Air System Basics

...... AIR SYSTEM BASICS

One of the fundamental concepts that apply to air systems is the fluid mechanics of conveying air. This article presents the basic principles that form the groundwork for the design, installation, operation, and troubleshooting of these systems. AIR SYSTEM BASICS

By GERALD J. WILLIAMS, PE, Air systems may be used to: Vice President, ✔ Provide a sufficient quantity and temperature of McClure Engineering Associates, air to maintain the space dry bulb temperature at a St. Louis, Mo. desired condition. ✔ Provide a sufficient quantity and dew point tem- ir handling systems have been designed perature of air to maintain the space specific humid- and installed in nearly every building cur- ity at a desired condition. A rently in use and will be utilized in almost ✔ Provide for space air circulation to promote heat every building design still on the drawing and moisture transfer for human comfort and to facili- board today. Air systems in buildings are used prin- tate proper mixing to obtain uniform space conditions. cipally as a means to transport energy or to remove ✔ Provide ventilation air from outdoors to replen- contaminants although their functions are actually ish oxygen, to dilute space contaminants, or to provide much more complex than these restricted defini- combustion air. tions. The energy required for the movement of air ✔ Clean outdoor and recirculated air for human for these purposes represents one of the largest cate- health and protect the system heat transfer equipment. gories of electrical consumption in most modern fa- ✔ Provide a means for the exhaust of specific con- cilities. Thus, a fundamental knowledge of the taminants from the space. physics underlying the function and operation of air ✔ Provide a source of exhaust or supply pressuriza- handling systems is vital to every practicing HVAC tion to contain the spread of smoke in a fire situation engineer today. within a building. However, even to deal with the fundamentals of The fundamental concepts underlying these func- air systems requires the HVAC engineer to be well tions span the gamut of the scientific disciplines indi- grounded in an extensive group of fundamental sci- cated above. This article will discuss only one portion entific concepts—physics, fluid mechanics, heat of the basics of air systems—fluid mechanics of con- transfer, psychrometrics, combustion, and human veying air. Basic principles will be presented that physiology, to name only a few. A brief list of the form the groundwork for the design, installation, op- functions of air systems clearly illustrates this point. eration, and troubleshooting of such systems. The

Atmospheric pressure Air flow Atmospheric Air flow Coil pressure P1 P1 P2

Air duct Air duct h Vessel Manometer h Manometer h Fluid

Pressure gauge Fluid Fluid

A B C 1 View A—measurement of static pressure, h. View B—measurement of static pressure, h, within a duct. View C—measurement of static pressure drop, h, across a heating or cooling coil.

HEATING / PIPING / AIR CONDITIONING MAY 1995 65 Air system basics

content has been arranged as a refresher for seasoned in. WG = 0.036 psi = 69.22 ft of air. practitioners and also as a bridge from theory to prac- The same fluid statics principle would apply in the tice for entry-level individuals. use of a manometer to measure an air pressure differ- Since air is a fluid, the four basic principles of fluid ence across an obstruction to flowing air, such as the mechanics all have application in the conveying of air coil indicated in Fig. 1C. Here, the pressure drop due in an effective and energy-conserving manner. These to the energy level reduction of the air as it passes concepts are fluid statics, conservation of mass, con- through the coil is registered by the deflection of the servation of energy, and conservation of momentum. column. The pressure drop is always considered posi- These will be treated separately before their practical tive when the pressure reduces in the direction of air application to air systems is presented. flow. Notice that no reference to atmospheric pressure is made in this measurement—only the pressure Fluid statics change that has occurred through the process. Unlike the other concepts of fluid mechanics, the Thus, the fluid statics principle provides us with concept of fluid statics is based on the physics of fluids the universal unit of inches water gauge to predict or at rest rather than in motion. Though it is unusual in measure pressures or pressure differences in air sys- HVAC work to consider air that is not in motion, the tems. Whether field readings are made with a U-tube concept of fluid statics provides the basis for manome- or inclined-tube manometer, whether the fluid is wa- ters and the resulting set of units necessary to mea- ter or gauge oil (with a lower density to increase de- sure air pressure. Consider the vessel shown in Fig. flections and make readings more accurate), or even if 1A, filled with fluid as indicated. The fluid statics the gauge does not function on a manometer principle principle indicates that the pressure read on the pres- at all (as in the case of a Magnehelic gauge), the prin- sure gauge attached to the vessel would be: ciple of fluid head as established by the fluid statics Ph=ρ ()1 concept is the basis for all air pressure calculations and measurements in the HVAC industry. where = Ppressure, lb per sq ft Conservation of mass ρ=density of fluid in vessel, lb per cu ft The law of conservation of mass, simply stated, is = hheight of fluid level above pressure gauge, ft that fluid mass flowing in an enclosed duct is con- The fluid creates a pressure on the gauge in excess served—it is neither created nor destroyed as it of atmospheric pressure based on the height of the passes through the system. In fluid mechanics, this fluid column and the density of the fluid in the vessel. concept is described by the continuity equation as dis- This principle permits the conversion of pressure to played in Fig. 2A. If air is flowing from left to right in a unit of fluid “head” if the density of the fluid is this duct at a constant flow rate (steady flow), the known. Based on the density of water at 70 F (62.3 lb mass flow rate would be given by the following equa- per cu ft), the fluid statics principle indicates a con- tion: version factor of 1 psi equal to 2.31 ft of water. mVA˙ ==ρconstant (2) Using the same principle, Fig. 1B extends the con- where cept of the measurement of air pressure in a duct us- = ing the fluid statics equation. Here, an air pressure, m˙ mass flow rate, lb per min ρ=air density, lb per cu ft P1, in excess of atmospheric pressure is exerted on one side of the manometer while the other side is exposed V=air velocity, fpm = to atmospheric pressure. The deflection of the fluid Aduct area, sq ft column indicates the head difference (and therefore Referring to Fig. 2A, writing the mass flow equation the pressure difference) between the air pressure at between Stations 1 and 2 would yield the following the sensed point and atmospheric pressure. This de- equation: ρρ= flection for air systems is commonly expressed as 11VA 1 22 VA 2 ()3 inches water gauge (in. WG) or inches water column If the density were assumed to be constant between (in. WC) as this represents a convenient unit for the these two stations, then the classical form of the conti- range of air pressures typically encountered in HVAC nuity equation for air systems would be derived: work. Since the pressure measured in this case was == QVAVA11 22 ()4 above atmospheric pressure (with the deflected col- where umn rising toward the atmosphere), the pressure is Q=volumetric flow rate, cfm termed positive. If the air pressure at P1 had been below atmospheric pressure, the fluid column would This equation forms the basis for the calculation of have deflected in the opposite direction, and the pres- accelerating and decelerating flows, which will have sure would be termed negative. Incidentally, the fluid significant application to all areas of air system tech- statics equation and the standard density of air (0.075 nology. But before exploring this concept more fully, lb per cu ft) would yield the following relationship: 1 let’s spend just a moment on the assumption of con-

