JWCL068_ch08_383-460.

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8.48 Water flows through a horizontal 60-mm-diameter galvanized 8.55 A 3-ft-diameter duct is used to carry ventilating air into a ve-
iron pipe at a rate of 0.02 m3 s. If the pressure drop is 135 kPa per hicular tunnel at a rate of 9000 ft3 min. Tests show that the pres-
10 m of pipe, do you think this pipe is (a) a new pipe, (b) an old sure drop is 1.5 in. of water per 1500 ft of duct. What is the value
pipe with a somewhat increased roughness due to aging, or (c) a of the friction factor for this duct and the approximate size of the
very old pipe that is partially clogged by deposits? Justify your an- equivalent roughness of the surface of the duct?
swer.
8.49 Water flows at a rate of 10 gallons per minute in a new hor- Section 8.4.2 Minor Losses (Also see Lab
izontal 0.75-in.-diameter galvanized iron pipe. Determine the pres- Problem 8.131.)
sure gradient, ¢p/, along the pipe.
8.56 Obtain photographs/images of various pipe components that
8.50 Two equal length, horizontal pipes, one with a diameter of would cause minor losses in the system. Print these photos and
1 in., the other with a diameter of 2 in., are made of the same ma- write a brief paragraph that discusses these components.
terial and carry the same fluid at the same flow rate. Which pipe
produces the larger head loss? Justify your answer. 8.57 An optional method of stating minor losses from pipe com-
ponents is to express the loss in terms of equivalent length; the
†8.51 A 6-inch-diameter water main in your town has become head loss from the component is quoted as the length of straight pipe
very rough due to rust and corrosion. It has been suggested that with the same diameter that would generate an equivalent loss. De-
the flowrate through this pipe can be increased by inserting a velop an equation for the equivalent length, /eq.
smooth plastic liner into the pipe. Although the new diameter
will be smaller, the pipe will be smoother. Will such a procedure 8.58 Given 90° threaded elbows used in conjunction with copper
produce a greater flowrate? List all assumptions and show all pipe (drawn tubing) of 0.75-in. diameter, convert the loss for a sin-
calculations. gle elbow to equivalent length of copper pipe for wholly turbulent
flow.
8.52 Blood (assume m  4.5  105 lb # s ft2, SG  1.0) flows
through an artery in the neck of a giraffe from its heart to its head 8.59 Based on Problem 8.57, develop a graph to predict equiva-
at a rate of 2.5  104 ft3  s. Assume the length is 10 ft and the di- lent length, /eq, as a function of pipe diameter for a 45° threaded
ameter is 0.20 in. If the pressure at the beginning of the artery (out- elbow connecting copper piping (drawn tubing) for wholly turbu-
let of the heart) is equivalent to 0.70 ft Hg, determine the pressure lent flow.
at the end of the artery when the head is (a) 8 ft above the heart,
8.60 A regular 90° threaded elbow is used to connect two
or (b) 6 ft below the heart. Assume steady flow. How much of this
straight portions of 4-in.-diameter galvanized iron pipe. (a) If
pressure difference is due to elevation effects, and how much is
the flow is assumed to be wholly turbulent, determine the equiv-
due to frictional effects?
alent length of straight pipe for this elbow. (b) Does a pipe fit-
8.53 A 40-m-long, 12-mm-diameter pipe with a friction factor of ting such as this elbow have a significant or negligible effect on
0.020 is used to siphon 30 °C water from a tank as shown in Fig. the flow? Explain.
P8.53. Determine the maximum value of h allowed if there is to be
8.61 To conserve water and energy, a “flow reducer” is installed
no cavitation within the hose. Neglect minor losses.
in the shower head as shown in Fig. P8.61. If the pressure at
point 112 remains constant and all losses except for that in the
“flow reducer” are neglected, determine the value of the loss co-
efficient 1based on the velocity in the pipe2 of the “flow reducer”
10 m if its presence is to reduce the flowrate by a factor of 2. Neglect
7m
gravity.
3m
1
__ in. Flow reducer washer
2

