fluid_mechanics

458 Chapter 8 ■ Viscous Flow in Pipes
K L exit = 1.0
K L elbow = 1.5
K L valve = 6.0
K L filter = 12.0
K L ent = 0.8
8.107 Air, assumed incompressible, flows through the two pipes
shown in Fig. P8.107. Determine the flowrate if minor losses are
neglected and the friction factor in each pipe is 0.015. Determine
the flowrate if the 0.5-in.-diameter pipe were replaced by a 1-in.-
diameter pipe. Comment on the assumption of incompressibility.
Filter
Pump
F I G U R E P8.99
200 ft. of 0.1-ft-diameter
pipe with ε/D = 0.01
p = 0.5 psi
T = 150°F
1 in. 0.50 in.
Section 8.5.1 Single Pipes—Determine Diameter
8.100 A certain process requires 2.3 cfs of water to be delivered
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 galvanized
iron pipe connecting the two locations is 200 ft long and contains
six threaded 90° elbows, determine the pipe diameter. Elevation
differences are negligible.
8.101 Water is pumped between two large open reservoirs through
1.5 km of smooth pipe. The water surfaces in the two reservoirs are
at the same elevation. When the pump adds 20 kW to the water the
flowrate is 1 m 3 s. If minor losses are negligible, determine the pipe
diameter.
8.102 Determine the diameter of a steel pipe that is to carry
2000 galmin of gasoline with a pressure drop of 5 psi per 100 ft of
horizontal pipe.
8.103 Water is to be moved from a large, closed tank in which the
air pressure is 20 psi into a large, open tank through 2000 ft of
smooth pipe at the rate of 3 ft 3 s. The fluid level in the open tank
is 150 ft below that in the closed tank. Determine the required diameter
of the pipe. Neglect minor losses.
8.104 Rainwater flows through the galvanized iron downspout
shown in Fig. P8.104 at a rate of 0.006 m 3 s. Determine the size
of the downspout cross section if it is a rectangle with an aspect
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
loss associated with the elbow.
*8.108 Repeat Problem 8.107 if the pipes are galvanized iron and
the friction factors are not known a priori.
†8.109 Estimate the power that the human heart must impart to
the blood to pump it through the two carotid arteries from the heart
to the brain. List all assumptions and show all calculations.
8.110 The flowrate between tank A and tank B shown in
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) running
from node C to tank B. If the elevation of the free surface in
tank A is 25 ft above that in tank B, determine the diameter, D, of
this new pipe. Neglect minor losses and assume that the friction
factor for each pipe is 0.02.
A
20 ft 20 ft
F I G U R E P8.107
6-in. diameter;
600 ft long
Diameter D, 500 ft long
F I G U R E P8.110
C
6-in. diameter;
500 ft long
B
70 mm
g
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 velocity
in each pipe. Neglect minor losses.
4 m
Elevation =
838 ft
Elevation =
850 ft
3 m
F I G U R E P8.104
A
D = 1.0 ft
= 800 ft
D = 1.1 ft
= 700 ft
B
Elevation =
805 ft
*8.105 Repeat Problem 8.104 if the downspout is circular.
Section 8.5.2 Multiple Pipe Systems
8.106 Obtain a photograph/image of a multiple pipe system with
series of parallel flows. Print this photo and write a brief paragraph
that describes the situation involved.
F I G U R E P8.111
D = 1.2 ft
= 600 ft
8.112 The three water-filled tanks shown in Fig. P8.112 are connected
by pipes as indicated. If minor losses are neglected, determine
the flowrate in each pipe.
C