Example 11.4: A cooling tower is to cool 20000 lb/h of water from 120 °F to 80 °F. Inlet air will have a dry bulb temperature of 60 °F and a wet bulb temperature of 50 °F. A mass transfer coefficient of 80 lb/(h·ft·mol ratio) is expected. G_y = 800 lb/(h·ft²). Cross sectional area of the tower is 20 ft². Use Merkel design equation to estimate the height of the tower.

Solution:

G_y = 800 lb/(h·ft²), m = 20000 lb/h, water temperature inlet, t₁ = 80 °F,

Water temperature outlet, t₂ = 120 °F

Assume specific heat of water, c = 1 Btu/(lb·°F)

Enthalpy of inlet air (60 °F dry bulb, 50 °F wet bulb), h₁ = 20.35 - 0.05 = 20.3 Btu/lb

Enthalpy of air at any temperature t in the tower, H = m/(AG_y)(t - t₁) + h₁

Enthalpy of outlet air, h₂ = 70.3 Btu/lb

Temp, t	H^*/(Btu/lb)	H/(Btu/lb)	1/(H^* - H)
80	43.7	20.3	0.0427
85	49	26.55	0.0445
90	56	32.8	0.0431
95	63.3	39.05	0.0412
100	72	45.3	0.0375
105	81.3	51.55	0.0336
110	92.3	57.8	0.029
115	105	64.05	0.0244
120	119.3	70.3	0.0204
		Mean	0.0316

Use Equation 11.4 given below to calculate number of transfer units

NTU = (h₂ - h₁)(1/(H^* - H)_av) = 1.582

Height of transfer unit can be found by using Equation 11.5 given below.

HTU = G_y/K_ya = 10

Height of Cooling Tower can be calculated through Equation 11.6 given below.

Z = HTU´NTU = 10´1.582 = 15.82 ft