(1)
30 m
Q
50 holes of
diameter 0.05 in.
h

F I G U R E P8.61

8.62 Water flows at a rate of 0.040 m3 s in a 0.12-m-diameter pipe

that contains a sudden contraction to a 0.06-m-diameter pipe. De-
termine the pressure drop across the contraction section. How much
F I G U R E P8.53 of this pressure difference is due to losses and how much is due to
kinetic energy changes?
8.54 Gasoline flows in a smooth pipe of 40-mm diameter at a rate 8.63 A sign like the one shown in Fig. P8.63 is often attached to
of 0.001 m3 s. If it were possible to prevent turbulence from oc- the side of a jet engine as a warning to airport workers. Based on
curring, what would be the ratio of the head loss for the actual tur- Video V8.10 or Figs. 8.22 and 8.25, explain why the danger areas
bulent flow compared to that if it were laminar flow? (indicated in color) are the shape they are.
JWCL068_ch08_383-460.qxd 9/23/08 11:01 AM Page 452

tube if it is to measure the average velocity in the pipe. (b) Repeat

part (a) for turbulent flow with Re ⫽ 10,000.
8.36 The kinetic energy coefficient, a, is defined in Eq. 5.86. Show
that its value for a power-law turbulent velocity profile (Eq. 8.31) is
given by a ⫽ 1n ⫹ 12 3 12n ⫹ 12 3 Ⲑ 34n4 1n ⫹ 3212n ⫹ 32 4 .
8.37 When soup is stirred in a bowl, there is considerable tur-
bulence in the resulting motion (see Video V8.7). From a very
simplistic standpoint, this turbulence consists of numerous inter-
twined swirls, each involving a characteristic diameter and ve-
10-mm-diameter
locity. As time goes by, the smaller swirls (the fine scale struc-
ture) die out relatively quickly, leaving the large swirls that
0.12 m continue for quite some time. Explain why this is to be expected.
0.25-mm-diameter
0.10-m-long needle
8.38 Determine the thickness of the viscous sublayer in a smooth
8-in.-diameter pipe if the Reynolds number is 25,000.
8.39 Water at 60 °F flows through a 6-in.-diameter pipe with an
average velocity of 15 ftⲐ s. Approximately what is the height of
the largest roughness element allowed if this pipe is to be classi-
patm = 101 kPa (abs) fied as smooth?
F I G U R E P8.30
Section 8.4.1 Major Losses (Also see Lab Problem 8.126.)
Section 8.3 Fully Developed Turbulent Flow 8.40 Obtain photographs/images for round pipes of different mate-
8.31 Obtain a photograph/image of a “turbulator.” (See Fluids in rials. Print these photos and write a brief paragraph that describes the
the News article titled “Smaller heat exchangers” in Section 8.3.1.) different pipes.
Print this photo and write a brief paragraph that describes its use. 8.41 A person with no experience in fluid mechanics wants to esti-
mate the friction factor for 1-in.-diameter galvanized iron pipe at a
8.32 For oil (SG ⫽ 0.86, m ⫽ 0.025 NsⲐm2) flow of 0.3 m3Ⲑs
Reynolds number of 8,000. They stumble across the simple equation
through a round pipe with diameter of 500 mm, determine the
of f ⫽ 64/Re and use this to calculate the friction factor. Explain the
Reynolds number. Is the flow laminar or turbulent?
problem with this approach and estimate their error.
8.33 For air at a pressure of 200 kPa (abs) and temperature of
8.42 Water flows through a horizontal plastic pipe with a diameter
15 °C, determine the maximum laminar volume flowrate for flow
of 0.2 m at a velocity of 10 cm/s. Determine the pressure drop per
