V E L O C I T Y a n d V E L O C I T Y P R E S S U R E I n A I R S Y S T E M S

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Godwin Copeland
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1 V E L O C I T Y n d V E L O C I T Y R E S S U R E I n A I R S Y S T E M S A nlysis of fluid systes using ir re usully done voluetric bsis so the pressure version of the Bernoulli eqution is used. This version of the eqution requires tht ech ter be in force per unit re of the fluid tht is floing. In the pound-force pound-ss syste pressure is in lbf per ft 2 nd voluetric flo rte is in ft 3 /inute. In ost ducted systes 1 pressure in lbf/ft 2 is sll nuber nd velocity pressure is not directly esurble in convenient fshion. Therefore it is coon prctice to use pitotsttic tube nd U-tube noeter contining ter to deterine totl pressure sttic pressure nd their difference velocity pressure. This technique expresses the ctul pressures of the ir in equivlent heds of ter (esured in inches). The reltionship beteen pressure nd hed you ill recll is: = γ 1 h 1 = γ 2 h 2 = γ n h n here the subscripts 1 2 nd n (4.1) denote fluids 1 2 or n. Judicious selection of the fluid kes the instruenttion prcticl. Meteorologists use this technique to deterine broetric (sttic) pressure except tht the fluid of choice in the noeter is ercury (specific grvity = 13.6). The noeter is seled t the top nd evcuted so tht the reference pressure is (nerly) perfect vcuu so the esureent is in bsolute. The to ost coon scles re clibrted in inches (stndrd se-level pressure is Hg) or illieters (stndrd se-level pressure is 760 Hg). Clerly the eteorologist ould rther esure the height of colun of ercury (bout 30 ) rther thn colun of ter (bout 34 ) or of ir (bout if the top of the colun could even be scertined) to deterine the sttic pressure t the botto. Becuse voluetric flo rte is usully expressed in cubic feet per inute (cf) it desirble to express velocity in feet per inute. Velocity cn be esured in ducted systes ith hot-ire neoeters nd other types of instruent hich tend to be expensive frgile or inccurte but the ost coon field technique esures velocity pressure fro hich velocity y be coputed. The velocity pressure ( v ) ter v 2 /2g c tells us tht the velocity pressure is function of velocity nd density of the fluid (in our cse ir). The theticl linkge beteen velocity nd velocity pressure becoes very hndy becuse e frequently need to esure flo rte in the syste. Flo rte is relted to velocity velocity is relted to velocity pressure nd velocity pressure cn be deterined by esureent. C:\Ind_Vent\Fluids\Htl\vel&vp\VEL&VR.DOC 9/28/97 HO-4 ME-456 pg 1 1 Ducted is used to denote round or rectngulr conduit contining ir t reltively lo gge pressure. Copressed ir systes t higher pressures typiclly use pipe or tubing s the conduit.

2 Tking the bove ter for velocity pressure nd solving for velocity e get: v = 2g c v here velocity is in ft./sec. (4.2) The ir systes engineer uses ter or red gge oil (sp. gr for better visibility) in the noeter becuse ost ir systes hether conveying energy or ss ill operte beteen +20 H 2 O nd -20 H 2 O or less. In eqution (4.2) for v of the ir e ill insert its esured equivlent γ h here the subscript denotes ter. If e nt velocity in feet per inute the eqution becoes: v = γ 2g c h ; substituting e get v = ( 2)( 32. 2)( 62. 3)( 3600)( ) ( 12)( ) h here 3600 converts sec 2 to in 2 nd 12 converts h in inches to feet. v = 1097 h (4.3) We leve h nd s vribles becuse h ill be esured in inches by the noeter nd e ill be deling ith ir t vrious densities s tepertures nd elevtions bove se level chnge fro syste to syste. Most systes re t or ner se level nd t or ner 75 F so stndrd ir is defined s hving density of lb per ft 3. Inserting tht vlue in the eqution yields: v = 4005 here v is in ft/in. nd h is in inches. (4.4) h Tbulted vlues for v nd h hve been published for stndrd conditions nd re included in the text Industril Ventiltion Tbles 5-7 & 5-7b. It should be noted tht the conventionl U-tube noeter nd pitot-sttic tube do not esure velocity pressure directly becuse the tip of the pitot tube hich fces upstre cnnot seprte the velocity pressure coponent fro the totl pressure it esures. If hoever the pitot tube is connected to the noeter such tht totl pressure is iposed on one end of the noeter nd sttic pressure on the other the noeter subtrcts sttic pressure fro totl pressure nd reds out in velocity pressure. Stndrd ir floing t 1266 ft./in. ill exert 0.1 of velocity pressure. Therefore t velocities belo bout 1000 ft./in. stndrd U-tube noeter is difficult to red. Severl types of inclined tube noeter hve been devised to del ith this proble. (See figures in the text). Other types of instruenttion re lso discussed in the text. C:\Ind_Vent\Fluids\Htl\vel&vp\VEL&VR.DOC 9/28/97 HO-4 ME-456 pg 2

