Question #255757

A gas turbine receives gases from the combustion chamber at 7 bar and

650°C, with a velocity of 9 m/s. The gases leave the turbine at 1 bar with a

velocity of 45 m/s. Assuming that the expansion is Adiabatic and reversible

in the ideal gas,

calculate the power Output per unit mass flow rate,

1=1.333, Cp=1.11 KJ/Kg.K


1
Expert's answer
2021-10-25T15:31:20-0400

We know that

W˙=m˙[(cp(T2T1)+(c22c12)2]\dot{W}=\dot{m}[(c_p(T_2-T_1)+\frac{(c^2_2-c^2_1)}{2}]

T1T2=(P2P2)γ1γ\frac{T_1}{T_2}=(\frac{P_2}{P_2})^\frac{\gamma-1}{\gamma}

T2=T11.626=567.7KT_2=\frac{T_1}{1.626}=567.7K

T1=650+273=923KT_1=650+273=923K

W˙=1×1.11×(567.7923)+452922×103\dot{W}=1\times1.11\times(567.7-923)+\frac{45^2-9^2}{2\times10^3}

W˙=394.4+0.97\dot{W}=-394.4+0.97 =-393.4KW


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