through a 2.0-cm-diameter tube.
meter of pipe using the Moody chart.
8.34 Show that the power-law approximation for the velocity pro- 8.43 For Problem 8.42, calculate the power lost to the friction per
file in turbulent pipe flow (Eq. 8.31) cannot be accurate at the cen- meter of pipe.
terline or at the pipe wall because the velocity gradients at these
locations are not correct. Explain. 8.44 Oil (SG ⫽ 0.9), with a kinematic viscosity of 0.007 ft2/s, flows
in a 3-in.-diameter pipe at 0.01 ft3/s. Determine the head loss per unit
8.35 As shown in Video V8.9 and Fig. P8.35, the velocity profile length of this flow.
for laminar flow in a pipe is quite different from that for turbulent
flow. With laminar flow the velocity profile is parabolic; with tur- 8.45 Water flows through a 6-in.-diameter horizontal pipe at a rate
bulent flow at Re ⫽ 10,000 the velocity profile can be approxi- of 2.0 cfs and a pressure drop of 4.2 psi per 100 ft of pipe. Deter-
mated by the power-law profile shown in the figure. (a) For lami- mine the friction factor.
nar flow, determine at what radial location you would place a Pitot 8.46 Water flows downward through a vertical 10-mm-diameter
galvanized iron pipe with an average velocity of 5.0 m Ⲑs and exits
Turbulent with Re = 10,000 as a free jet. There is a small hole in the pipe 4 m above the outlet.
u = 1 – __r 1/5
1.0 __
Vc [ R ] 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 0.5 mⲐs.
r
__
R 8.47 Air at standard conditions flows through an 8-in.-diameter,
14.6-ft-long, straight duct with the velocity versus pressure drop
Laminar with Re < 2100 data indicated in the following table. Determine the average fric-
u = 1 – __
r 2 tion factor over this range of data.
0.5
__
Vc (R)
u
V (ft min) p (in. water)
R r
3950 0.35
Vc 3730 0.32
3610 0.30
3430 0.27
0 0.5 1.0 3280 0.24
u
__
Vc
3000 0.20
2700 0.16
F I G U R E P8.35
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Problems
Note: Unless otherwise indicated use the values of fluid prop- calculated by assuming the flow is laminar. For tubes of diameter
erties found in the tables on the inside of the front cover. Prob- 0.5, 1.0, and 2.0 mm, determine the maximum flowrate allowed
lems designated with an 1*2 are intended to be solved with the (in cm3/s) if the fluid is (a) 20 °C water, or (b) standard air.
aid of a programmable calculator or a computer. Problems
designated with a 1†2 are “open-ended” problems and require
8.8 Carbon dioxide at 20 °C and a pressure of 550 kPa (abs) flows
in a pipe at a rate of 0.04 Ns. Determine the maximum diameter al-
critical thinking in that to work them one must make various
lowed if the flow is to be turbulent.
assumptions and provide the necessary data. There is not a
unique answer to these problems. 8.9 The pressure distribution measured along a straight, horizontal
Answers to the even-numbered problems are listed at the portion of a 50-mm-diameter pipe attached to a tank is shown in the
end of the book. Access to the videos that accompany problems table below. Approximately how long is the entrance length? In the
can be obtained through the book’s web site, www.wiley.com/ fully developed portion of the flow, what is the value of the wall
college/munson. The lab-type problems and FlowLab problems shear stress?
can also be accessed on this web site.

