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Modern Engineering Thermodynamics

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13.5 Operating Efficiencies 465<br />

Station 3—Condenser exit<br />

p 3 = p 2s = 14:7 psia<br />

Station 4s—Boiler inlet<br />

p 4s = p 1 = 100 psia<br />

x 3 = 0 s 4s = s 3<br />

h 3 = h f ð14:7 psiaÞ = 180:1 Btu/lbm<br />

v 3 = v f ð14:7 psiaÞ = 0:01672 ft 3 /lbm<br />

Then, the isentropic efficiency of this system is given by Eq. (13.9b) as<br />

ðη T Þ maximum<br />

Rankine<br />

= h 1 − h 2s − v 3 ðp 4 − p 3 Þ<br />

h 1 − h 3 − v 3 ðp 4 − p 3 Þ<br />

ð1187:8 − 1047:5 Btu/lbmÞ− 0:01672 ft 3 /lbm 100: − 14:7 lbf/in 2 <br />

144 in 2 /ft 2 <br />

118:16 ft . lbf/Btu<br />

=<br />

ð1187:8 − 180:1 Btu/lbmÞ− 0:01672 ft 3 /lbm 100: − 14:7 lbf/in 2 <br />

144 in 2 /ft 2 <br />

118:16 ft . lbf/Btu<br />

= 0:139 = 13:9%<br />

T<br />

1<br />

h<br />

4s<br />

1<br />

3,4s 2s<br />

3<br />

2s<br />

s<br />

s<br />

FIGURE 13.13<br />

Example 13.4, T–s diagram.<br />

b. Here, we use Eq. (13.9a) with (η s ) pm = 0.550. and (η s ) p = 0.650.<br />

ð<br />

ðη T Þ Rankine<br />

= h 1 − h 2s Þðη s Þ pm<br />

− v 3 ðp 4 − p 3 Þ/ ðη s Þ p<br />

h 1 − h 3 − v 3 ðp 4 − p 3 Þ/ ðη s Þ p<br />

ð1187:8 − 1047:5 Btu/lbmÞð0:550Þ− 0:01672 ft 3 /lbm 100: − 14:7 lbf/in 2 <br />

144 in 2 /ft 2 <br />

<br />

1<br />

118:16 ft . lbf/Btu 0:650<br />

=<br />

ð1187:8 − 180:1 Btu/lbmÞ− 0:01672 ft 3 /lbm 100: − 14:7 lbf/in 2 <br />

144 in 2 /ft 2 <br />

<br />

1<br />

118:16 ft . lbf/Btu 0:650<br />

= 0:0762 = 7:62%<br />

c. If the actual power output from the engine is 1400 hp and the isentropic efficiency of the engine is 55%, then the mass<br />

flow rate of steam required is<br />

_m =<br />

_W actual ð1400: hpÞð2545 Btu/hp . hÞ<br />

=<br />

= 46,200 lbm/h<br />

ðh 1 − h 2s Þðη s Þ pm ð1187:8 − 1047:5 Btu/lbmÞð0:550Þ<br />

Exercises<br />

10. Determine the mass flow rate of steam required for the Corliss engine in Example 13.4 if it produced only 1000. hp<br />

instead of 1400. hp. Assume all the other variables remain unchanged. Answer: _m = 33,000 lbm/h.<br />

11. If the isentropic efficiency of the Corliss engine in Example 13.4 were increased from 55.0% to 75.0%, determine<br />

the mass flow rate then required to produce 1400. hp. Assume all the other variables remain unchanged. Answer:<br />

_m = 33,860 lbm/h.<br />

12. If the condenser pressure in Example 13.4 were reduced from 14.7 psia to 1.00 psia, recalculate items a, b, and c in<br />

Example 13.4. Assume all the other variables remain unchanged. Answer: a.(η T ) max Rankine = 26.1%, b. (η T ) Rankine = 14.3%,<br />

and c. _m = 22,3000 lbm/h.

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