66 MAY 1995 HEATING / PIPING / AIR CONDITIONING 1 2 Air duct

V1 V2 pressibility of a flowing air stream is correct within an accuracy limit of approximately ±10 percent for typi- A1 A2 cal HVAC processes. Since the accuracy is acceptable A for most measurements that are made in the field, the assumption is valid. However, when evaluating the necessity of a safety factor in calculating pressure re- Reheat quirements for the selection of a fan, remember this 1 coil 2 margin of error is inherent in the incompressible fluid mechanics on which most of our calculations are V 1 55 FV2 = 1.073V1 95 F based. The real power of the continuity equation comes from its ability to predict the volumetric flow rate A1 A2 B based on the duct area and velocity and its ability to predict duct velocities based on changes in the geometry of the duct system. Fig. 2C indicates the use of the 1 continuity equation for a simple process. Air flowing 2 from Station 1 to Station 2 passes through a transition fitting. Since the area of the duct at Station 2 is

V1 V2 smaller than at Station 1, it is intuitively obvious that the flow has accelerated between these two stations. The continuity equation permits the exact calculation A2 A of this effect based on the use of Equation 4: 1 Transition section = C VVAA2112(/) ()5 Knowing the velocity entering the fitting and the 2 View A—classical form of the continuity equation for air ratio of the flow areas, we can calculate the velocity systems is Q = V1A1 = V2A2, where Q = volume, V = velocity, leaving the fitting. and A = area. View B—change in density between 1 and 2 above is Ð7.3 percent. If A1 = A2, V2 = 1.073V1. Therefore, Conservation of energy the assumption of incompressibility of a flowing air The law of conservation of energy is based on the stream is correct within an accuracy limit of ±10 percent principle that energy is neither created nor destroyed for typical HVAC processes. View C—When duct size as it passes through a system. The steady flow energy changes, velocity also changes: V2 = V1(A1/A2). equation that is developed from this concept sets up an accounting format to keep track of all of the energy stant density that was made to derive Equation 4. forms. It is obtained from the first law of thermody- The assumption of constant density for a flowing air namics, which considers both mechanical and ther- stream (or to put it another way, the assumption that mal forms of energy. It states that the amount of heat the flow can be considered incompressible, as for a wa- added to the air stream as it passes through a system ter stream) is only an approximation. Even if the duct is equal to the change in energy content of the air is fully insulated with no temperature change in the stream plus any work done by the air stream. The air stream, any real duct system will experience pres- steady flow equation written between Stations 1 and sure losses in the direction of air flow due to frictional 2 in Fig. 2A per pound of air flowing would have the and dynamic effects. This reduction in air pressure at following form: a constant temperature will, according to the perfect 2 WVgJUJQPvZ−−+++++=(/)2 gas law, reduce the density of the air slightly as it 12 1 112111 2 +++ passes down the duct stream flowing with losses. For (/)V226 g JU2222 P v Z () a constant area duct with a pressure drop from Sta- where tion 1 to Station 2 of 10 in. WG, the density of the air at W =work done on the air stream between Station 2 will decrease by 2.4 percent and, based on 12− Stations 1 and 2 (this value would be Equation 3, the velocity will increase by 2.4 percent. If we superimpose on this the effect of temperature, the negative if it represented work done by deviation becomes more extreme, as indicated in Fig. the air stream), ft - lb per lb of air 2B. flowing or ft Assume that a duct-mounted reheat coil with a V =air stream velocity, fps pressure drop of 0.5 in. WG heats an air stream from g =acceleration of gravity, 32.2 fps2 55 to 95 F. Under these conditions, the density of the J =mechanical equivalent of heat, air at Station 2 will decrease by 7.3 percent and, as- 778.2 ft - lb per Btu suming A = A , the velocity at Station 2 will increase 1 2 U =internal energy, Btu per lb by 7.3 percent. Therefore, the assumption of incom-