3 roper esuring technique is iportnt to ccurtely deterine verge velocity becuse ost systes ill hve syetric velocity profiles donstre of obstructions or direction chnges. Deterining Density Dry ir is physicl ixture of nitrogen oxygen rgon crbon dioxide nd other trce gses in reltively fixed proportions. As such its density cn be clculted for ny teperture nd pressure by the idel gs l nd its specific eight deterined by grvittionl field in hich it exists. Hoever in nture dry ir virtully does not exist becuse there is lys soe ter vpor included in the ixture. Becuse ter vpor is lighter thn ir (copre their oleculr eights) nd becuse the ount of ter vpor in one unit (usully one lb) of dry ir cn vry idely the folloing eqution 1 is recoended for coputing ir density. = ( sφ) +.754( t+ 460) G φ s (4.5) here: s φ G t is broetric pressure in inches ercury is prtil pressure of the ter vpor t sturtion t teperture t in inches ercury. [see Tble 1.7 pg1-11 in FE] is reltive huidity (unit less) is specific grvity of the gs (unit less) nd is 1.0 for ir is the density of ter vpor reltive to the density of ir (hich is pproxitely 0.622) 2. is the dry bulb teperture of the ixture in degrees F Substituting nd siplifying the eqution becoes: = (. 378s φ). 754( t + 460) (4.6) This eqution sys in effect tht cubic foot of dry ir nd ter vpor ill be less dense thn dry ir lone becuse ter vpor is less dense thn ir t given teperture. Notice tht the eqution is in the for of the idel gs l except tht the second ter in the nuertor corrects for the effects of the lighter-thn-ir ter vpor. Fro the definition of reltive huidity φ e get the folloing eqution: φ= (4.7) s C:\Ind_Vent\Fluids\Htl\vel&vp\VEL&VR.DOC 9/28/97 HO-4 ME-456 pg 3 1 Jorgensen R; Fn Engineering; pg. 1-17; Bufflo Forge Co.; The reltive density vries s the product of reltive huidity nd sturted vpor pressure to the.704 poer divided by 1130 plus At oderte tepertures nd reltive huidifies the dded ccurcy over.622 isn t orth the trouble.

4 An eqution proposed by Crrier 1 cn be used to find prtil pressure of superheted ter vpor in ir : ( s ')( t t') = s' t' (4.8) Where: is prtil pressure of ter vpor in inches of ercury s sturtion pressure t the et-bulb teperture t t is the dry-bulb teperture in o F t is the et-bulb teperture in o F is the broetric pressure in inches of ercury nd the sturtion pressure cn be found by the folloing eqution 2 : s ' = 2. 96x10 t' 159. x10 t' (4.9) 40 0 F < t < 90 0 F The sturtion pressure over liquid ter for the teperture rnge of 32 to 392 o F is given by Hylnd nd Wexler (1983): ln( s ) = C 8 /T = C 9 + C 10 T + C 11 T 2 + C 12 T 3 + C 13 ln(t) Where: s = psi T = bsolute teperture C 8 = E+04 C 9 = E+01 C 10 = E-02 C 11 = E-05 C 12 = E-09 C 13 = Reltive Huidity φ= = s v sv C:\Ind_Vent\Fluids\Htl\vel&vp\VEL&VR.DOC 9/28/97 HO-4 ME-456 pg 4 1 Crrier W. H.; Rtionl sychoetric Forule; Trnsctions of A.S.M.E.; vol pp Lbortory Methods of Testing Fns for Rting. ;AMCA Stndrd ASHRAE Stndrd pp12 & 42 3 Jorgensen Robert; Fn Engineering; Bufflo Forge Copny; 8 th edition; 1983

5 Huidity Rtio W = = gs Specific Huidity H = + = ix Absolute Huidity = Q Degree of Sturtion µ= W W s tp Specific Volue vol oist ir ixture ss dry ir ( ) RT W ν= RT = W ( ) h = t+ W t Enthlpy ( ) td = + bα+ cα + dα + e De oint Teperture ( ) 32 < T < 200 o F W = t d = α α 2 T > 32 o F α=ln( ) = b = c = d = e = ' ' ( t ) W ( t t' ) t t' s C:\Ind_Vent\Fluids\Htl\vel&vp\VEL&VR.DOC 9/28/97 HO-4 ME-456 pg 5

Chapter 14. Gas-Vapor Mixtures and Air-Conditioning. Study Guide in PowerPoint

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