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