HEATING / PIPING / AIR CONDITIONING MAY 1995 67 Air system basics

gy, p = fan energy source (electric motor, steam turbine, etc.) Q12− heat transfer into the system between Stations 1 and 2 (this value would be to the air stream to provide the motivating energy for negative if heat were transferred from air movement. It is the only point within an air system (except at heating sources) when the air stream the system), Btu per lb = energy level increases. At all other locations, the net P air pressure, lb per sq ft energy level is decreasing. The terms Pv and V2/2g are = v fluid specific volume, cu ft per lb illustrated in Fig. 3A since their use forms the basis of = Z elevation of air above a datum plane, ft almost all measurements and analysis work done on This is an energy statement since each component HVAC air systems. Pv is called flow work but is re- represents the energy of the air per unit of mass flow- ferred to as static pressure (SP) or static head in air ing (ft-lb per lb or simply ft). The various energy com- systems. V2/2g is called kinetic energy but is referred ponents would generally be referred to as follows: to as velocity pressure (VP) or velocity head in air sys- W = work energy tems. The numerical sum of these two energy compo- 2 Vg2 /2 = kinetic energy nents (Pv + V /2g) is referred to as total pressure (TP) or total head. All of these components are normally re- JU = internal energy = ferred to in units of inches water gauge as registered JQ heat energy by the manometer arrangements shown in Fig. 3A. = Pv flow work energy With these two terms now defined, Equation 7 can = Z potential energy be applied to two common situations that require Fortunately, when we use this equation for air analysis in typical HVAC duct systems. Fig. 3B shows systems, several of the terms can usually be elimi- a section of an air duct system containing a supply fan nated, thus simplifying things a bit. If we assume and a section of supply air ductwork. Equation 7 can that the air system does not receive or dissipate be rewritten into a similar form to determine the out- heat, then Q1-2 = 0. If the duct system is horizontal, come of the work performed by the fan: then Z = Z , and the steady flow energy equation for 2 2 1 2 WVVgPvPvJUU− =−[( ) /2 ] + ( − ) + ( − ) an air system can be restated as follows: 12 2 1 22 11 2 1 2 2 ()8 WVgJUPvVg−+++=+(/)22 (/) 12 1 1112 Analysis of this equation indicates that the work + JU222 P v ()7applied to the fan wheel creates in the air stream an Three of the terms of this equation are quite impor- increase in kinetic energy (or velocity pressure), an in- tant and deserve further discussion. The term W1-2 re- crease in flow work energy (or static pressure), and an lates to the work done by a fan in moving air through increase in internal energy. Recognizing the thermo- a system. It refers to the shaft energy imparted by the dynamic property of enthalpy, we can write: hPvJU=+(/) ()9

Total pressure = Static pressure + Velocity pressure where TP = SP + VP = hair enthalpy, Btu per lb Air flow Impact tube Substituting into Equation 8 yields the following TP TP form: SP SP =−2 2 + − WVVgJhh12−[( 2 1 ) /210 ] [ (21 )] ( ) Since the enthalpy rise for a perfect gas is given by the following: ∆∆= hCt1 p ()11 where ∆h= air stream enthalpy change, Btu per lb C= specific heat capacity of air at constant Static pressure, Total pressure, Velocity pressure, p in. WG in. WG VP = TP – SP pressure, Btu per lb - F in. WG ∆= A tair stream temperature change, F 2 Supply it follows that a large portion of the work put in at duct 1 3 the fan shows up as a heat rise across the fan. A more Supply continued on page 72 fan 3 View A—illustration of Pv and V2/2g. Flow work energy, Pv, is referred to as static pressure (SP). The kinetic en- 2 Work (W1-2) ergy term V /2g is referred to as velocity pressure (VP). Return View B—addition of a fan to an air duct system increases duct B the flow work, kinetic energy, and internal energy of the air stream.