Section 8.1 General Characteristics of Pipe Flow (Also

x (m) (ⴞ0.01 m) p (mm H2O) (ⴞ5 mm)
see Lab Problem 8.130.)
0 (tank exit) 520
8.1 Obtain a photograph/image of a piping system that would 0.5 427
likely contain “pipe flow” and not “open channel flow.” Print this 1.0 351
photo and write a brief paragraph that describes the situation in- 1.5 288
volved. 2.0 236
8.2 Water flows through a 50-ft pipe with a 0.5-in. diameter at 2.5 188
5 gal/min. What fraction of this pipe can be considered an entrance 3.0 145
region? 3.5 109
4.0 73
8.3 Rainwater runoff from a parking lot flows through a 3-ft-diam- 4.5 36
eter pipe, completely filling it. Whether flow in a pipe is laminar or 5.0 (pipe exit) 0
turbulent depends on the value of the Reynolds number. (See Video
V8.2.) Would you expect the flow to be laminar or turbulent? Sup-
port your answer with appropriate calculations.
8.10 (See Fluids in the News article titled “Nanoscale flows,” Sec-
8.4 Blue and yellow streams of paint at 60 °F (each with a density tion 8.1.1.) (a) Water flows in a tube that has a diameter of
of 1.6 slugs  ft3 and a viscosity 1000 times greater than water) enter D  0.1 m. Determine the Reynolds number if the average veloc-
a pipe with an average velocity of 4 ft s as shown in Fig. P8.4. ity is 10 diameters per second. (b) Repeat the calculations if the
Would you expect the paint to exit the pipe as green paint or sepa- tube is a nanoscale tube with a diameter of D  100 nm.
rate streams of blue and yellow paint? Explain. Repeat the problem
if the paint were “thinned” so that it is only 10 times more viscous
than water. Assume the density remains the same. Section 8.2 Fully Developed Laminar Flow
Green? 8.11 Obtain a photograph/image of a piping system that contains
Yellow 2 in. both entrance region flow and fully developed flow. Print this
Splitter photo and write a brief paragraph that describes the situation in-
volved.
8.12 For fully developed laminar pipe flow in a circular pipe, the
Blue
25 ft velocity profile is given by u(r)  2 (1  r2R2) in m/s, where R
is the inner radius of the pipe. Assuming that the pipe diameter is
F I G U R E P8.4
4 cm, find the maximum and average velocities in the pipe as well
as the volume flow rate.
8.5 Air at 200 °F flows at standard atmospheric pressure in a pipe
at a rate of 0.08 lb/s. Determine the minimum diameter allowed if 8.13 The wall shear stress in a fully developed flow portion of a
the flow is to be laminar. 12-in.-diameter pipe carrying water is 1.85 lbft2. Determine the
pressure gradient, 0p 0x, where x is in the flow direction, if the
8.6 To cool a given room it is necessary to supply 4 ft3/s of air pipe is (a) horizontal, (b) vertical with flow up, or (c) vertical with
through an 8-in.-diameter pipe. Approximately how long is the en- flow down.
trance length in this pipe?
8.14 The pressure drop needed to force water through a horizon-
8.7 A long small-diameter tube is to be used as a viscometer by tal 1-in.-diameter pipe is 0.60 psi for every 12-ft length of pipe. De-
measuring the flowrate through the tube as a function of the pres- termine the shear stress on the pipe wall. Determine the shear stress
sure drop along the tube. The calibration constant, K  Q  ¢p, is at distances 0.3 and 0.5 in. away from the pipe wall.
JWCL068_ch08_383-460.qxd 9/23/08 11:01 AM Page 454

454 Chapter 8 ■ Viscous Flow in Pipes

Estimate the extra pressure drop between points (1) and (2) caused
by these straws.

C1130F

WARNING Stand clear of

Hazard areas while engine is
running
(1)
Tightly packed 0.25-in.-diameter,
12-in.-long straws

(2)
12 in.

WARNING Stand clear of

Hazard areas while engine is
running
F I G U R E P8.66

8.67 Repeat Problem 8.66 if the straws are replaced by a piece of

porous foam rubber that has a loss coefficient equal to 5.4.
8.68 As shown in Fig. P8.68, water flows from one tank to an-
other through a short pipe whose length is n times the pipe diam-
eter. Head losses occur in the pipe and at the entrance and exit.
F I G U R E P8.63 (See Video V8.10.) Determine the maximum value of n if the ma-
jor loss is to be no more than 10% of the minor loss and the fric-
tion factor is 0.02.
8.64 (See Fluids in the News article titled “New hi-tech foun-
tains,” Section 8.5.) The fountain shown in Fig. P8.64 is de-
signed to provide a stream of water that rises h  10 ft to
h  20 ft above the nozzle exit in a periodic fashion. To do this
the water from the pool enters a pump, passes through a pres-
sure regulator that maintains a constant pressure ahead of the
flow control valve. The valve is electronically adjusted to pro-
vide the desired water height. With h  10 ft the loss coefficient D
for the valve is KL  50. Determine the valve loss coefficient
needed for h  20 ft. All losses except for the flow control valve ᐉ = nD
are negligible. The area of the pipe is 5 times the area of the exit
nozzle.
F I G U R E P8.68

h 8.69 Air flows through the fine mesh gauze shown in Fig. P8.69
with an average velocity of 1.50 m/s in the pipe. Determine the
loss coefficient for the gauze.

