Air enters a 40-cm-diameter cooling section at 1 atm, 32°C, and 70 percent relative humidity at 120 m/min. The air is cooled by passing it over a cooling coil through which cold water flows. The water experiences a temperature rise of 6°C. The air leaves the cooling section saturated at 20°C. Determine (a) the rate of heat transfer, (b) the mass flow rate of the water, and (c) the exit velocity of the airstream.
FIGURE P14–79
(a)
The rate of heat transfer.
Answer to Problem 79P
The rate of heat transfer is
Explanation of Solution
Express the dew point temperature of the incoming air at a temperature of
Here, the saturation pressure at temperature of
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
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 |
3.33 | |
4 | 28.96 |
Use excels and tabulates the values from Table (2) in Equation (VI) to get,
Substitute
Refer Figure A-31, “psychometric chart at
Refer Figure A-31, “psychometric chart at
Here, final specific volume is
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 79P
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 79P
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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