68 MAY 1995 HEATING / PIPING / AIR CONDITIONING Air system basics

continued from page 68 rigorous treatment of this phenomenon1 indicates (or a heating or cooling coil) does the temperature of that all of the shaft work done by the fan appears as the air stream change. heat (otherwise known as fan heat rise or simply fan Since the steady flow energy equation should be heat). Since the term in Equation 8 for the rise in in- valid for flow with or without frictional and dynamic ternal energy is related to inefficiencies in the fan loss effects, our second and more important recogni- pressure increase process, the temperature rise for tion from Equation 13 relates to duct air stream en- standard air can be approximated by the following: ergy levels and the source of the losses. Rearranging ∆∆tTP= /.27η ( 12 ) Equation 13 yields the following: fan f 2 +=2 ++ − (/)VgPvVgPvJUU22222 (/) 3 33 ( 3 2 )() 15 where J(U – U ) represents fluid friction and turbulence ∆= 3 2 tfan air temperature rise across fan, F in the form of kinetic energy in eddies transformed ∆TP = total pressure increase across fan, in. WG into thermal energy. This heat addition occurs inter- η = f fan efficiency, decimal nally in an irreversible process as a result of frictional Another important concept identified by Equation 8 dissipation of mechanical energy into internal heat in is that the fan imparts its energy rise to the air stream the gas stream. (This internal heat addition counter- not only in the form of static pressure increase but acts the reduction in temperature that would have oc- also in the form of velocity pressure increase. Thus, curred in a reversible polytropic gas process con- the total pressure rise across the fan is the only truly ducted in a reversible manner for this reduction in meaningful method of assessing fan performance and pressure.1) Stated in words, Equation 15 reveals that power required.2 Our industry’s fondness with static the static pressure plus the velocity pressure at Sta- pressure and ratings based on fan static pressure can- tion 2 are equal to the static pressure plus the velocity not negate the principles of fluid mechanics on which pressure at Station 3 plus the pressure loss that has Equation 8 is based. occurred between these two stations. Using the rela- Referring again to Fig. 3B, consider a second appli- tionship that the total pressure is equal to the static cation of Equation 7 as it relates to duct system losses. pressure plus the velocity pressure, the following If we consider the run of ductwork between Stations 2 equation is derived: =+ and 3, our experience tells us that for any real duct TP23 TP() TPloss 23− ()16 system, a pressure drop will occur in the direction of Three very important observations are apparent air flow between these two points. As we will discuss from this equation: in a later section, these losses are generally character- ● In any duct section without a fan, the total pres- ized as frictional losses, which relate to fluid viscosity sure is constantly dropping in the direction of air flow. and the roughness of the confining duct walls, or to Such a statement cannot necessarily be made with re- dynamic losses, which relate to duct stream turbu- spect to static pressure or velocity pressure. lence or obstructions to straight-ahead flow. For the ● The measure of the energy level in an air stream purpose of the current discussion, though, we will re- at any point is uniquely given by the total pressure fer to these effects collectively as losses to see what in- only. Reference to static pressures or velocity pres- sight the steady flow energy equation can yield into sures alone in this regard can be quite misleading. this phenomenon. If no work is done on the system (no ● The losses in duct systems occurring due to fric- fan is in this section of ductwork) and no heat is added tional and dynamic effects must, based on the equa- to or dissipated from the air system, Equation 7 re- tion, be losses in total pressure. Any other evaluation duces to the following: of losses must be qualified by assumptions regarding 2 ++=2 ++ (/)VgPvJUVgPvJU2221322 2 (/) 3 33 3 ()the duct system geometry (such as that the area of the Substituting Equation 9 would yield the following: duct does not change). 2 +=2 + (/)VgJhVgJh22223 (/)3 () 14 Our first realization from the equation then relates Conservation of momentum to temperature conditions as the pressure is progres- Newton’s first law of motion states that a body will sively lost. It can be shown1 that the processes gener- maintain its state of rest or uniform motion (at con- ating duct losses approximate a classical throttling stant velocity) along a straight line unless compelled process wherein the enthalpy remains constant. Re- by some unbalanced force to change that state. The ferring to Equation 11 and recognizing that in an momentum of a body, given by the product of its mass equal area duct the velocity would not change be- and its velocity, will thus tend to be conserved. Mo- tween Stations 2 and 3 (except for the slight varia- mentum is a vector quantity whose direction is that of tions in air density described in the section on the con- its velocity so that a change of direction must be tinuity equation), one can see that the temperature of caused by an unbalanced force. Conservation of mo- the air stream does not change as the air passes mentum concepts in fluid mechanics are usually used through pressure drops. Only at the location of a fan to calculate the dynamic forces exerted by moving fluids on fixed obstructions to the flow path. Though this 1Superscript numerals indicate references at end of article. is not a concern in most HVAC applications, the law of

72 MAY 1995 HEATING / PIPING / AIR CONDITIONING conservation of momentum does play into certain of secondary air is entrained into the air stream. Solv- types of processes and dynamic loss effects. ing Equation 19 indicates that the velocity at Station Consider a rectangular sidewall supply air outlet, 2 is reduced to 500 fpm. Application of Equation 4 in- as shown in Fig. 4, delivering air into a room at the dicates that the flow area increased to 4 sq ft. This same temperature as the room air (delivering air stream spread has occurred as a matter of course due above or below room temperature introduces buoy- to the basic principles of the law of conservation of mo- ancy effects that are superimposed on the momentum mentum and the continuity equation. Further analy- effects, thus complicating the analysis). Air emerging sis would indicate that for an opening as shown in Fig. from the grille will entrain room air. This induction 4, the spread of the air stream in both planes will open at between 14 and 24 deg, giving a spread in either direction of approximately 1 ft in every 5 to 8 ft of throw. 1 2 It should be remembered that discharging air, whether into a room or into a plenum, will exhibit this same geometry unless the air stream is coerced to do otherwise. 14 to Total air flow 24 deg A3, M3, V3 Though the principle of the conservation of momentum is not one of the areas most emphasized in air A1, M1, V1 Supply system technology, its importance to the design of air flow Entrained room air duct fittings and duct configurations and their result- M2, V2 = 0 ing dynamic losses is profound. As we will see later, failure to consider the law of conservation of momen- 4 Discharge pattern of air leaving a rectangular sidewall tum and the dynamic losses generated as a direct re- grille in both the horizontal and vertical planes. sult of its effects has contributed to many problems in operating systems. effect, according to the law of conservation of momen- The four basic concepts of fluid mechanics dis- tum, will decrease the velocity of the total air stream cussed in the previous paragraphs form the ground- while increasing its volume. If M1 and V1 are the mass work for the technology of air systems as it is cur- and velocity of the supply air, M2 and V2 are the mass rently employed for HVAC work. The following and velocity of the entrained room air, and M3 and V3 sections will deal with a few selected application ar- are the mass and velocity of the total air mixture, then eas in which these principles become important, the law of conservation of momentum yields the fol- sometimes uniquely but more often as a combination lowing equation: of more than one of the concepts mentioned. MV+= MV MV ()17 11 22 33 Flow processes, measurements Since V2, for all practical purposes, may be consid- The concepts of static pressure (SP), velocity pres- ered zero prior to the acceleration of the entrained air sure (VP), and total pressure (TP) were developed and and since M3 = M1 + M2, Equation 17 becomes: discussed earlier with regard to the law of conservation of energy and are depicted graphically in Fig. 3A. =+ MV11() M 1 M 2 V 3 ()18 Static pressure exerts itself in all directions in the