4 ft
Gauze over
end of pipe

V = 1.5 m/s

Pump Flow control valve Water

Pressure regulator 8 mm
F I G U R E P8.64

F I G U R E P8.69
*8.65 Water flows from a large open tank through a sharp-edged
entrance and into a galvanized iron pipe of length 100 m and di-
ameter 10 mm. The water exits the pipe as a free jet at a distance 8.70 Water flows steadily through the 0.75-in-diameter galva-
h below the free surface of the tank. Plot a log–log graph of the nized iron pipe system shown in Video V8.14 and Fig. P8.70 at
flowrate, Q, as a function of h for 0.1 h 10 m. a rate of 0.020 cfs. Your boss suggests that friction losses in the
straight pipe sections are negligible compared to losses in the
8.66 Air flows through the mitered bend shown in Fig. P8.66 at threaded elbows and fittings of the system. Do you agree or dis-
a rate of 5.0 cfs. To help straighten the flow after the bend, a set agree with your boss? Support your answer with appropriate cal-
of 0.25-in.-diameter drinking straws is placed in the pipe as shown. culations.
JWCL068_ch08_383-460.qxd 9/23/08 11:02 AM Page 458

458 Chapter 8 ■ Viscous Flow in Pipes

KL exit = 1.0 8.107 Air, assumed incompressible, flows through the two pipes
KL elbow = 1.5 shown in Fig. P8.107. Determine the flowrate if minor losses are
neglected and the friction factor in each pipe is 0.015. Determine
KL valve = 6.0
the flowrate if the 0.5-in.-diameter pipe were replaced by a 1-in.-
KL filter = 12.0 KL ent = 0.8 diameter pipe. Comment on the assumption of incompressibility.
200 ft. of 0.1-ft-diameter
Filter pipe with ε/D = 0.01 p = 0.5 psi
Pump
T = 150°F
F I G U R E P8.99 1 in. 0.50 in.

Section 8.5.1 Single Pipes—Determine Diameter 20 ft 20 ft

8.100 A certain process requires 2.3 cfs of water to be delivered

F I G U R E P8.107
at a pressure of 30 psi. This water comes from a large-diameter
supply main in which the pressure remains at 60 psi. If the galva-
nized iron pipe connecting the two locations is 200 ft long and con- *8.108 Repeat Problem 8.107 if the pipes are galvanized iron and
tains six threaded 90° elbows, determine the pipe diameter. Eleva- the friction factors are not known a priori.
tion differences are negligible.
†8.109 Estimate the power that the human heart must impart to
8.101 Water is pumped between two large open reservoirs through the blood to pump it through the two carotid arteries from the heart
1.5 km of smooth pipe. The water surfaces in the two reservoirs are to the brain. List all assumptions and show all calculations.
at the same elevation. When the pump adds 20 kW to the water the
flowrate is 1 m3Ⲑ s. If minor losses are negligible, determine the pipe 8.110 The flowrate between tank A and tank B shown in
diameter. Fig. P8.110 is to be increased by 30% (i.e., from Q to 1.30Q) by
the addition of a second pipe (indicated by the dotted lines) run-
8.102 Determine the diameter of a steel pipe that is to carry ning from node C to tank B. If the elevation of the free surface in
2000 galⲐ min of gasoline with a pressure drop of 5 psi per 100 ft of tank A is 25 ft above that in tank B, determine the diameter, D, of
horizontal pipe. this new pipe. Neglect minor losses and assume that the friction
8.103 Water is to be moved from a large, closed tank in which the factor for each pipe is 0.02.
air pressure is 20 psi into a large, open tank through 2000 ft of
smooth pipe at the rate of 3 ft3 Ⲑ s. The fluid level in the open tank
is 150 ft below that in the closed tank. Determine the required di- 6-in. diameter; 6-in. diameter;
ameter of the pipe. Neglect minor losses. 600 ft long 500 ft long

8.104 Rainwater flows through the galvanized iron downspout C

shown in Fig. P8.104 at a rate of 0.006 m3Ⲑ s. Determine the size
A

of the downspout cross section if it is a rectangle with an aspect

B
ratio of 1.7 to 1 and it is completely filled with water. Neglect the
velocity of the water in the gutter at the free surface and the head Diameter D, 500 ft long
loss associated with the elbow.
F I G U R E P8.110

70 mm 8.111 The three tanks shown in Fig. P8.111 are connected by pipes
with friction factors of 0.03 for each pipe. Determine the water ve-
locity in each pipe. Neglect minor losses.
g

