Problem 8.32
Water is pumped between two tanks as shown in the figure below. The energy line is as
indicated. Is the fluid being pumped from A to B or B to A? Explain. Which pipe has the
larger diameter: A to the pump or B to the pump? Explain.
Solution 8.32
The energy line is horizontal if there is no head loss. With friction (a head loss) the
Energy line
P
AB
Problem 8.33
A person with no experience in fluid mechanics wants to estimate the friction factor for
1-in.– diameter galvanized iron pipe at a Reynolds number of
8
000. The person stumbles
across the simple equation of =64
Re
f and uses this to calculate the friction factor. Explain
the problem with this approach and estimate their error.
Solution 8.33
For Re 8000= under standard conditions, the pipe flow will be turbulent.
Problem 8.34
During a heavy rainstorm, water from a parking lot completely fills an 18–in.– diameter,
smooth, concrete storm sewer. If the flowrate is
3
ft
1
0s, determine the pressure drop in a
100-ft horizontal section of the pipe. Repeat the problem if there is a 2-ft change in
elevation of the pipe per 100 ft of its length.
Solution 8.34
Equivalent Roughness,
ε
Pipe Feet Millimeters
Riveted steel 0.003–0.03 0.9–9.0
Concrete 0.001–0.01 0.3–3.0
(1)
(2)
ℓ
= 100 ft
D
= 18 m
V
1
V
2
a) With =
12
zz
Eq. (2) gives
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
103
2(103)468
104
2(104)468
105
2(105)468
106
2(106)468
107
2(107)468
0.05
0.04
0.03
0.02
0.015
0.01
0.008
0.006
Re = VD
_____
μ
ρ
Problem 8.35
Water flows through a horizontal plastic pipe with a diameter of 0.2 m at a velocity of
cm
1
0s. Determine the pressure drop per meter of pipe and the power lost to the friction per
meter of pipe.
Solution 8.35
The pressure drop in the pipe can be found from
ρ
Δ=
2
2
V
pf
D
The friction factor is determined from the Moody chart.
So Δ
p
per meter =
(1 m)
Δ=0.649 Pap per meter of pipe
Power can be found from
Problem 8.36
Water flows downward through a vertical 10-mm– diameter galvanized iron pipe with an
average velocity of m
5
s and exits as a free jet. There is a small hole in the pipe 4 m above
the outlet. Will water leak out of the pipe through this hole, or will air enter into the pipe
through the hole? Repeat the problem if the average velocity is m
0.5 s.
Solution 8.36
γ
2
Dg , or
With
ε
from the table below,
Equivalent Roughness,
ε
Pipe Feet Millimeters
Riveted steel 0.003–0.03 0.9–9.0
Concrete 0.001–0.01 0.3–3.0
4 m = ℓ
D
= 0.01 m
?
(1)
•
Q
Thus, from Eq. (1),
()
2
5
133 2
4m 1 kg m N N
0.045 999 5 9800 4m 1.86 10
0.01m 2 s
mm m
p
=−=×
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.05
0.04
0.03
0.02
0.015
μ
Problem 8.37
Air at standard conditions flows through an 8-in.- diameter, 14.6-ft– long, straight duct
with the velocity versus head loss data indicated in the following table. Determine the
average friction factor over this range of data.
V (ft/min) h (in. water)
3950 0.35
3730 0.32
3610 0.30
3430 0.27
3280 0.24
3000 0.20
2700 0.16
Solution 8.37
γγ
++=+ ++
22
2
11 2 2
12
222
pV p V V
zzf
ggDg
where == Δ=− =
12 1212
VV V, ,z
p
pp z
Calculated values are given below:
V (ft/min) h (in. water) f
3950 0.35 0.0161
Problem 8.38
Water flows through a horizontal 60-mm– diameter galvanized iron pipe at a rate of
3
m
0.02 s. If the pressure drop is 135 kPa per 10 m of pipe, do you think this pipe is (a) a
new pipe, (b) an old pipe with a somewhat increased roughness due to aging, or (c) a very
old pipe that is partially clogged by deposits? Justify your answer.
Solution 8.38
For the horizontal pipe, =
()zz
with =
VV
, the energy equation
for a new galvanized iron pipe (see the table below),
Equivalent Roughness,
ε
Pipe Feet Millimeters
Riveted steel 0.003–0.03 0.9–9.0
Concrete 0.001–0.01 0.3–3.0
ℓ
= 10 m
D
= 0.06 m
p
1
–
p
2
= 135 kPa
(2)(1)
V
Since this is less than the actual =0.324,f the pipe is not a new pipe.
