### More Helpful Formulas for Power Engineering Calculations

MORE HELPFUL FORMULAS FOR POWER ENGINEERING CALCULATIONS

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 … 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) (Δ T) (cp) / HV

where:
HV = latent heat of vaporization of water = ca. 1,000 Btu/pound
Δ T = 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.)

From a simplified heat balance around an evaporative cooling tower:

(E)(H) = (C)(DT)(cp)

where:
E = evaporation rate    E
H = heat of vaporization of water = ca. 1,000 BTU/pound    H
C = circulating water rate    C
DT = water temperature drop from top to bottom of tower = delta T    DT
cp = specific heat of water = 1 BTU/pound/degree F    cp

E and C may be in gallons/minute, m3/hour, pounds/hour, etc. as long as they are both in the same units.

If you want more explanation, read pages 144-147 of "Aqueous Wastes from Petroleum and Petrochemical Plants" by M.R. Beychok, published by John Wiley and Sons, 1967.

Don't forget that, in addition to the evaporation loss, there is also a small amount of windage loss.

Where: E = Rate of evaporation GPM (if not accurately known, evaporation can be approximated by multiplying total water flow rate in GPM times the cooling range (F) times 0.0008). (Formula 3)    2400    10    0.0008    19.2    60    72

Evaporation Loss: from a cooling tower (E) = .001 (Cr) (DT) where Cr = circulation rate in gallons per minute and D T = temperature differential between hot and cold water in °F. The evaporation rate amounts to 1% of the recirculation rate for every 10°F DT.    0.001    2400    10    24    60    72
Average

Cast in place cold water basin    7.48    gallons per cubic foot
Cubic feet of cold water basin     12,475
Depth of basin    8
Surface area of basin     1,559
Redundant basin     2
Net Surface Area     780
Square root= A x B     28

12,475
93,312

Circumference of a circle    3.1416 x d
Volume of a cylinder    3.1416 x radius(sq) x height            3.1416 x diameter x height
Volume of a cone    (1/3 x radius(sq) x 3.1416) x height

Lake evaporation rate is approximately 70% of NOAA Class A pan evaporation rate see My Pictures\panevap

In mathematics, an "oval" is more correctly called an ellipse, and the
area of an ellipse is given by Pi*a*b, where 2*a is the length of the
longer side (measured at its greatest width) and 2*b is the length of
the shortest side (measured at its greatest height).