The velocity of the mixture stream, V3, has been re- duct, irrespective of whether the air is in motion or at duced from V1 since M1 + M2 must be greater than M1. rest. Positive static pressure indicates pressure at- Furthermore, as the geometry of the grille changes, tempting to burst the duct while negative static pres- the induction ratio, (M1 + M2)/M1, changes, entraining sure attempts to collapse the duct. It is a measure of varying amounts of air (with long, narrow outlets hav- potential energy of the air stream since this pressure ing a significantly higher induction ratio than square can create flow (kinetic energy) if it is released. Veloc- outlets). The law of conservation of momentum, there- ity pressure, on the other hand, exists only due to the fore, can predict the spread of the air stream as it ex- velocity of a moving air stream and exerts itself only its the opening. To do so, since the density of the air in the direction of air flow. It is a measure of the ki- existing the opening is the same as the room air, one netic energy possessed by the air due to its velocity. can substitute the volumetric flow rate for the mass Total pressure is the sum of these two energy types, flow rate, yielding the following: representing in one statement both the sum of these two energy levels and the total energy possessed by QV=+() Q Q V ()19 11 1 2 3 the air stream at the point of measurement.

with Q1 being the volumetric flow rate of the exiting The properties of the energy equation and the fluid supply (primary) air and Q2 being the volumetric flow statics principle can be combined to determine a use- rate of the entrained (secondary) air. Assume an ful concept with respect to air measurement. The ki- 2 opening of 1 sq ft (A1) discharges 1000 cfm at 1000 netic energy term, V /2g, from the energy equation fpm, and at Station 2 on Fig. 4, an additional 1000 cfm represents velocity pressure in terms of ft-lb per lb of

HEATING / PIPING / AIR CONDITIONING MAY 1995 73 Air system basics

Pitot-static tube Air flow Duct wall air systems. Consider the duct section shown in Fig. Eight 0.04-in. holes 6. Air flow is from left to right, moving from Station 90 deg from air flow 1 to 2 in a duct that is assumed, for the purpose of circling outer tube this illustration, to be without losses. It therefore follows that if there are no losses, the total pressure TP SP (TP) relating to the overall air stream energy level VP would be unchanged between these two stations. This is indicated by the plot of total pressure shown below the duct section, with pressures given as positive values with respect to surrounding air pressure Manometer (Pa). At Station 1, which represents a relatively high- velocity duct section, the total pressure TP1 is com- 5 The pitot-static tube (a modified pitot tube) is almost posed of static pressure SP1 and velocity pressure universally used in the field to determine the total, static, VP1. Since the flow area at Station 1 is smaller than and velocity pressures of a fluid stream. When VP is that at Station 2, the continuity equation (Equation known, the fluid velocity can be calculated. 4) indicates that the velocity at Station 2 must decrease. Based on Equation 21, this dictates that the air flowing or simply head in terms of ft of air. Setting velocity pressure VP2 must decrease compared to the kinetic energy term equal to the velocity pressure VP1. However, assuming no losses occur between head and with appropriate conversions for ft of air to these two stations, the energy equation (Equation inches water gauge, one can derive the following 13) dictates that the static pressure at Station 2 equation: must increase. Notice, referring again to Fig. 6, that VP= (/ V 1096 )2 ρ () 20 a tradeoff has occurred between static pressure and a velocity pressure based on straightforward applica- where tion of basic fluid mechanics concepts and the geom- VP = velocity pressure, in. WG etry of the system with no actual losses occurring. V = air velocity, fpm The phenomenon depicted here is called static ρ = a density of air, lb per cu ft pressure regain, and it is a very important principle For standard air (sea level pressure, 75 F, and a re- of air system design. A similar principle explains the sulting density of 0.075 lb per cu ft), the equation reduces to: = 2 Transition section P VP(/ V 4005 ) () 21 a 2 This is one of the simplest yet most powerful equa- 1 tions in all of air system technology since it permits Air flow the measurement of flow quantities in operating ductwork and therefore permits the field balancing A1, V1 A2, V2 of air systems. Without this principle, flow tests in operating air systems would be much more difficult. Fig. 3A indicated a field test arrangement to mea- VP2 VP1 sure velocity pressure utilizing the properties of to- TP Positive 1,2 pressures tal, static, and velocity pressures. In the early 1700s, SP2 a French physicist named Henri Pitot invented a de- SP1 vice to simplify measurements of this type through a Pa (Datum pressure) single duct insertion point. This device, shown in TP = TP = SP + VP = SP + VP Fig. 5, is known today as a pitot-static tube and is 1 2 1 1 2 2 used almost universally for field velocity measure- 6 Interchangeability of static and velocity pressures in air ment of duct air flow. Devices of very similar config- systems. Graph below the duct shows the change in VP uration are utilized in flow hoods to measure the air and SP as the fluid flows from the smaller duct through the delivered to rooms through diffusers. Measurement transition section and into the larger duct. of the velocity pressure permits the direct calculation of the duct velocity, using Equation 20, if the air basis of operation of a centrifugal fan. One of the density is known. Use of the continuity equation main purposes of a fan is not only to move air but to (Equation 4) then permits the determination of the increase the pressure of the air to overcome losses in air flowing in the duct or out the flow hood if the flow the remainder of the system. As air passes through area is known. the fan, kinetic energy is imparted to the air stream Another concept relating fluid statics, the continu- and the velocity of the air is increased. As the air ity equation, and the energy equation relates to the passes at high velocity from the relatively small interchangeability of static and velocity pressures in blade passages to the connecting ductwork, the ve-

