fluid_mechanics

Problems 259
5.110 The hydroelectric turbine shown in Fig. P5.110 passes 8 million
gal/min across a head of 600 ft. What is the maximum amount of
power output possible? Why will the actual amount be less?
600 ft
5.114 A centrifugal air compressor stage operates between an inlet
stagnation pressure of 14.7 psia and an exit stagnation pressure
of 60 psia. The inlet stagnation temperature is 80 °F. If the loss of
total pressure through the compressor stage associated with irreversible
flow phenomena is 10 psi, estimate the actual and ideal
stagnation temperature rise through the compressor. Estimate the
ratio of ideal to actual temperature rise to obtain an approximate
value of the efficiency.
5.115 Water is pumped through a 4-in.-diameter pipe as shown in
Fig. P5.115a. The pump characteristics (pump head versus
flowrate) are given in Fig. P5.115b. Determine the flowrate if the
head loss in the pipe is h L 8V 2 2g.
Turbine
F I G U R E P5.110
5.111 A pump is to move water from a lake into a large, pressurized
tank as shown in Fig. P5.111 at a rate of 1000 gal in 10 min or
less. Will a pump that adds 3 hp to the water work for this purpose?
Support your answer with appropriate calculations. Repeat the problem
if the tank were pressurized to 3, rather than 2, atmospheres.
12 ft
V
Pump
(a)
h p , ft
F I G U R E P5.115
20
16
h p = 16 – 5Q
12
8
4
0
0 1 2 3
Q, ft 3 /s
(b)
20 ft
Air
p = 2 atm
5.116 Water is pumped from the large tank shown in Fig. P5.116.
The head loss is known to be equal to 4V 2 2g and the pump head is
h , where h is in ft when Q is in ft 3 p 20 4Q 2
p
s. Determine the
flowrate.
Pump
F I G U R E P5.111
5.112 A hydraulic turbine is provided with 4.25 m 3 /s of water at
415 kPa. A vacuum gage in the turbine discharge 3 m below the
turbine inlet centerline reads 250 mm Hg vacuum. If the turbine
shaft output power is 1100 kW, calculate the power loss through
the turbine. The supply and discharge pipe inside diameters are
identically 80 mm.
5.113 Water is supplied at 150 ft 3 s and 60 psi to a hydraulic turbine
through a 3-ft inside diameter inlet pipe as indicated in Fig.
P5.113. The turbine discharge pipe has a 4-ft inside diameter. The
static pressure at section 122, 10 ft below the turbine inlet, is 10-in.
Hg vacuum. If the turbine develops 2500 hp, determine the power
lost between sections 112 and 122.
Section (1)
p 1
Q
= 60 psi
= 150 ft 3 /s
D 1 = 3 ft
13 ft
Q V
Pump
Pipe area = 0.10 ft 2
F I G U R E P5.116
5.117 When a fan or pump is tested at the factory, head curves
(head across the fan or pump versus volume flowrate) are often
produced. A generic fan or pump head curve is shown in
Fig.P5.117a. For any piping system, the drop in pressure or head
involved because of loss can be estimated as a function of volume
flowrate. A generic piping system loss curve is shown in
Fig.P5.117b. When the pump or fan and piping system associated
with the two curves of Fig.P5.117 are combined, what will the
flowrate be? Why? How can the flowrate through this combined
system be varied?
10 ft
Turbine
p 2 = 10-in. Hg
vacuum
D 2 = 4 ft
Section (2)
H, Head across
fan or pump
Q, Volume flowrate
(a)
H, Head loss in
piping system
Q, Volume flowrate
(b)
F I G U R E P5.113
F I G U R E P5.117