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Problems
otes on Pipe Diameter for Chapter 10 Problems
When a pipe diameter is given using the label “NPS” or “nominal,” find the dimensions using Table 10.1 on
p. 319. Otherwise, assume the specified diameter is an inside diameter (ID).
Classifying Flow
10.1
Kerosene (20°C) flows at a rate of 0.04 m
3
/s in a 25 cm diameter pipe. Would you expect the flow to be
laminar or turbulent? Calculate the entrance length.
10.2
A compressor draws 0.3 m
3
/s of ambient air (20°C) in from the outside through a round duct that is 10 m
long and 150 mm in diameter. Determine the entrance length and establish whether the flow is laminar or
turbulent.
Answer:
Flow is turbulent,
L
e
= 7.5 m
10.3
Specify the diameter and length for a tube that carries SAE 10 W30 oil at 38°C. The design requires
laminar flow, fully developed flow, and a discharge of
Q
= 0.2 L/s.
DarcyWeisbach Equation
10.4
Using Section 10.3 and other resources, answer the following questions. Strive for depth, clarity,
and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness
of your communication.
a. What is pipe head loss? How is pipe head loss related to total head loss?
b. What is the friction factor
f
? How is
f
related to wall shear stress?
c. What assumptions need to be satisfied to apply the DarcyWeisbach equation?
10.5
For each case that follows, apply the DarcyWeisbach equation from Eq. (10.12) to calculate the
head loss in a pipe. Apply the grid method to carry and cancel units.
a. Water flows at a rate of 20 gpm and a mean velocity of 180 ft/min in a pipe of length 200 feet. For a
resistance coefficient of
f
= 0.02, find the head loss in feet.
b. The head loss in a section of PVC pipe is 0.8 m, the resistance coefficient is
f
= 0.012, the length is
15 m and the flow rate is 1 cfs. Find the pipe diameter in meters.
10.6
As shown, air (20°C) is flowing from a large tank, through a horizontal pipe, and then discharging to
ambient. The pipe length is
L
= 50 m, and the pipe is schedule 40 PVC with a nominal diameter of 1 inch.
The mean velocity in the pipe is 10 m/s, and
f
= 0.015. Determine the pressure (in Pa) that needs to be
maintained in the tank.
PROBLEM 10.6
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Answer:
p
tank
= 1.75 kPa gage
10.7
Water (15°C) flows through a garden hose (ID = 18 mm) with a mean velocity of 1.5 m/s. Find the
pressure drop for a section of hose that is 20 meters long and situated horizontally. Assume that
f
= 0.012.
10.8
As shown, water (15°C) is flowing from a tank through a tube and then discharging to ambient. The tube
has an ID of 8 mm, a length of
L
= 6 m, and the resistance coefficient is
f
= 0.015. The water level is
H
= 3 m. Find the exit velocity in m/s. Find the discharge in
L
/s. Sketch the HGL and the EGL. Assume
that the only head loss occurs in the tube.
PROBLEM 10.8
Answer:
V
= 2.19 m/s,
Q
= 0.110 L/s
10.9
Water flows in the pipe shown, and the manometer deflects 90 cm. What is
f
for the pipe if
V
= 3 m/s?
PROBLEM 10.9
Flow in Pipes (Laminar Flow)
10.10
Using Section 10.5 and other resources, answer the questions that follow. Strive for depth, clarity,
and accuracy while also combining sketches, words, and equations in ways that enhance the effectiveness
of your communication.
a. What are the main characteristics of laminar flow?
b. What is the meaning of each variable that appears in Eq. (10.27)?
c. In Eq. (10.33), what is the meaning of
h
f
10.11
A fluid ( = 10
2
N · s/m
2
; ρ = 800 kg/m
3
) flows with a mean velocity of 4 cm/s in a 10 cm smooth pipe.
a. What is the value of Reynolds number?
b. What is the magnitude of the maximum velocity in the pipe?
c. What is the magnitude of the friction factor
f
?
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d. What is the shear stress at the wall?
e. What is the shear stress at a radial distance of 25 mm from the center of the pipe?
10.12
Water (15°C) flows in a horizontal schedule 40 pipe that has a nominal diameter of 0.5 in. The Reynolds
number is Re = 1000. Work in SI units.
a. What is mass flow rate?
b. What is the magnitude of the friction factor
f
?
c. What is the head loss per meter of pipe length?
d. What is the pressure drop per meter of pipe length?
Answer:
= 0.0141 kg/s,
f
= 0.064,
h
f
≠ L = 0.00108 m per meter of pipe length,
p
/L = 10.6 Pa per meter of pipe
length
10.13
Flow of a liquid in a smooth 3 cm pipe yields a head loss of 2 m per meter of pipe length when the mean
velocity is 1 m/s. Calculate
f
and the Reynolds number. Prove that doubling the flow rate will double the
head loss. Assume fully developed flow.