74 MAY 1995 HEATING / PIPING / AIR CONDITIONING locity is decreased, as at Station 2 in Fig. 6, and the pressure as is often the assumption. If, however, we static pressure is increased. Application of this prin- are dealing with a section of ductwork where the ve- ciple is vital to the operational performance of fans. locity remains constant and therefore the velocity Likewise, any ductwork geometry (such as discharge pressure is constant, the change in total pressure into an open plenum) that does not allow this regain will equal the change in static pressure. In this spe- to occur at the fan discharge in a controlled manner cial case only will Equation 22 predict the static will degrade the capacity and performance of the pressure drop due to frictional losses. fan. Another observation has to do with the relation- Fig. 6 also depicts the difficulty in field measure- ships among the parameters affecting frictional ments using only static pressure. Connecting a simple losses. The equation clearly shows that the losses manometer between Stations 1 and 2 and reversing are directly proportional to the friction factor, the the air flow (right to left from Station 2 to Station 1) length, and the square of the velocity and are in- would indicate that a large pressure drop had oc- versely proportional to the diameter of the duct. Fur- curred between these two points. This is deceptive, thermore, using the continuity equation (Equation however, since by definition for this example, no true 4), we see that if the area of the duct remains con- energy losses have been considered. The static pres- stant, the loss is directly proportional to the square sure drop measured between Stations 2 and 1 due to a of the volumetric flow rate or cfm. The last relation- velocity pressure increase would represent no real loss and no additional burden to be overcome by the TABLE 1—Frictional pressure drop, in. WG per 100 ft. fan. Thus, the energy forms of static pressure and velocity pressure are interchangeable, with the only 1985 ASHRAE 1993 ASHRAE truly significant term being their sum, the total pres- Handbook of Handbook of sure. Condition Fundamentals* Fundamentals* 10 in. round duct 0.16 0.155 Losses and system curves 1000 fpm (Ð3.1%) Any real duct system operating with air flow will experience losses based on the term J(U3 – U2) from 10 in. round duct 1.30 1.15 the energy equation (Equation 15). These losses will 3000 fpm (Ð11.5%) be a function of the velocity of the air flow, the config- 20 in. round duct 0.068 0.066 uration of the duct system, and several other vari- 1000 fpm (Ð2.9%) ables. For the purposes of analysis and calculations, these losses are neatly divided into two categories— 20 in. round duct 0.54 0.51 3000 fpm (Ð5.6%) frictional losses and dynamic losses. Though convenient for these purposes, the separation of these two 40 in. round duct 0.029 0.029 types of losses becomes somewhat difficult in field 1000 fpm (0%) testing, where frequently the effects are superim- 40 in. round duct 0.24 0.23 posed. For the purpose of this discussion, however, we 3000 fpm (Ð4.2%) will treat each of these effects separately. Frictional losses occur in straight ductwork mea- *See the chapter “Duct Design.” sured from centerline to centerline when fittings are involved. These losses occur due to the dissipation of ship is particularly important in the establishment mechanical energy from fluid viscosity and momen- of system curves, as we will see shortly. tum interchange between particles moving at differ- If the friction factor from Equation 22 were a con- ent velocities within the duct. Frictional losses can be stant, the value of many of the duct sizing programs calculated through the use of the Darcy-Weisbach and slide rules would be greatly diminished. How- equation, stated here for systems conveying air at ever, the friction factor actually turns out to be a standard conditions: complex function of air velocity and viscosity, duct ∆hfLDV=(/)(/4005 )2 ( 22 )size, and duct surface roughness. At low air veloci- f ties approaching laminar flow, the friction factor has where actually been shown to be inversely proportional to ∆ = hf frictional loss of total pressure, in. WG the velocity, which when substituted in Equation 22 f=friction factor, dimensionless makes the frictional pressure drop vary directly as L=duct length, ft the velocity or cfm, not as the square. Fortunately, D=duct diameter, ft this situation occurs in air systems at relatively few locations, usually limited to cooling coils, heating V=air velocity, fpm coils, and filter sections. One important observation initially is that the Data in the ASHRAE Handbook of Fundamentals3 equation predicts the loss in total pressure, not static provides data on frictional losses based on air veloc-

