#### Sample Gas Turbine Problem with solution

**Given Data:**

T_{1} = 520 ⁰R = 288.88 K

T_{2} = 2700 ⁰R = 1500 K

P_{1} = 14 Psi

P_{2}= P_{3} = 140 Psi

Net power output W_{net} = 20 MW

**Required:**

Turbine power output W_{Turbine}

Compressor percent power consumption

Thermal efficiency of the cycle η_{th}

**Solution:**

Calculating compressor output temperature T_{2s}, considering isentropic compression.

T_{2s} = T_{1} * (P_{2}/P_{1})^{γ-1/ γ}

Taking γ = 1.4

T_{2s} = 288.88 * (140/14)^{0.285}

**T _{2s} = 556.82 K**

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

T_{4s} = T_{3}*(P_{4}/P_{3}) ^{γ-1/ γ}

T_{4s} = 1500*(14/140)^{0.285}

**T _{4s} = 778.2 K**

Now mass flow rate can be determined from below equation.

W_{net }= ṁ*C_{p}*[( T_{3} – T_{4s}) – (T_{2s} – T_{1})]

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

ṁ = 20000/456.13

**ṁ = 43.84 kg/sec**

W_{turbine} = ṁ*C_{p}*(T_{3} – T_{4s})

Where C_{p} = 1.005 kJ/kg.K for air

W_{turbine} =43.84 * 1.005 * (1500 – 778.2)

**W _{turbine} = 31801.93 kW**

W_{net} = W_{turbine} – W_{compressor}

20000 = 31801.93 – W_{compressor}

W_{compressor} = 11801.93 kW