Heat exchanger is to create superheated steam from water usi

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.

Solution

A)

m = h / (c_p dt)

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

B)

Q = m*C_p*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 =