Heat exchanger is to create superheated steam from water using hot combustion ga

Question

Heat exchanger is to create superheated steam from water using hot combustion gases. The water enters at 3000psi, 300 degrees F and is heated to 1000 degrees F. The hot gases enter at 2400 degrees F and 14.7 psi. The gases may be treated as ideal with R=53.5 ft*lbf/lbm R and Cp=.260 Btu/lbm R. The gas flow rate is 12 times the water flow rate. It is estimated that to generate 10MW of power, we will need to transfer 28500 Btu/s of heat to the water.

A) find mass flow rate of the water in lbm/s

B) find exit temperature of the hot gases in degrees F.

C) find the exit velocity (ft/s) of the hot gas ifthey are flowing through a rectangular duct that is 10ft by 8ft.

Explanation / Answer

A)

m = h / (cp dt)

hence, m= 10000/((4.2 kJ/kg oC) (388.89oC)) = 6.12 kg/s = 13.49 lbm/s

B)

Q = m*Cp*dt

dt= 28500 Btu/s / (12*13.49 lbm/s *0.260 Btu/ lbmR) = 677.139

hence gas final temp. will be = 2400-677.139 = 1722.861 F

C)

Flow rate equation: Q = VA hence V= Q/A =

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