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HEATING VENTILATING AIR CONDITIONING GUIDE 1944 enthalpy diagram. The slope of this operating line is ^ Since the heat capacity of water is approximately unity, this slope is the ratio of the water to the air rate. Equation 3 indicates that the potential for energy transfer at any section is the difference between the enthalpy of saturated air at the main-body water temperature at that section and the enthalpy of the air stream in contact with that water. This potential is the difference in the ordinates of the saturation and operating lines for Fig. 5. Temperature Enthalpy Diagram for Air, Water Vapor Mixture Showing the Operating Line for Example 1 the water temperature at the plane in the tower which-is. under con sideration. Combination of Equations 2 and 3 results in the expression: Gdh = Ka W-fta) dV (4) Integrating this equation over the length of the exchanger: The integration of the left side of Equation 5 determines the tower volume required to achieve the desired energy exchange. This summation is readily accomplished for counter and parallel flow arrangements. G and Ka are usually independent of the tower volume and Equation 5 then becomes: . <6> Where NTU is defined as the Number of Transfer Units and is a measure of the difficulty of the cooling process. 538 CHAPTER 27. SPRAY EQUIPMENT The integration is made numerically or graphically.. In the graphical integration ^ ^7^ is evaluated as a function of h^. This determination involves the use of the energy balance equation integrated from one section to the section in question. The area under the curve between any two abscissae is the number of transfer units required to change the air state from Aj to hi. An approximate value for the number of transfer units can also be determined by a simple graphical method of direct construction on the temperature enthalpy diagram8. This method cannot be applied very satisfactorily to cooling towers as the operating range is small and the value of the NTU is near unity. When the relationship between the enthalpy of the saturated air and the temperature is linear over the range of water temperatures involved, it can be shown9 that the logarithmic mean of the terminal potentials, Aim, is the correct driving force. This is true to a good approximation when the water cooling does not exceed 15 F. The approximation to linearity may be determined by inspection of Table 6, Chapter 1, or the temperature enthalpy diagram of Fig. 5. If the logarithmic mean is a valid potential, Equation 6 may be written: hi -h, = KaV AAlm G . w and the need for the numerical integration for the determination pf the tower volume is eliminated. The overall rate coefficient, Ka, must be known if the tower volume is to be determined. Experiments conducted on towers containing different packing construction have yielded some magnitudes of this coefficient, evaluated on an overall basis. These data are presented in Fig. 6 as a function of the gas mass velocity through the packing, and apply only to the particular packing structure for which they were obtained. The overall rate coefficient (Ka) may also be a function of the water rate, since a reduction of the water rate may reduce the wetted area within the exchanger10. The results included in Fig. 6 probably represent magnitudes of Ka which were obtained for complete wetting. Within the cooling tower operating range the overall, rate coefficient for energy transfer is nearly the same numerically as the overall rate coefficient for mass trans fer. The conditions of test corresponding to the data presented in Fig. 6 are not well enough known in most cases to warrant recomputation of Ka. Therefore the magnitudes of the overall rate coefficient for. mass transfer presented in Fig. 6 may be used directly in Equations 5 and 6, the .units oi Ka in these equations being Btu per hour per cubic foot per pound of dry air. A typical design procedure is outlined in an illustrative example: Example 1. The rate of air flow, arbitrarily assumed in the data given, is related to the tower volume by economic considerations. A balance between air rate and tower ' Graphical Method of Determining Number Transfer Units, by T. Baker (Industrial and Engineering Chemistry, August, 1936, VoL 27. p. 977). Loc. Cit. Note 4. p. 79. Loc. Cit. Note 6. 539