Document Ner4apo4NpxmGa8KnQORpKRJg

666________________________________________ CHAPTER 37 ______________________ 1943 Guide -succession of air and water states existing in the exchanger sections must combine to form a straight line (for L = constant) on the temperature enthalpy diagram. The slope of this operating line is: dh __ Lc ' dt G 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 the water temperature at the plane in the tower which is under con sideration. Combination of Equations .2 and 3. results in the expression-: Gdk = KoW-hJdV Integrating this equation over the length of the exchanger: -i dh Ka A"` -- Aa (4) (5) 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: KaV G (6) djK? of the coolfng'process!16 f and 3 measureof 1116 Spray Apparatus 667 The integration is made numerically or graphically. In' the graphical integration ^ is evaluated as a function of fta- This determination involves the use of the-energy balance equa-tion int.egra- t,e. dA from onet______ ________ 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 ftj. 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 shown* 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 deg. The approximation to linearity may be determined by inspectibh'of Table 1, Chapter 3, or the temperature enthalpy diagram of Fig. 5. If the logarithmic mean is a valid potential, Equation 6 may be written-: Ai -- A = KaV AAim G (7) and the need for the numerical integration for the determination of the tower volume is eliminated. The over-all rate coefficient, Ka, must be known if the tower volume is to be determined. Experiments conducted oh towers containing different packing construction have yielded some magnitudes of this coefficient, evaluated on an over-all 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 over-all 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 exchanger5. The results included in Fig. 6 probably represent magnitudes of Ka which were obtained for complete wetting. Within the cooling tower operating range the over-all rate coefficient for energy transfer is nearly the same numerically as the over-all 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 over-all rate coefficient for mass transfer presented in Fig. 6 may be used directly in Equations 5 and 6, the units of Ka in these equations being Btu per (hour) (cubic foot per pound of dry air). Application of Design Procedure A typical procedure which may be followed in designing a cooling tower is illustrated in the following Example 1. 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 volume rests on consideration of the costs of producing air flow-and of the tower con struction 10. A counter-flow forced draft cooling tower is to cool 36,000 lb of water per hour from an initial temperature of 110 F to a final temperature of 80 K. Air having an initial condition of 65 F dry-bulb and 58 F wet-bulb temperature will be forced