**How to calculate Cycles, Blow down, Evaporation, Makeup**

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:

In the customary USA units:

M = Make-up water in gal/min

C = Circulating water in gal/min

D = Draw-off water in gal/min

E = Evaporated water in gal/min

W = Windage loss of water in gal/min

X = Concentration in ppmw (of any completely soluble salts à 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 û E) = 1 + {E / (D + W)}

From a simplified heat balance around the cooling tower:

(E) = (C) (ΔT) (cp) / HV

where:

HV = latent heat of vaporization of water = ca. 1,000 Btu/pound

ΔT = water temperature difference from tower top to tower bottom, in °F

cp = specific heat of water = 1 Btu/pound/°F

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.)

In SI metric units:

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 à 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 û E) = 1 + {E / (D + W)}

From a simplified heat balance around the cooling tower:

(E) = (C) (ΔT) (cp) / HV

where:

HV = latent heat of vaporization of water = ca. 2260 kJ / kg

ΔT = water temperature difference from tower top to tower bottom, in °C

cp = specific heat of water = 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 or less 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 blow down are synonymous. Windage and drift are also synonymous.)