[mbeychok]

Here are the governing relationships for the makeup flow rate, the evaporation and windage losses, the draw-off rate, and the concentration cycles in an evaporative cooling tower system:
 

 
M = Make-up water in m³/hr
C = Circulating water in m³/hr
D = Draw-off water in m³/hr
E = Evaporated water in m³/hr
W = Windage loss of water in m³/hr
X = Concentration in ppmw (of any completely soluble salts  … usually chlorides)
Xm = Concentration of chlorides in make-up water (M), in ppmw
Xc = Concentration of chlorides in circulating water (C), in ppmw
Cycles = Cycles of concentration = Xc / Xm
ppmw = parts per million by weight

A water balance around the entire system is:

 M = E + D + W

Since the evaporated water (E) has no salts, a chloride balance around the system is:

M (Xm) = D (Xc) + W (Xc) = Xc (D + W)
 
and, therefore:
 
 Xc / Xm = Cycles = M / (D + W) = M / (M – E) = 1 + {E / (D + W)}
 
From a simplified heat balance around the cooling tower:
 
  (E) = (C) (?T) (c_p) / Hv
 
where:
Hv = latent heat of vaporization of water = ca. 2260 kJ / kg
?T = water temperature difference from tower top to tower bottom, in °C
c_p = specific heat of water = ca. 4.184 kJ / kg / °C
 
Windage losses (W), in the absence of manufacturer's data, may be assumed to be:
 
    W = 0.3 to 1.0 percent of C for a natural draft cooling tower
    W = 0.1 to 0.3 percent of C for an induced draft cooling tower
    W = about 0.01 percent of C if the cooling tower has windage drift eliminators

Concentration cycles in petroleum refinery cooling towers usually range from 3 to 7.  In some large power plants, the cooling tower concentration cycles may be much higher.
 
(Note: Draw-off and blowdown are synonymous. Windage and drift are also synonymous.)

Milton Beychok
(Visit me at www.air-dispersion.com)