With =×
5
Re 3.79 10 and =0.324f, we obtain from the figure above a relative roughness of
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
Re = VD
_____
μ
ρ
Problem 8.39
Water flows at a rate of 10 gallons per minute in a new horizontal 0.75-in.– diameter
galvanized iron pipe. Determine the pressure gradient, Δ
p
, along the pipe.
Solution 8.39
33
3
gal 1min 231in. 1gal ft
10 0.0223
min 60s 1gal s
1728in.
Q
==
Thus,
Thus,
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.05
0.04
0.03
0.02
0.015
0.01
Re = VD
_____
μ
Problem 8.40
Carbon dioxide at a temperature of 0C
and a pressure of 600 kPa (abs) flows through a
horizontal 40-mm– diameter pipe with an average velocity of
m
2
s. Determine the friction
factor if the pressure drop is 2
N
235 m per 10-m length of pipe.
Solution 8.40
For a horizontal pipe,
ρ
Δ= 2
1
2
p
fV
D, or
ρ
Δ
=2
2Dp
fV
where
Problem 8.41
Blood (assume 5
2
lb s
4.5 10 , 1.0
ft SG
µ
−⋅
=× =
) flows through an artery in the neck of a giraffe
from its heart to its head at a rate of
3
4ft
2
.5 10 s
−
×. Assume the length is 10 ft and the
diameter is 0.20 in. If the pressure at the beginning of the artery (outlet of the heart) is
equivalent to 0.70 ft Hg , determine the pressure at the end of the artery when the head is
(a) 8 ft above the heart, or (b) 6 ft below the heart. Assume steady flow. How much of this
pressure difference is due to elevation effects, and how much is due to frictional effects?
Solution 8.41
== =
64 64 0.0778
Re 823
f
(1)
(2)
D = 0.20 in.
Vℓ = 10 ft
(a) With −=
21
8 ftzz ,
(b) With −=−
21 6 ftzz ,
Problem 8.42
A 40-m– long, 12-mm- diameter pipe with a friction factor of 0.020 is used to siphon 30 C
water from a tank as shown in the figure below. Determine the maximum value of h
allowed if there is to be no cavitation within the hose. Neglect minor losses.
Solution 8.42
The minimum pressure is the vapor pressure =4.243 kPa
v
p (abs) (see Table B.2 Physical
Properties of Water [SI Units]). Assume the minimum pressure is at the top of the hose
=
3.
v
p
p We will check this assumption after we obtain h.
7 m
10 m
30 m
h
3 m
7 m
10 m
(1)
•
(3)
Thus,
or
m
2.56 s
V
=
Obtain h from
Check if minimum pressure occurs at (3). Consider point (4).
we obtain
()
γρ
=−+ 2
424
1
2
L
pzzf V
D
or
Problem 8.43
Gasoline flows in a smooth pipe of 40-mm diameter at a rate of
3
m
0.001 s . If it were
possible to prevent turbulence from occurring, what would be the ratio of the head loss for
the actual turbulent flow compared to that if it were laminar flow?
Solution 8.43
Let ( )t denote the turbulent flow and ( ) the laminar flow.
From Table 1.5 Approximate Physical Properties of Some Common Liquids (SI Units)
Hence, from the figure below, for a smooth pipe =0.0192
t
f
Transition range
Laminar flow
Wholly turbulent flow
0.1
0.09
0.08
0.07
0.06
0.05
0.04
103
104
105
106
107
0.05
0.04
0.03
0.02
0.015
0.01
Re = VD
_____
μ
ρ
while for laminar flow −
== = ×
×
4
4
64 64 9.16 10
Re 6.98 10
f
Thus, from Eq. (1)
Problem 8.44
A 3-ft- diameter duct is used to carry ventilating air into a vehicular tunnel at a rate of
3
9000 ft /min . Tests show that the pressure drop is 1. 5 in . of water per
1
500 ft of duct. What
is the value of the friction factor for this duct and the approximate size of the equivalent
roughness of the surface of the duct?
Solution 8.44
γγ
++=+ ++
22
2
11 2 2
12
222
pV p V V
zzf
ggDg
, (1)
Thus, from Eq. (1)
ρ
−= 2
12
1
2
p
pf V
D or