Elevation =
850 ft

Elevation =
4m
838 ft

D = 1.1 ft
D = 1.0 ft ᐉ = 700 ft B
ᐉ = 800 ft
Elevation =
A 805 ft
3m
F I G U R E P8.104

D = 1.2 ft C
ᐉ = 600 ft
*8.105 Repeat Problem 8.104 if the downspout is circular.
F I G U R E P8.111
Section 8.5.2 Multiple Pipe Systems
8.106 Obtain a photograph/image of a multiple pipe system with 8.112 The three water-filled tanks shown in Fig. P8.112 are con-
series of parallel flows. Print this photo and write a brief paragraph nected by pipes as indicated. If minor losses are neglected, deter-
that describes the situation involved. mine the flowrate in each pipe.
JWCL068_ch08_383-460.qxd 9/23/08 11:02 AM Page 457

Problems 457
the flowrate passing between the tanks? Assume the friction fac-
tor to be equal to 0.02 and minor losses to be negligible.
20 m †8.96 Gasoline is unloaded from the tanker truck shown in
Diffuser Fig. P8.96 through a 4-in.-diameter rough-surfaced hose. This is a
“gravity dump” with no pump to enhance the flowrate. It is claimed
T
that the 8800-gallon capacity truck can be unloaded in 28 minutes.
1m Do you agree with this claim? Support your answer with appropri-
120 m of 0.30-m-diameter ate calculations.
cast-iron pipe
F I G U R E P8.91

*8.92 In some locations with very “hard” water, a scale can build Midstate Gasoline
up on the walls of pipes to such an extent that not only does the
roughness increases with time, but the diameter significantly de-
creases with time. Consider a case for which the roughness and di-
ameter vary as e ⫽ 0.02 ⫹ 0.01t mm, D ⫽ 50 (1 ⫺ 0.02t) mm,
where t is in years. Plot the flowrate as a function of time for t ⫽ 0
to t ⫽ 10 years if the pressure drop per 12 m of horizontal pipe re-
mains constant at ¢p ⫽ 1.3 kPa.
8.93 Water flows from the nozzle attached to the spray tank shown F I G U R E P8.96
in Fig. P8.93. Determine the flowrate if the loss coefficient for the
nozzle (based on upstream conditions) is 0.75 and the friction fac- 8.97 The pump shown in Fig. P8.97 delivers a head of 250 ft to
tor for the rough hose is 0.11. the water. Determine the power that the pump adds to the water.
The difference in elevation of the two ponds is 200 ft.
Nozzle diameter
= 7.5 mm
KL = 1.0
exit

p = 150 kPa Pump

KL = 1.5
elbow
D = 15 mm KL = 5.0
valve
0.80 m ᐉ = 1.9 m Pipe length = 500 ft
Pipe diameter = 0.75 ft
40° KL = 0.8 Pipe roughness = 0
ent

F I G U R E P8.93 F I G U R E P8.97
8.94 When the pump shown in Fig. P8.94 adds 0.2 horsepower to
the flowing water, the pressures indicated by the two gages are 8.98 Water flows through two sections of the vertical pipe shown
equal. Determine the flowrate. in Fig. P8.98. The bellows connection cannot support any force in
the vertical direction. The 0.4-ft-diameter pipe weighs 0.2 lb兾ft, and
Length of pipe between gages ⫽ 60 ft the friction factor is assumed to be 0.02. At what velocity will the
Pipe diameter ⫽ 0.1 ft force, F, required to hold the pipe be zero?
Pipe friction factor ⫽ 0.03
Filter loss coefficient ⫽ 12
Free jet
Filter Pump

f = 0.020 Pipe weighs

0.20 lb/ft

F I G U R E P8.94
D = 0.40 ft
8.95 Water is pumped between two large open tanks as shown in
Fig. P8.95. If the pump adds 50 kW of power to the fluid, what is Bellows

V
Diameter
Dm = 0.5 m
Water
Pump F I G U R E P8.98

8.99 Water is circulated from a large tank, through a filter, and back
Pipe length = 600 m to the tank as shown in Fig. P8.99. The power added to the water by
F I G U R E P8.95 the pump is 200 ft # lbⲐ s. Determine the flowrate through the filter.
JWCL068_ch08_383-460.qxd 9/30/08 8:41 AM Page 459

