Page Points Max. Pts. 1 2 34 66 .~~ ~ MAE 101 B - Spring 2014 - Midterm Exam I Name _________________ ID # Directions: Read each problem carefully before starting. Note attached reference sheets. Answers should be clear, complete, and explicit. SHOW ALL WORK. 1. (34pts) Consider fully develoj>ed laminar and turbulent flows in a smooth pipe section of diameter, D, and length, L. Assume both flows have the same volume flowrate and fluid properties. a. Is the average velocity in thE. laminar flow (larger, smaller, same) compared with the turbulent flow? Clearly explain physics and/or justify with equations. b. Is the wall shear stress in the aminar flow (larger, smaller, same) compared with the turbulent flow? Clearly explain ph::'sics and justify with equations (Hint: sketch velocity profiles). c. Is the pressure drop in the laminar flow (larger, smaller, same) compared with the turbulent flow? Clearly explain ph:rsics and justify with equations. 1 2. (66pts) Two large resevoirs wLh a difference in water-surface elevation of 15 m are connected by 50 m total length of 12 cm diameter wrought iron pipe. Additional components are indicated in the figure below. Assume the ;vater is at 20°C and the resevoirs are open to the ambient air pressure of 101 kPa. Determine the volumetric flow rate [m 3 /s] through the pipe. Given: Solution: 2 Reference Sheet I Conservation of Mass ~:~ a r + pcN at lcv r pv .dA .!cs Conservation of Momentum v v v.dA a r pcN + r P .!cs at lcv Fs +Fa Conservation of Energy -f) 8t ( ) P1 Vi2 -+a1-+gz1 p 2 1 CV epcN + 1 . . .. CS . Win + -.rn epV · dA L V Waut rn V.;liues of (V<l) for water at 60°F (velocity, ft/s 0.2 0.1 0.4 0.6 0.8 I 6 8 IO 20 40 60 2 fD -2 x 80 100 diameter, in) 200 400 600 800 1000 2000 4000 8000 10,000 6000 Values of (Vd) hr atmospheric air at 60'F . 8000 80 000 20 40 :ICJ 1100! 200 400 600 800 1000 2000 4000 6000 10,000 20.000 40,000 60,000 100,000 0.10~1T"""T""~,-...,.-...,.-~,T""T'",.,...,-~~,,.,.-,-~,-...,.--,--.,-,.~-,~,..,...,..,,~,--,.--...,.....---~----------...,.....-~~~~~ I 0 .09 08 O. 0.07 I I I Laminar-Critical I I'k 11 I I I· I ·+++-1t-,+,~,,~,c---+---f-++-++++-+,-++++-----t-1--++-++++-+-+++1--i--+-+-+-+-+++-+-+-+-H ' -flow - zone Transiti-+-on._..:_-:_~-_,_t--TI-ti ·+1+-1t--It-It-It-lt--IHll--t-1--+1--il-lf-IHl-+l+l-+l-+-+-++-----t----t-+-+++-+-t--1-H-t-t---+---+--+-+-t-t+++++-H e=m=fftliltztontet!§'~·~tC~o·mplete '., ---,.. - ' turbulence, rough pipes -+-+-++--~+-+_,_,H-++-+-+-+-++--+---+-4--+--l-+-I_,_,--+-->-+-< j'+::i:t"t::ttffi~~=:j:::~~ti=~#~=:j:::=:j:::p~ti=~#~=:j:::~:l":j:::j::j:#:l":j:~ 0.05 0.04 0.06 1-+-t-t+\--+--+-t- 0.03 l 0.02 O.D15 II ......, ... 0.03 0.01 0.008 0.006 ~ 0.004 g u <.::! ·.g "'"' ~ 'fili 2= 4) 0.025 0.002 § & w/"<3 0.02 ,__,__+-++-+-+-1-H.+-+-H-+-+-+-+-t--+---+-+-+-1 .._"""' ~ 0.001 0.0008 0.0006 0.0004 ~ ~r-.... H-+-++-+-+-H-++-H-H-+++-+--+-+-+ ++t-+-+-TI-+-" "'r-.... ~ O.Q15 ,__,__+-++-+-+-+-+-+-+--H-+-+-+-++-+---+-+-+--t-+-+-+-+-+-l+---~0"~"..Pokf""""":-f-f-Hl'l--.....t=-++-t--+-H"ld-H-1+---+~-+-H-H-1-+-H-H H-+-++-+-+-1-+-++-H-1-+-+++-+--+-+-+-H-t--1-+-1-1+-~oo "~.