Problem 10-1 - Example 10-1 An ideal Brayton cycle is used...

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Example 10-1 An ideal Brayton cycle is used to produce 500 hp of net work. Air enters the compressor at 70°F, 14.7 psia and is compressed to 120 psia. The mass flow rate is 150 lbm/min. Assuming constant specific heats at 77°F, a) Find the turbine inlet temperature b) Calculate cycle efficiency Solution: The compressor is isentropic, so 1 22 11 k k TP ⎛⎞ = ⎜⎟ ⎝⎠ Btu cp(Air, 77) 0.24 lbm K cp T == = Btu cv(Air, 77) 0.171 lbm K cv T = 0.24 1.4 0.171 cp k cv = () 1.4 1 1.4 o 2 120 70 460 966R 506 F 14.7 T =+ = = From the first law for the compressor ee ii QW m h m h −= ± ± ±± 21 Wm h h ± ± ( ) 12 p hh m c TT =− = ± Using c p at 77°F,
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() o lbm Btu Btu 150 0.24 70 506 F 15,696 min lbm R min W ⎛⎞ =− = ⎜⎟ ⎝⎠ ± Btu 15,696 min C W = ± Btu 1hp 15,696 370hp Btu min 42.41 min C W == ± Tn e t C WW W =+ ±± ± 500 370 870hp T W =+= ± For the turbine, from the first law ( ) 34 Tp Wm h h m c T T = ± T p W TT mc ± ± Btu 42.41 min 1hp lbm Btu 150 0.24 min lbm R = 1025R equation(1) Since the turbine is isentropic and we are assuming constant specific heats 1 44 33 k k TP =
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1 41 32 k k TP ⎛⎞ = ⎜⎟ ⎝⎠
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Problem 10-1 - Example 10-1 An ideal Brayton cycle is used...

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