HEATING / PIPING / AIR CONDITIONING MAY 1995 75 Round ductwork Square ductwork Air system basics

D X π 2 D 2 ity, air quantity, and round duct size. It should be 7 Comparison of 4 Area x a round and noted that many of the duct sizing programs and π Wetted square duct on D 4x manual duct sizing slide rules relating flow, duct perimeter size, and frictional loss per unit length in use today the basis of the D Hydraulic radius, x 4 hydraulic radius, 4 Rh 4 are based on research done prior to 1950. This re- R . The round search was done on a limited number of duct sizes h With equal flow areas duct is the more 2 πD 2 and was based on duct materials and joining tech- efficient means of = x D = 1.13x 4 niques that are quite different from those used com- conveying air. mercially today. Data based on this research ap- peared in copies of the ASHRAE Handbook of fore, the hydraulic radius of the round duct (D/4) is Fundamentals up to and including 1985. New re- larger than the hydraulic radius of the square duct search, completed in 1987,5 conclusively showed that (X/4) if their flow areas are equal. The result is that the frictional losses then in use were conservative, with the same flow velocity and the same flow area particularly in smaller ductwork at higher veloci- for each duct, the round duct has a larger hydraulic ties. Table 1 is a comparison of friction loss per unit radius and therefore a lower pressure drop. On the length based on results from the 1985 ASHRAE basis of this relationship, the round duct is the more Handbook of Fundamentals utilizing the earlier efficient means of conveying air between two points. data versus the 1993 edition of the same volume uti- The equivalent square duct with the same pressure lizing the results of the most recent friction loss test- drop per unit length will have a larger flow area with ing.5 a lower mean velocity than the round duct. As the Conversion equations also appear in the ASHRAE aspect ratio of the rectangular duct increases, the Handbook of Fundamentals for the determination of mean velocity must be reduced even further to pro- equivalent rectangular and flat oval ducts from the vide an equal pressure drop per unit length, making round ductwork described in Equation 22. This in- high aspect ratio ducts more expensive to construct formation is fairly straightforward and will not be and more prone to temperature losses or gains due to discussed here. However, the basis of this conversion their higher perimeter. can reveal insight into the efficiency of various duct The second type of duct system loss, dynamic loss, shapes at conveying air. It has been determined that results from flow disturbances and turbulence ductwork flowing air at the same mean velocity will caused by changes in flow direction, flow area, or ob- have the same frictional pressure crop per unit structions to the path of the air flow. These losses, length if the ducts have the same ratio of cross-sec- which are now considered the predominant losses in tional area to wetted perimeter. This function is most air duct systems, occur due to the effects of the called the hydraulic radius and is designated as Rh. law of conservation of momentum and a related pro- Fig. 7 shows a comparison of round ductwork versus cess termed flow separation. Fig. 8A shows an elbow square ductwork on the basis of this parameter. No- in a typical rectangular duct system. As indicated in tice that with equal flow areas, the round duct diam- the figure, as the air flow passes the heel of the el- eter D is larger than the square duct side X. There- bow, the air has no intention of making the 90 deg

Main duct Main duct Bag filter section Branch duct Separation Entry point Separation duct point

Co = 1.0 Co = 1.2 14 to 24 deg angle of spread Elbow A Elbow BC

8 View A—loss coefficient, Co, relates to the number of velocity heads in a given fitting configuration or flow geometry. Note how the momentum effect bunches the air flow pattern toward the bottom of the duct in the elbow. The slight decrease in pressure at the top of the bend causes turbulence, resulting in a total pressure loss downstream. View B—flow pattern shown in View A has a serious effect on performance when a branch duct is placed too close to the elbow. Uni- form duct flow has not yet recovered, and flow streamlines oppose entry into the branch duct. View C—lack of properly designed transition from a duct supplying a filter section causes uneven flow through filters (heavy in the center and lighter at the outer filters), resulting in uneven filter loading.

