# Sample Gas Turbine Problem with solution

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#### Sample Gas Turbine Problem with solution

Given Data:

T1 = 520 ⁰R = 288.88 K

T2 = 2700 ⁰R = 1500 K

P1 = 14 Psi

P2= P3 = 140 Psi

Net power output Wnet = 20 MW

Required:

Turbine power output WTurbine

Compressor percent power consumption

Thermal efficiency of the cycle ηth

Solution:

Calculating compressor output temperature T2s, considering isentropic compression.

T2s = T1 * (P2/P1)γ-1/ γ

Taking γ = 1.4

T2s = 288.88 * (140/14)0.285

T2s = 556.82 K

Using same relation to find temperature at turbine outlet i.e. T4s

T4s = T3*(P4/P3) γ-1/ γ

T4s = 1500*(14/140)0.285

T4s = 778.2 K

Now mass flow rate can be determined from below equation.

Wnet = ṁ*Cp*[( T3 – T4s) – (T2s – T1)]

20000 = ṁ*1.005*[( 1500 – 778.2) – (556.82 – 288.88)]

ṁ = 20000/456.13

ṁ = 43.84 kg/sec

Wturbine = ṁ*Cp*(T3 – T4s)

Where Cp = 1.005 kJ/kg.K for air

Wturbine =43.84 * 1.005 * (1500 – 778.2)

Wturbine = 31801.93 kW

Wnet = Wturbine – Wcompressor

20000 = 31801.93 – Wcompressor

Wcompressor =  11801.93 kW