Problems 459
Elevation = 60 m 8.116 A 2-in.-diameter orifice plate is inserted in a 3-in.-diameter
pipe. If the water flowrate through the pipe is 0.90 cfs, determine
Elevation = 20 m the pressure difference indicated by a manometer attached to the
flow meter.
Elevation = 0
D = 0.10 m 8.117 Air to ventilate an underground mine flows through a large
ᐉ = 200 m 2-m-diameter pipe. A crude flowrate meter is constructed by placing
f = 0.015
a sheet metal “washer” between two sections of the pipe. Estimate
the flowrate if the hole in the sheet metal has a diameter of 1.6 m and
the pressure difference across the sheet metal is 8.0 mm of water.
D = 0.08 m D = 0.08 m
ᐉ = 200 m ᐉ = 400 m 8.118 Water flows through a 40-mm-diameter nozzle meter in a
f = 0.020 f = 0.020 75-mm-diameter pipe at a rate of 0.015 m3  s. Determine the pres-
F I G U R E P8.112 sure difference across the nozzle if the temperature is (a) 10 °C,
or (b) 80 °C.
8.113 (See Fluids in the News article titled “Deepwater pipeline,” 8.119 Air at 200 °F and 60 psia flows in a 4-in.-diameter pipe at
Section 8.5.2.) Five oil fields, each producing an output of Q bar- a rate of 0.52 lb s. Determine the pressure at the 2-in.-diameter
rels per day, are connected to the 28-in.-diameter “main line pipe” throat of a Venturi meter placed in the pipe.
(A– B–C) by 16-in.-diameter “lateral pipes” as shown in Fig. 8.120 A 2.5-in.-diameter flow nozzle is installed in a 3.8-in.-
P8.113. The friction factor is the same for each of the pipes and diameter pipe that carries water at 160 °F. If the air –water
elevation effects are negligible. (a) For section A– B determine the manometer used to measure the pressure difference across the me-
ratio of the pressure drop per mile in the main line pipe to that in ter indicates a reading of 3.1 ft, determine the flowrate.
the lateral pipes. (b) Repeat the calculations for section B–C.
8.121 A 0.064-m-diameter nozzle meter is installed in a 0.097 m-
diameter pipe that carries water at 60 °C. If the inverted air –water
Q Lateral Q U-tube manometer used to measure the pressure difference across
Q the meter indicates a reading of 1 m, determine the flowrate.
A B C 8.122 Water flows through the Venturi meter shown in
Main line Q Fig. P8.122. The specific gravity of the manometer fluid is 1.52.
Q Determine the flowrate.
F I G U R E P8.113

Q
†8.114 As shown in Fig. P8.114, cold water (T  50 F) flows 6 in. 3 in.
from the water meter to either the shower or the hot water heater.
In the hot water heater it is heated to a temperature of 150 F. Thus,
with equal amounts of hot and cold water, the shower is at a com- 2 in.
fortable 100 F. However, when the dishwasher is turned on, the SG = 1.52
shower water becomes too cold. Indicate how you would predict
this new shower temperature (assume the shower faucet is not ad- F I G U R E P8.122
justed). State any assumptions needed in your analysis.
8.123 Water flows through the orifice meter shown in Fig. P8.123
at a rate of 0.10 cfs. If d  0.1 ft, determine the value of h.

h
Hot Dishwasher
Shower

Cold d
Q 2 in.
Water meter
Hot water heater

F I G U R E P8.123

F I G U R E P8.114
8.124 Water flows through the orifice meter shown in Fig. P8.123
such that h  1.6 ft with d  1.5 in. Determine the flowrate.
Section 8.6 Pipe Flowrate Measurement (Also see Lab
8.125 The scale reading on the rotameter shown in Fig. P8.125
Problem 8.127.) and Video V8.14 (also see Fig. 8.46) is directly proportional to the
8.115 Obtain a photograph/image of a flowrate measurement de- volumetric flowrate. With a scale reading of 2.6 the water bubbles
vice. Print this photo and write a brief paragraph that describes the up approximately 3 in. How far will it bubble up if the scale read-
measurement range of the device. ing is 5.0?