fluid_mechanics

Problems 455
90° threaded
elbows
6-in. length
4-in. length
Closed ball
valve
6-in. length
0.60-in. dia.
Reducer
Q = 0.020 cfs
1-in. length
Tee
and the branch line is shut off. Determine the minimum height, h,
of the water tank under the assumption that (a) minor losses are negligible,
(b) minor losses are not negligible.
8.78 Repeat Problem 8.77 with the assumption that the branch
line is open so that half of the flow from the tank goes into the
branch, and half continues in the main line.
8.79 The exhaust from your car’s engine flows through a complex
pipe system as shown in Fig. P8.79 and Video V8.12. Assume that
the pressure drop through this system is ¢p 1 when the engine is
idling at 1000 rpm at a stop sign. Estimate the pressure drop (in
terms of ¢p 1 ) with the engine at 3000 rpm when you are driving
on the highway. List all the assumptions that you made to arrive
at your answer.
F I G U R E P8.70
Section 8.4.3 Noncircular Conduits
8.71 Obtain a photograph/image of a noncircular duct. Print this
photo and write a brief paragraph that describes the situation involved.
8.72 Given two rectangular ducts with equal cross-sectional area,
but different aspect ratios (width/height) of 2 and 4, which will
have the greater frictional losses? Explain your answer.
8.73 Air at standard temperature and pressure flows at a rate of
7.0 cfs through a horizontal, galvanized iron duct that has a rectangular
cross-sectional shape of 12 in. by 6 in. Estimate the pressure
drop per 200 ft of duct.
8.74 Air flows through a rectangular galvanized iron duct of size
0.30 m by 0.15 m at a rate of 0.068 m 3 s. Determine the head loss
in 12 m of this duct.
8.75 Air at standard conditions flows through a horizontal 1 ft by
1.5 ft rectangular wooden duct at a rate of 5000 ft 3 min. Determine
the head loss, pressure drop, and power supplied by the fan to overcome
the flow resistance in 500 ft of the duct.
Section 8.5.1 Single Pipes—Determine Pressure Drop
8.76 Assume a car’s exhaust system can be approximated as 14 ft
of 0.125-ft-diameter cast-iron pipe with the equivalent of six 90°
flanged elbows and a muffler. (See Video V8.12.) The muffler acts
as a resistor with a loss coefficient of K L 8.5. Determine the
pressure at the beginning of the exhaust system if the flowrate is
0.10 cfs, the temperature is 250 °F, and the exhaust has the same
properties as air.
8.77 The pressure at section 122 shown in Fig. P8.77 is not to fall
below 60 psi when the flowrate from the tank varies from 0 to 1.0 cfs
Exhaust header
F I G U R E P8.79
8.80 According to fire regulations in a town, the pressure drop in
a commercial steel horizontal pipe must not exceed 1.0 psi per
150 ft of pipe for flowrates up to 500 galmin. If the water temperature
is above 50° F, can a 6-in-diameter pipe be used?
8.81 As shown in Video V8.14 and Fig. P8.81, water “bubbles up”
3 in. above the exit of the vertical pipe attached to three horizontal
pipe segments. The total length of the 0.75-in.-diameter galvanized
iron pipe between point (1) and the exit is 21 in. Determine
the pressure needed at point (1) to produce this flow.
3 in.
4 in.
F I G U R E P8.81
8.82 Water at 10 °C is pumped from a lake as shown in
Fig. P8.82. If the flowrate is 0.011 m 3 s, what is the maximum
length inlet pipe, /, that can be used without cavitation
occurring?
(1)
Muffler
Exhaust
6 ft
10 ft
600 ft
with 15
90° elbows
F I G U R E P8.77
h
All pipe is 6-in.-diameter plastic
( /D = 0), flanged fittings
∋
Branch line
900 ft
(2) Main
line
Elevation
650 m
Length
D = 0.07 m
= 0.08 mm
∋
F I G U R E P8.82
Elevation
653 m
Q =
0.011 m 3 /s
8.83 Water flows through the pipe system shown in Fig. P8.83
at a rate of 0.30 ft 3 /s. The pipe diameter is 2 in., and its roughness
is 0.002 in. The loss coefficient for each of the five filters is 6.0,
and all other minor losses are negligible. Determine the power