The inlet velocity, pressure and temperature at the compressor for a turbo-jet e

Question

The inlet velocity, pressure and temperature at the compressor for a turbo-jet engine are 275 feet per second, 7 psia and -30 degrees farenheit. the pressure at the compressor outlet is 70 psia. Temperature limit for the engine is 1800 degrees farenheit. Assuming the compression and expansion processes are isentropic calculate the thrust for 1 lbm per second of air flow, the power in horsepower of the thrust and the heat input per lbm of air. Assume constant specific heat and neglect the velocity coming out of the turbine.

Explanation / Answer

Thrust = m*(Vin - Vout) = (1/32.2)*(275 - 0) = 8.54 lb,

T2 / T1 = (P2/P1)^((k-1)/k)

T2 / (-30+460) = (70/7)^((1.4-1)/1.4)

T2 = 830 R = 830 - 460 = 370 deg F

T3/T4 = (P3/P4)^((k-1)/k)

(1800+460)/T4 = (70/7)^((1.4-1)/1.4)

T4 = 1170 R = 1170-460 = 710 deg F

W_turbine = m*Cp*(T3 - T4)

W_turb = 1*0.24*(1800 - 710)

W_turb = 261.6 Btu

W_compressor = m*Cp*(T2 - T1)

W_comp = 1*0.24*(370 - (-30))

W_comp = 96 Btu

Net power = W_turb - W_comp = 261.6 - 96 = 165.6 Btu

Heat input Q = m*Cp*(T3 - T2)

Heat input Q = 1*0.24*(1800 - (-30))

Q = 439.2 Btu

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