~~~ft'~f;;;;t-'rt-fl;;;=-tr-----t---t'~f~i't'~~H""'t-1;:;~;;;;;f~::::;:;j;:;;j;+=1;;!;+:j;;;j;;~ 0.0002 rQh· ,.,, ~ 1-+-+-++-+-+-H-++-H-H-t-tt-+--t-t-t-.,-t-tt-t-t-t-tt--t-~~8'-'N~~,...i..:=,l'-kl~......._---=1"-~-=c-1--_H-1-+-H-H"l>.,-,+--+--+-+++-H--H-+-++ 'i-. ..........._ 0.0001 ... .__ ~----+--+-+-+-+-++-r-+-+-+-++-----+---+-+-+-ttttttti---t--r-ttttittttft"""~~t::::S.:,t,:ttiitttr'tj:::::f::::~~~+:++:!+l 0.000,05 0.011--t-i++-+-+--+-+++-H--t+t++-+--+--+-+--"-++-+-+++1-+--+-++-++++-++++l----P-~.._"-k~~~,++++++11--+--+-++-t+-Pf..t-+++i 0.009H--i++-+-+--H-++-H--H-t++-+-+--+-+-~++-+-++-++-+--+-++-++++++++ll---+-+-~'-F"j.~~~~,+'l";.i...___ =-1---j-++-++++-+++-A o.oos ttttt=:t::tttttttttttl=:t:ttt:.:tt1tttttt=I=1::.ttltttttt:tt=1=1=ttltttJ:§tt;-:;,:b:t;.__tl:ti:littttJ 0.000,01 103 2(103) 3 4 5 6 8104 2(104) 3 4 5 6 8105 2(105) 3 4 5 6 8106 2(106) 3 4 5 6 8107 2(107) 3 4 5 6 8108 Reynolds number Re = vVd £ I d = 0.000,00 I ~ d = 0.000,005 > ·~ ~ Reference Sheet II TaDle 8.2 Minor Loss Coefficients for Pipe Entrance;s (Data from [12).) Minor Loss Coefficient, K0 Entrance Type Reentrant Square-edged Rounded ---- 0.78 &..... 0.5 r-- t D ~1 r/D 0.02 0.06 K 0.28 0.15 r-t- ~ 0.15 0.04 Fig. 8.15 Loss coefficients for flow through sudden area changes. (Data from [1 ].) • Based on h1. = K(V2/2), where Vis the mean velocity in the,pipe. Table 8.1 Roughness for Pip~-;-~f C~mmon Engineering Ma·~ri~;{oata ;;;;;[a1}1-··~ ------Milli mete~'. Roug1·!mess, e ------- Pipe .Feet 0.9-9 ~ 0.3-3 ·~ 0.2-0.9 j 0.26 ··1 0.15 0.12 0.003-0.03 0.001 -0.01 0.0006-0.003 0.00085 0.0005 0.0004 Riveted steel Concrete Wood stave Cast iron Gal\anized iron Asphalted cast iron Commercial steel or wrought iron Drawn tubing 0.046 0.0015 0.00015 0.000005 Table 8.4 Representative Dimensionless Equivalent Lengths (Le/D) for Valves and Fittings (Data from [12].) Equivalent Length,0 L.ID Fitting Type Valves (fully open) Gate valve Globe valve Angle valve Ball valve Lift check valve: globe lift : angle lift Foot valve with strainer: poppet disk : hinged disk Standard elbow: 90° : 45° Return bend, close pattern Standard tee: flow through run : flow through branch -2 •Basedonh1• = TableA.8 Properties of Water (SI Units) Temperature, Density, Dynamic Viscosity, T(OC) p (kg/m 3 ) µ (N · s/m2 ) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 1000 1000 1000 999 998 997 996 994 992 990 988 986 983 980 978 975 972 969 965 962 958 l.75E-03 l.50E-03 l.30E-03 1.14E-03 l.OOE-03 8.90E-04 7.97E-04 7.18E-04 6.5IE-04 5.94E-04 5.44E-04 5.0lE-04 4.63E-04 4.30E-04 4.00E-04 3.74E-04 3.51E-04 3.30E-04 3.l!E-04 2.94E-04 2.79E-04 Kinell!iatlc Visco::lity, 11 (m:h) l.75E -06 I.SOE -06 l.30E· -06 l.14E· -06 1.00E ·06 8.93E--07 8.0lE·-07 7.23E·-07 6.57E--07 6.00E-··07 5.51E--07 5.08£·;·07 4.71E·i·07 4.38E.,·07 4.lOE--·07 3.84E-07 3.61E- 07 3.41E- 07 3.23£-.07 3.06E-·07 2.91E-07 u (Nim) Vapor Pressure, Pv (kPa) Bulk Modulus, Ev (GPa) 0.0757 0.0749 0.0742 0.0735 0.0727 0.0720 0.0712 0.0704 0.0696 0.0688 0.0679 0.0671 0.0662 0.0654 0.0645 0.0636 0.0627 0.0618 0.0608 0.0599 0.0589 0.661 0.872 1.23 1.71 2.34 3.17 4.25 5.63 7.38 9.59 12.4 15.8 19.9 25.0 31.2 38.6 47.4 57.8 70.1 84.6 101 2.01 Surface Tension, 2.21 2.29 2.12 f~ ~. 8 340 150 3 600 55 420 75 30 16 50 20 60
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