now available from intense ground -based radar tracking of satellite orbital decay and from satellite -borne accelerometers and remote sensors. These data provide global coverage over a wide range of thermospheric alti tudes. Operational assimilative empirical models, utilizing the orbital drag data, have reduced model errors by almost a factor of two. Together with evolving new solar and geomagnetic inputs, the satellite -borne sensors support development of advanced ope rational assimilative first principles forecast models. We look forward to the time when satellite drag is no longer the largest error source in determining or bits of low altitude satellites. I. Introduction Aerodynamic drag continues to be the larg est uncertainty in precision orbit determin ation for satellites operating below about 600 km. Drag errors impact many aerospace missions including satellite orbit location and prediction, collision avoidance warnings, reentry prediction, lifetime estimates and attitude dynamics. -
List of Symbols
List of Symbols a atmosphere speed of sound a exponent in approximate thrust formula ac aerodynamic center a acceleration vector a0 airfoil angle of attack for zero lift A aspect ratio A system matrix A aerodynamic force vector b span b exponent in approximate SFC formula c chord cd airfoil drag coefficient cl airfoil lift coefficient clα airfoil lift curve slope cmac airfoil pitching moment about the aerodynamic center cr root chord ct tip chord c¯ mean aerodynamic chord C specfic fuel consumption Cc corrected specfic fuel consumption CD drag coefficient CDf friction drag coefficient CDi induced drag coefficient CDw wave drag coefficient CD0 zero-lift drag coefficient Cf skin friction coefficient CF compressibility factor CL lift coefficient CLα lift curve slope CLmax maximum lift coefficient Cmac pitching moment about the aerodynamic center CT nondimensional thrust T Cm nondimensional thrust moment CW nondimensional weight d diameter det determinant D drag e Oswald’s efficiency factor E origin of ground axes system E aerodynamic efficiency or lift to drag ratio EO position vector f flap f factor f equivalent parasite area F distance factor FS stick force F force vector F F form factor g acceleration of gravity g acceleration of gravity vector gs acceleration of gravity at sea level g1 function in Mach number for drag divergence g2 function in Mach number for drag divergence H elevator hinge moment G time factor G elevator gearing h altitude above sea level ht altitude of the tropopause hH height of HT ac above wingc ¯ h˙ rate of climb 2 i unit vector iH horizontal -
Airfoils and Wings
Airfoils and Wings Eugene M. Cliff 1 Introduction The primary purpose of these notes is to supplement the text material re- lated to aerodynamic forces. We are mainly interested in the forces on wings and complete aircraft, including an understanding of drag and related nomeclature. 2 Airfoil Properties 2.1 Equivalent Force Systems In some cases it’s convenient to decompose the forces acting on an airfoil into components along the chord (chordwise) and normal to it. These forces are related to lift and drag through the geometry shown in Figure 1. From l n d α c Figure 1: Force Systems the figure we have c(α)=cn(α)cosα − cc(α)sinα cd(α)=cn(α)sinα + cc(α)cosα Obviously, we can also express the normal and chordwise forces in terms of section lift and drag. 1 Figure 2: Flow Decomposition 2.2 Circulation Theory of Lift A typical flow about a lift-producing airfoil can be decomposed into a sum of two flows, as shown in Figure 2. The first flow (a) is ’symmetric’ flow and so produces no lift. The ’circulatory’ flow (b) is responsible for the net higher speed (and hence lower pressure) on the top of the airfoil (the suction side). This can be quantified by introducing the following line integral −→ −→ ΓC = u · d s C This is the circulation of the flow about the path C. It turns out that as long as C surrounds the airfoil (and doesn’t get too close to it), the the value of Γ is independent of C. -
MATH 240: HOMEWORK #4 1. the Drag Equation Suppose That An
MATH 240: HOMEWORK #4 DUE IN FLORA'S MAILBOX BY NOON ON NOV. 25. 1. The drag equation Suppose that an object of mass m is falling toward the earth, and that it has height h(t) above the surface at time t. Newton's law says that (1.1) Force = mass × acceleration: Two kinds of forces act on the object: A. A downward force of gravity having magnitude mg, where g is the gravitation constant. B. The drag force FD due to wind resistance. This acts in the opposite direction to the velocity h0(t), and its magnitude is 0 2 (1.2) jFDj = cA(t)h (t) where c > 0 is constant and A(t) is the cross sectional area of the object at time t. Notice that if A(t) is constant, the drag force goes up as the square of the velocity. This is due to the fact that the energy imparted by each molecule of air hit during the fall is proportion to velocity, and the number of molecules hit per second is also proportional to velocity. 1. Show that if we assume h(t) is decreasing with time (corresponding to falling toward the earth), (1.1) becomes (1.3) −mg + cA(t)h0(t)2 = mh00(t) In particular, explain the signs of the terms on the left. 2. Suppose now that the object is a parachutist with a circular parachute. They open the parachute so that it's radius is b=pjh0(t)j at time t for some constant b > 0. Are they making the parachute larger or smaller as the velocity decreases in magnitude? What is A(t) in this case, and what differental equation does (1.3) become? Note: Be careful to make sure that the signs of terms in the differential equation agree with the fact that the drag force acts in the opposite direction to the velocity of the parachutist.