10.14
As shown, a round tube of diameter 0.5 mm and length 750 mm is connected to plenum. A fan produces
a negative gage pressure of 1.5 inch H
2
O in the plenum and draws air (20°C) into the microchannel.
What is the mean velocity of air in the microchannel? Assume that the only head loss is in the tube.
PROBLEM 10.14
Answer:
V
2
= 0.215 m/s
10.15
Liquid (γ = 10 kN/m
3
) is flowing in a pipe at a steady rate, but the direction of flow is unknown. Is the
liquid moving upward or moving downward in the pipe? If the pipe diameter is 8 mm and the liquid
viscosity is 3.0 × 10
3
N · s/m
2
what is the magnitude of the mean velocity in the pipe?
PROBLEM 10.15
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10.16
Oil (S = 0.97, = 10
2
lbfs/ft
2
) is pumped through a nominal 1 in., schedule 80 pipe at the rate of 0.004
cfs. What is the head loss per 100 ft of level pipe?
Answer:
h
f
= 66.4 ft per 100 ft run of pipe
10.17
A liquid (ρ = 1000 kg/m
3
; = 10
1
N · s/2 m
2
; ν = 10
4
m
2
/s) flows uniformly with a mean velocity of
1.5 m/s in a pipe with a diameter of 100 mm. Show that the flow is laminar. Also, find the friction factor
f
and the head loss per meter of pipe length.
10.18
Kerosene (S = 0.80 and
T
= 68°F) flows from the tank shown and through the 1/4 in.–diameter (ID) tube.
Determine the mean velocity in the tube and the discharge. Assume the only head loss is in the tube.
PROBLEM 10.18
Answer:
V
= 0.81 ft/s,
Q
= 2.76 × 10
4
cfs
10.19
Oil (S = 0.94; = 0.048 N · s/m
2
) is pumped through a horizontal 5 cm pipe. Mean velocity is 0.5 m/s.
What is the pressure drop per 10 m of pipe?
10.20
As shown, SAE 10 W30 oil is pumped through an 8 m length of 1 cm–diameter drawn tubing at a
discharge of 7.85 × 10
4
m
3
/s. The pipe is horizontal, and the pressures at points 1 and 2 are equal. Find
the power necessary to operate the pump, assuming the pump has an efficiency of 100%. Properties of
SAE l0W30 oil: kinematic viscosity = 7.6 × 10
5
m
2
/s; specific weight = 8630 N/m
3
.
PROBLEM 10.20
Answer:
P
= 1340 W
10.21
Oil (S = 0.9; = 10
2
lbfs/ft
2
; ν = 0.0057 ft
2
/s) flows downward in the pipe, which is 0.10 ft in diameter
and has a slope of 30° with the horizontal. Mean velocity is 2 ft/s.What is the pressure gradient (
dp
/
ds
)
along the pipe?
PROBLEM 10.21
10.22
In the pipe system for a given discharge, the ratio of the head loss in a given length of the 1 m pipe to the
head loss in the same length of the 2 m pipe is (a) 2, (b) 4, (c) 16, or (d) 32.
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PROBLEM 10.22
Answer:
Correct choice is (d)
10.23
Glycerine (
T
= 68°F) flows in a pipe with a 1/2 ft diameter at a mean velocity of 2 ft/s. Is the flow laminar
or turbulent? Plot the velocity distribution across the flow section.
10.24
Glycerine (
T
= 20°C) flows through a funnel as shown. Calculate the mean velocity of the glycerine
exiting the tube. Assume the only head loss is due to friction in the tube.
PROBLEM 10.24
Answer:
V
2
= 0.0409 m/s
10.25
What nominal size of steel pipe should be used to carry 0.2 cfs of castor oil at 90°F a distance of 0.5 mi
with an allowable pressure drop of 10 psi ( = 0.085 lbfs/ft
2
)? Assume S = 0.85.
10.26
Velocity measurements are made in a 30 cm pipe. The velocity at the center is found to be 1.5 m/s, and
the velocity distribution is observed to be parabolic. If the pressure drop is found to be 1.9 kPa per 100 m
of pipe, what is the kinematic viscosity n of the fluid? Assume that the fluid's specific gravity is 0.80.
Answer:
ν = 8.91 × 10
5
m
2
/s
10.27
The velocity of oil (S = 0.8) through the 5 cm smooth pipe is 1.2 m/s. Here
L
= 12 m,
z
1
= 1 m,
z
2
= 2 m,
and the manometer deflection is 10 cm. Determine the flow direction, the resistance coefficient
f
, whether
the flow is laminar or turbulent, and the viscosity of the oil.
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