1. A steam power plant is to be built to provide 10 MW of electricity. The turbi

Question

1.       A steam power plant is to be built to provide 10 MW of electricity. The turbine to be used has an efficiency of 45% and heat loss equivalent to 5% of the power (i.e.  q(dot)= 5% w(dot)). The boiler operates at 500 kPa. The turbine material can tolerate a temperature of 600 oC. The pressure at the exit of the turbine is 110 kPa and 95% quality.

The water flow into the boiler can be assumed saturated liquid. The fuel capacity is 35 MJ/Liter and it costs 0.15 dollar per liter. The boiler efficiency is 95% and the generator efficiency is 99%.

      What is the mass flow rate in the turbine?

Explanation / Answer

1. from the data provided

Steam conditions for turbine

pressure at inlet of turbine = 500 kPa and 600 C so hi = 3702 kJ/kg K;

pressure at exit of turbine = 110 kPa and quality =0.95 he = hf + x hfg = 417 + 0.95 * 2675 = 2958.25 kJ/kg K
;

let the mass flow rate in the turbine be m';

then as per the question m'( hi - hf) = W ;

where hi, hf are the enthalpy values at inlet and exit of turbine respectively;

turbine efficiency = 0.45 and heat loss = 0.05 * W ;

Thus total energy input to the turbine E = 10 /0.45 * 0.05 * 10 ;

E = 22.52 MW;

mass flow rate m' * ( 3702 - 2958) = 22.52 * 10 ^6 ;

m' = 30.268 * 10 ^3 Kg/s

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