a gas turbine is designed to produce 3000hp when using air at a maximum inlet te

Question

a gas turbine is designed to produce 3000hp when using air at a maximum inlet temperature of 650k and assuming a heat loss of 70 kj/s. if the exhaust temperature is desired to be no greater than 200 degrees Celsius, determine the mass flow rate of air required. im having trouble setting up the eqaution of the mass flow rate i believe the answer needs to be in lbm/s. the textbook states eqautions Qadd= mcp(tin-tout)
how would you find the mass flow if you dont know the pressure ratio of (qadd) when solving for wk/themal efficency to get the Qadd part of the eqaution to solve for M.

Explanation / Answer

W output = 3000 hp = 3000 x 0.746 = 2238 KW (as i0.746 KW = 1 hp)

T1 = 650 K

T2 = 200 C = 200 + 273 = 473 K

Q out = 70 Kj/s = 70 KW

Now W + Q = m_rate x Cp x (T1 - T2)

Here assuming Cp of air to be constant = 1.005 Kj/Kg.K

2238 + 70 = m_rate x 1.005 x (650 - 473)

m_rate = 12.97 Kg/s = mass flow rate

{ here mass flo rate will be in kg/s and not lb/s as all units are SI

Secondly we dont need pressure ratio as W ideal = mcp(tin-tout) , but here we have added heat losses to W done. }

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