Repeat Prob. 14–79 for a total pressure of 88 kPa for air.
(a)
The rate of heat transfer.
Answer to Problem 80P
The rate of heat transfer is
Explanation of Solution
Express initial partial pressure.
Here, relative humidity at state 1 is
Express the dew point temperature of the incoming air.
Here, initial specific humidity is
Express initial partial pressure.
Here, initial pressure is
Express initial specific volume.
Here, universal gas constant of air is
Express initial specific humidity.
Express initial enthalpy.
Here, initial specific enthalpy at saturated vapor is
Express final partial pressure.
Here, relative humidity at state 2 is
Express final partial pressure.
Here, final pressure is
Express final specific volume.
Here, final temperature is
Express final specific humidity.
Express final enthalpy.
Here, final specific enthalpy at saturated vapor is
Express initial volume rate of air.
Here, initial volume and area is
Express the mass flow rate of air at inlet.
Here, initial specific volume is
As the process is a steady flow and thus the mass flow rate of dry air remains constant during the entire process.
Here, mass flow rate of dry air at exit is
Express water mass balance to the combined cooling to obtain the mass flow rate of water.
Here, mass flow rate of water at inlet and exit is
Express the cooling rate when the condensate leaves the system by applying an energy balance on the humidifying section.
Here, rate of heat rejected or cooling rate when the condensate leaves the system is
Conclusion:
Refer Table A-4, “saturated water-temperature table”, and write saturation pressure at temperature of
Write the formula of interpolation method of two variables.
Here, the variables denote by x and y is temperature and saturation pressure respectively.
Show the saturation pressure corresponding to temperature as in Table (1).
Temperature |
Saturation pressure |
30 | 4.2469 |
32 | |
35 | 5.6291 |
Substitute
Thus, the saturation pressure at temperature of
Substitute
Substitute
Here, saturation temperature at pressure of
Refer Table A-5, “saturated water-pressure table”, and write saturation temperature at pressure of
Show the saturation temperature corresponding to pressure as in Table (2).
Pressure |
Saturation temperature |
3 | 24.08 |
3.332 | |
4 | 28.96 |
Use excels and tabulates the values from Table (2) in Equation (XVI) to get,
Substitute
Substitute
Refer Table A-2, “ideal-gas specific heats of various common gases”, and write the gas constant and specific heat at constant pressure of air.
Substitute
Substitute
Refer Table A-4, “saturated water-temperature table”, and write the specific enthalpy saturated vapor at temperature of
Show the specific enthalpy saturated vapor corresponding to temperature as in Table (3).
Temperature |
specific enthalpy saturated vapor |
30 | 2555.6 |
32 | |
35 | 2564.6 |
Use excels and tabulates the values from Table (3) in Equation (XVI) to get,
Substitute
Refer Table A-4, “saturated water-temperature table”, and write saturation pressure at temperature of
Substitute
Substitute
Substitute
Substitute
Refer Table A-4, “saturated water-temperature table”, and write the specific enthalpy saturated vapor at temperature of
Substitute
Refer Table A-4, “saturated water-temperature table”, and write the enthalpy of water at temperature of
Here, specific enthalpy saturation liquid at temperature of
Perform unit conversion of diameter from
Substitute
Substitute
Substitute
Substitute
Hence, the rate of heat transfer is
(b)
The mass flow rate of the water.
Answer to Problem 80P
The mass flow rate of the water is
Explanation of Solution
Express the mass flow rate of the water.
Here, mass flow rate of the water is
Conclusion:
Refer Table A-2, “ideal-gas specific heats of various common gases”, and write specific heat at constant pressure of water.
Substitute
Hence, the mass flow rate of the water is
c)
The exit velocity of the airstream.
Answer to Problem 80P
The exit velocity of the airstream is
Explanation of Solution
Express the exit velocity of the airstream.
Conclusion:
Substitute
Hence, the exit velocity of the airstream is
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Chapter 14 Solutions
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