76 MAY 1995 HEATING / PIPING / AIR CONDITIONING left turn necessary to adhere to the duct wall. The where ∆= momentum of the air stream causes the air to sepa- httotal pressure drop due to the combined rate from the duct wall at this point. This separation effects of frictional and dynamic losses, effect causes a wake area beyond the elbow, with ed- in. WG dying flow causing drag and loss of energy. This en- Combining terms, we can write this equation in ergy loss appears as a reduction in air stream total the following form: pressure as given by the following equation for stan- ∆hfLDCV=+[( / ) ](/4005 )2 ( 25 ) dard air conditions: to ∆ = 2 Since for a fixed system the value of f(L/D) + Co hCVd o(/4005 ) () 23 would be composed of a set of constants, the total where pressure drop would be proportional to the square of ∆ = hddynamic loss of total pressure, in. WG the velocity and (with the duct sizes set) to the = square of the volumetric flow rate or cfm. In equa- Colocal loss coefficient, dimensionless = tion form, this relationship is stated as follows: Vair velocity, fpm ∆h =×constant(() cfm)2 26 The local loss coefficient, Co, is cataloged in the t ASHRAE Handbook of Fundamentals3 and relates or to the number of velocity heads lost in a given fitting ∆ 2 configuration or flow geometry. The interesting ht ~(cfm) (27 ) thing about dynamic losses is that the momentum This equation is the basis of the system curve. It effects that contribute to these losses can cause far represents a plot of the pressures required to move more damage than the simple pressure drop they air through the duct system analyzed at various flow create. Note how the air flow pattern is bunched to- rates. This parabolic relationship, shown as System ward the bottom of the duct in Fig. 8A. This situation is not a problem unless the branch duct of Fig. 8B is 9 System curves added. Now the situation becomes very serious since are the basis for the flow streamlines oppose entry into the branch System curve B air system analy- duct shown. Such configurations can be found in nu- sis. Curve A merous existing duct systems, and the poor perfor- illustrates flow mance of these branch ducts in terms of inadequate through a duct air flow is always the result. A similar situation can ∆P alone. Curve B be seen in Fig. 8C. Here, the pressure loss sustained System curve A shows the effects ∆ 2 of overall system from the free exit into the plenum is only part of the ht ~ (cfm) concern. The inability of the air stream to fill the pressure drop, including ducts, plenum due to the momentum effects described ear- cfm coils, and filters. lier causes the succeeding filter section to load un- evenly. Little air will flow across the outer filters, and the increased flow across the center filters will Curve A in Fig. 9, has become the basis of system increase their expected pressure drop if the entire analysis for air systems. plenum was provided with a uniform entering air Deviations from Equation 27 occur only where ele- flow velocity. Failure to recognize such momentum ments of the duct system, such as coils or filters, may effects increases dynamic losses and contributes to exhibit near laminar flow characteristics, as dis- the types of problems shown here. By visualizing cussed earlier. In this case, the pressure drop char- momentum effects during the design of a duct sys- acteristics for these components should be sepa- tem, a designer can improve air separation geome- rately evaluated using the following equation: tries, thus reducing the local loss coefficient (C ) for o ∆ =×N the fittings used, reducing pressure drops, and hcf, constant(() cfm) 28 avoiding the types of problems shown in Figs. 8B where and 8C. ∆h =total pressure drop through coil or filter, Based on these discussions, the total pressure cf, in. WG drop in a duct system would then be equal to the sum = of the frictional and dynamic losses. The following N flow exponent (based on the mix of equation can be derived by combining Equations 22 turbulent and laminar flow characteristics and 23: unique to that component) To determine the flow exponent N for a given coil ∆∆∆hhh=+ t fd or filter, obtain two pressure drops, ∆h1 and ∆h1, =+22from the manufacturer’s rating information at two fL( / DV )( /4005 ) Co ( V / 4005 ) ( 24 ) different flow rates, Q1 and Q2. The following equa-

HEATING / PIPING / AIR CONDITIONING MAY 1995 77 Air system basics

tion can then be used to evaluate the exponent: ics of conveying air. The other aspects of the basics of air systems related to heat transfer, psychrometrics, N= Log(/)/(/)∆∆ h h Log Q Q ()29 12 12 fans, and air distribution effects on human physiol- Flow exponents for typical coils range from 1.46 to ogy are equally rich in theoretical background and 1.81 and for typical filters from 1.01 to 1.79.6 System deserve separate treatment. ⍀ Curve B in Fig. 9 shows the effects of such components on the overall system pressure drop characteristics, including ductwork, coils, and filters. This References type of curve would be derived by adding the system 1) Williams, Gerald J., “Fan Heat: Its Source and Signif- curve characteristics of the ductwork and fittings as icance,” Heating/Piping/Air Conditioning, January 1989. given by Equation 26 to the component system curve 2) Graham, J. Barrie, “The Importance of Fan Total characteristics of the coils and filters as given by Pressure,” Heating/Piping/Air Conditioning, September Equation 28. This combined curve would represent 1994. the true pressure required to move air through an 3) 1993 ASHRAE Handbook of Fundamentals, Chapter actual system composed not only of ductwork and fit- 32, “Duct Design.” tings but also of heating coils, cooling coils, and filters. Air volume and system pressure drop are the 4) Wright, D. K., “A New Friction Chart for Round same for both Curve A and B. The deviations created Ducts,” ASHVE Transactions, Volume 51, 1945. by the latter components may become important 5) Griggs, E. I., W. B. Swim, and G. H. Henderson, “Re- when performance changes are required in existing sistance to Flow of Round Galvanized Ducts,” ASHRAE systems.6 Transactions, 1987. 6) Coad, W. J., J. B. Graham, and G. J. Williams, Air Conclusion Systems Design and Retrofit for Energy/Cost Effective- This article has discussed only a few highlights of ness, Chapter 3, ASHRAE Professional Development Sem- the basics of air systems related to the fluid mechan- inar textbook, 1982.

78 MAY 1995 HEATING / PIPING / AIR CONDITIONING