Question

The gas generator of a two-shaft gas turbine has a compressor pressure ratio of 5 and compressor and turbine inlet temperatures of 80°F and 2000°F, respectively, at sea level. All turbomachines have efficiencies of 90%, and the inlet air flow is 50 lbm/s. (a) What are the net work, pressure ratio, and horsepower of the power turbine and the cycle efficiency? (b) Suppose the power turbine is removed and the gas generator exhaust gas flows isentropically through a convergent-divergent propulsion nozzle that is fully expanded (exit pressure is ambient). What are the nozzle exhaust velocity and the static thrust? (c) Repeat part (b) for a choked convergent nozzle.

          The gas generator of a two-shaft gas turbine has a compressor pressure ratio of 5 and compressor and turbine inlet temperatures of 80°F and 2000°F, respectively, at sea level. All turbomachines have efficiencies of 90%, and the inlet air flow is 50 lbm/s. (a) What are the net work, pressure ratio, and horsepower of the power turbine and the cycle efficiency? (b) Suppose the power turbine is removed and the gas generator exhaust gas flows isentropically through a convergent-divergent propulsion nozzle that is fully expanded (exit pressure is ambient). What are the nozzle exhaust velocity and the static thrust? (c) Repeat part (b) for a choked convergent nozzle.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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The gas generator of a two-shaft gas turbine has a compressor pressure ratio of 5 and compressor and turbine inlet temperatures of 80°F and 2000°F, respectively, at sea level. All turbomachines have efficiencies of 90%, and the inlet air flow is 50 lbm/s. (a) What are the net work, pressure ratio, and horsepower of the power turbine and the cycle efficiency? (b) Suppose the power turbine is removed and the gas generator exhaust gas flows isentropically through a convergent-divergent propulsion nozzle that is fully expanded (exit pressure is ambient). What are the nozzle exhaust velocity and the static thrust? (c) Repeat part (b) for a choked convergent nozzle.
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Transcript

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00:01 The derivative of your turbine efficiency is equal to h3 minus h4 divided by h3 minus h4s.
00:09 So that's 0 .88 divided by h3 minus 959 .2 divided by h3 minus h4s.
00:17 So the value of h3 by trial and error method would be 1790 kilobarons divided by kg.
00:23 The entropy value at h3 would be 1790 and kg versus 1600 as per the equation 6 .75.
00:31 Now finding the mass per wave would be t1 divided by bar t1.
00:38 So that's coming here multiplied by 8 to the power of k divided by 6g whole divided by 0 .267 multiplied by 313.
00:48 So m would be 15 .77 kg divided by seconds.
00:54 So the e power output would be m h2 minus h1.
01:03 So that's 15 .77, 758 .65 minus 313 .6...
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