Answer to Question #319038 in Molecular Physics | Thermodynamics for wonder

Question

1. A 92 kg/s flow of steam enters a turbine at 100 bar, 774 K and a velocity of 35 m/s. The machine is well insulated and the steam leaves at 0.1 bar, 365 K and at a velocity of 350 m/s. Calculate the power output from the turbine and the inlet and outlet pipe diameters required assuming that steam is an ideal gas with Cp=1901 J/kg.K.

Answer 1

v1 = v2, Z1 = Z2, Q = 0

Find the work done

W = P/m

W = 500 kW / 1.35 kg/s = 370 kJ/kg

Since ∆KE = 0 and ∆PE = 0

We get

∆h = W

∆h = 370 kJ/kg

v1 = 60 m/s, v2 = 360 m/s, Z1 = 0, Z2 = 3 m, Q = 0

W= ∆h + ∆KE + ∆PE

∆KE = (v22 - v12) / 2 = ((360 m/s)2 – (60 m/s)2) / 2 = 63 kJ/kg

∆PE = g × (Z2 - Z1) = 9.81 × 3 = 29.43 J/kg = 29.43 ×10-3 kJ/kg

We find ∆h

∆h = W – (∆KE + ∆PE) 

Finally

∆h = 370 kJ/kg – (63 kJ/kg + 29.43 ×10-3 kJ/kg) = 307 kJ/kg