Document m1RkM9D8Mqz5k0Qe58Z8x28k

760 CHAPTER 34 1952 Guide circulating water as a result of evaporation;- that the water suspended in the tower is surrounded by a film of air which is saturated with water vapor and at the temperature of the water surrounded; and that the basic theory of cooling tower operation proposed by Lewis13 and developed by. Merkel14 is applicable. This theory refers to the fact that the numerical value of the coefficient of sensible heat transfer, when divided by the numerical value of the coefficient of diffusion, equals the specific heat (at constant pressure) of air. .The reader should observe that this relationship refers to the numerical values of three distinct constants, the units for each being different. The above relationship makes it possible to simplify the.heat transfer equation'by combining the two driving forces into one potential represented as the difference between the enthalpy of the air'film (at water temperature) surrounding the water, and rthe enthalpy of the main air stream. . . ' conditions 1 WATER .. L FLOW LB PER HR '' ACTIVE: i TOWER VOLUME V I AIR \o 13 FLOW LB PER HR CONDITIONS 2 Fig. 10. Operations in a Typical ' Wateb Cooling Toweb ' Tower Performance Factor ; The operations taking place in a.typical water-cooling tower are shown in Fig. 10. -If the reduction in water flow rate^ due to evaporation witfiirt the volume, is neglected, and the'usualconcepts of heat flow and mass heat transfer are applied, the equations typifying cooling tower operation are: KaV `G f1 dh h K' - K (3) and i KaV _ rl de jL ~ 2 h' -K "(4) where v d = overall average wetted area (surface of;water drops plus wetted tower sur face), square feet per cubic foot of active tower volume. (?, ='weight rate of flow of air, pounds of dry air per hour. h = enthalpy, Btu per pound of dry ais Spray Apparatus 761 ' h0 = enthalpy of air-vapor mixture, Btu per pound of dry air. ; *; h" = enthalpy, of saturated air-vapor mixture at water temperature, Btu per pound of dry air:. . . . ; ........... ..........\ ' K, -- overall energy, unit conductance, Btu per (hour) (square foot overall average wetted area) (Btu enthalpy.difference per pound of dry air). L = water rate, pounds per hour. . .. . '7 e = temperature of water in tower, Fahrenheit. :! 9i = temperature of inlet,water,.Fahrenheit. . .. 9t = temperature of: outlet,water, Fahrenheit.. .. -V =:active tower'volume; cubic feet. . ' . .7 " . Either term or may be. called the Tower Performance Factor : tr - L ' '! ' or Number of Tower Units (NTU). - ., Fig.' 11.- Temperatuhe-Enthalpy Diagram fob Air-Wateb Yapob' Mixtube Showing Operating Lines fob Example 2 These equations indicate that the rate of heat transfer from the water to the air defends `primarily' upon the enthalpy of the air, the latter being dependent only on the wet-bulb temperature of the air. This explains the common observation that cooling tower performance is independent of inlet dry-bulb air temperature, and that adiabatic conditions exist. The integration of Equations 3 and 4 must be performed by mechanical or graphical means;-because direct mathematical , integration would be accurate only within narrow temperature limits. The temperature en thalpy tfiagram ip. Fig: 11 represents the conditions for either of.the above equations.-, "fibe water is cooled from the temperature <?i to J92, arifi the enthalpy of the air film surrounding it follows,the saturation line h".... Air enters the tower at a. wet-bulb temperature of (, and an,enthalpy,of.%. ;It is heated. to an outlet wet-bulb temperature of t{, wiih, an enthalpy of Ai.. Since-the heat rejected by the water equals the heat absorbed .by the,air, the heat absorbed per pound of air is a function of the pounds,of water per pound of' air going through the tower, and the slope, of the air operating fine is the.L/G ratio.,