Modern Engineering Thermodynamics

6.9 Shaft Work Machines 189
1
Basement wall
p 1 = 85.0 psig
City
water
main
2
p 2 = 10.0 psig
W shaft
To water
meter
FIGURE 6.12
Example 6.5.
Now, (2.50 gal/h)(0.13368 ft 3 /gal)(1 h/3600 s) = 9.283 × 10 −5 ft 3 /s. So,
_W shaft = ð9:283 × 10 −5 ft 3 /sÞ½ð85:0 − 10:0Þ lbf/in 2 Šð144 in 2 /ft 2 Þ
= 1:00 ft.lbf/s:
= ð1:00 ft.lbf/sÞ½1 hp/ð550 ft.lbf/sÞŠ = 1:82 × 10 −3 hp
= ð1:82 × 10 −3 hpÞð746 W/hpÞ = 1:36 W
Therefore, the amount of power we get out of such a device would be extremely low and probably would not justify its
initial expense. 7
Suppose, now, we calculate an instantaneous power instead of the average power. For this calculation, we assume an instantaneous
water flow of 5 gal/min. Then, the hydraulic power produced is
= ð1:36 WÞð5 gal/minÞð60 min/hÞ½1/ð2:50 gal/hÞŠ
_W Shaft instantaneous
=163 W
Which is more reasonable. This is enough power to light two 75 W lightbulbs, but since this water flow rate does not occur
continuously the bulbs would not be lit very often.
Exercises
12. What flow rate of water would be required in Example 6.5 to produce 1.00 hp of shaft output power?
Answer: _m w = 22.9 gal/min.
13. Determine the inlet water pressure required in Example 6.5 to produce a continuous shaft output power of 163 W with
a water flow rate of 2.50 gal/h. Answer: (p inlet ) w = 9.00 × 10 3 psig.
14. It has been suggested that, by installing a hydraulic turbine powered electric generator on the main water pipe supplying
all the open flow devices in a house (sinks, toilets, washing machines, etc.), some of the water flow energy that is
ordinarily wasted could be converted into useful electrical energy. Discuss the feasibility of this proposal in a short
paragraph. Hint: Consider the economic costs of such a system and the required payback time. Estimate how much
electrical power could be generated by analyzing the water flow in your home.
7 This conclusion might change if we were dealing with the domestic water flow into a large factory or multistory office or apartment building.
EXAMPLE 6.6
Determine the quality of the steam at the outlet of an insulated steam turbine producing 2000. kJ of energy per kilogram of
steam flowing through the turbine. The steam at the inlet of the turbine is at 2.00 MPa, 800.°C and the outlet pressure is
1.00 kPa. Neglect any changes in specific kinetic or potential energy of the flow stream, and assume a steady state operation.
Solution
First, draw a sketch of the system (Figure 6.13).
The system is open, and the unknown is the turbine’s outlet steam quality x 2 , as shown in Figure 6.13. The material is
steam.
(Continued )