Question

Separate streams of air and water flow through the compressor and heat exchanger arrangement shown below. Steady state operating data are provided on the figure. Heat transfer with the surroundings can be neglected as can all kinetic and potential energy effects. The air is modeled as an ideal gas. Determine: (a) the total power required by both compressors, in kW. (b) the mass flow rate of the water, in kg/s.

Separate streams of air and water flow through the compressor and heat exchanger arrangement shown below. Steady state operating data are provided on the figure. Heat transfer with the surroundings can be neglected as can all kinetic and potential energy effects. The air is modeled as an ideal gas. Determine: (a) the total power required by both compressors, in kW. (b) the mass flow rate of the water, in kg/s.

Answer 1

Consider energy bal ance for compressor A Vi m1 = m2) ideal gas model (A-A)-СР@Te.G-T,) 300+600 Ta,-450K Specific heat of air at average temperature. CPA 450K 1.02 kJ/kgK = 0.6× 1.02(300-600) T,--183.6 kW

consider energy balance for compressor B 450+800 T625 K Specific heat of air at average temperature 625 K by interpolating the values between 600K an 650K. C600x CPg 65ox P@625Kー 1.051+1.063 kJ/kgK P625 Ср@625K-1.057 kJ/kgK TB-0.6 1.057(450-800) TB -221-97 kW

Calculate total power required by both compressors. W2t --183.6 221.97 =-405.57 kW ta Obtain enthalpy of the saturated water 1 bar and 20°C from steam tables h5 83.9 kJfkg Obtain enthalpy of the saturated water 1 bar and 30°C from steam tables h5 125.832 kJ/kg Apply energy bal ance relati on for heat exchanger, neglect heat transfer, work done, kinetic, and potential energies. mep@rn (7-5) = mas (4-%) 600+450 Ta 525 K Ср@525 :: 1.0455 kJ/kgk. 0.6x1.0455(600-450) (125.8-83.9) m 2.24 kg/s