Cooling Tower Calculations

The purpose of a cooling tower is to conserve water. The heat picked up in the heat exchanger is returned to the cooling tower where it is rejected to the atmosphere by evaporative and convective cooling. The water that is evaporated at the cooling tower is pure, that is, it doesn’t contain any of the dissolved minerals present in the makeup water. As the evaporation process continues, these mineral solids concentrate in the recirculating water. If left unchecked, the solids eventually concentrate to the point of saturation. Here the dissolved solids precipitate to form a mineral scale or sludge deposit in the system This normally occurs in areas of high heat transfer such as in a heat exchanger.

The cycles of concentration or concentration ratio is defined as the ratio between the impurity levels in the recirculating water to the same impurity level in the makeup water. Generally the chloride ratio, conductivity ratio, or magnesium ratio is taken as the indicator of cycles of concentration, since these impurities are relatively soluble as compared to calcium carbonate.

Cycles of concentration = ClB = MgB = CondB

                                          ClMU MgMU CondMU

The cycles of concentration are controlled by the deliberate bleeding of water from the system. The bleed off water discharges the concentrated solids in the cooling water to drain. The water lost by evaporation and bleed off is replaced by fresh makeup water. The relationship between the required bleed rate and the cycles of concentration is given by the expression:

Bleed, gpm = Evaporation, gpm

                       (Cycles – 1)

Makeup rate, gpm = Evaporation + Bleed

These relationships indicate that the higher the cycles of concentration, the lower the bleed rate and, therefore, the lower the makeup rate. Since the purpose of the cooling tower is to conserve water, it is desirable to operate at the highest concentration ratio, while, at the same time, staying below the solubility limits of the dissolved minerals in the makeup.

Determining Cycles of Concentration

Several “rules of thumb” have been developed to determine the optimum cycles of concentration. Unfortunately, because of the numerous variables involved in cooling water chemistry, there is no universally accepted method for determining the maximum cycles of concentration. The Langelier and Ryznar Indices are often cited as the best indicator of the scaling or corrosive tendency of the recirculating water. These indices use the total dissolved solids, temperature, calcium hardness, and total alkalinity of the cooling water to compute the pH of saturation or pHs. The pHs is the theoretical pH at which calcium carbonate is in equilibrium with the calcium hardness and total alkalinity. The actual water pH, which we’ll indicate as pHa, and the pHs are used to calculate the index numbers according to the following relationships.

Langelier Index = pHa – pHs

Ryznar Index = 2pHs – pHa

In the case of the Langelier Index, positive index numbers indicate a scaling condition and negative numbers a corrosive or non-scaling condition. The Ryznar index uses the same operating variables, but the index value is always positive. Ryznar indices less than 6 indicate that calcium carbonate is likely to precipitate from the water, and values greater than 6 suggest the water will dissolve calcium carbonate, i.e. the water is corrosive. In either case, the objective is to set the bleed off rate to limit the cycles of concentration such that the cooling water chemistry is maintained on the non-scaling side of the index. However, more recently, several cooling water treatment programs have been marketed that permit the operation of the cooling tower within the scaling range of the index.

In many cases the value and usefulness of the Langelier and Ryznar indices is overstated. According to James McCoy, author of The Chemical Treatment of Cooling Water, “the Langelier Saturation Index applies only to the equilibrium between CO2 and CaCO3. Neither the pH of saturation nor the values derived from it are significant in industrial cooling systems.” More over, the LSI and RSI are not accurate indicators of the corrosion potential in the system unless you are concerned with the deterioration of concrete pipe.

More recently, the Practical Scaling Index (PSI) has been advanced as more accurate and useful than the LSI or RSI values. With the PSI value, the same operating parameters of total dissolved solids, temperature, calcium hardness and total alkalinity are used to compute the pH of saturation. To determine the PSI value, however, a pH of equilibrium, pHeq, is calculated from the total alkalinity, TA, of the recirculating water according to the following equation.

pHeq = 1.465log(TA) + 4.54

In 1977, Kunz and others published a method for predicting cooling water pH using an empirical formula derived from 400 data points obtained from actual operating systems. His equation is as follows:

pH = 1.6log(TA) + 4.40

In reviewing these equations for pH calculation, Jack Matson, PhD from the University of Houston, says in his paper “Precise Prediction of Cooling Water pH,” that neither equation is very precise in determining pH from the total alkalinity because they do not take into consideration the partial pressure of the carbon dioxide in the atmosphere.

With regard to determining the PSI value, the calculated pH of equilibrium, pHeq, is used instead of the actual pHa in the Ryznar formula to determine the PSI index value as follows:

PSI = 2pHs – pHeq

From this we can conclude that the LSI, RSI and PSI indices are imprecise indicators of the scaling or corrosive tendencies of the cooling water. Nevertheless, they are one of the few tools available to the water chemist to determine the optimum concentration ratio in the system.

Other Limiting Factors

The LSI, RSI and PSI indices are useful predictors of the solubility of calcium carbonate. With waters high in calcium hardness and total alkalinity, this is the primary scale-forming impurity.

Scale-forming impurities other than calcium carbonate are known to cause problems in cooling water systems. Calcium sulfate, tricalcium phosphate, silica, suspended solids, and process contaminants often limit the maximum permissible cycles of concentration. Solubility charts and related equations are available to determine the maximum concentration ratio of these impurities. Some useful guidelines are as follows:

Calcium Carbonate Deposition


Without Treatment

With Treatment



0 to +2.5



4.0 to 4.6

Calcium Sulfate Deposition

Calcium sulfate is more soluble than calcium carbonate. However, waters high in sulfate pose significant scaling problems. Once formed, calcium sulfate (gypsum) is more difficult to remove than calcium carbonate.

As a rule of thumb, the product of the calcium concentration times the sulfate concentration should be maintained at or below 500,000 to prevent calcium sulfate deposition.

[Ca] x [SO4] = less than 500,000

Tricalcium Phosphate Deposition

Polyphosphate is used in cooling water treatment programs to control scale deposition and corrosion. Over time, polyphosphate reverts to form orthophosphate. Orthophosphate, in turn, reacts under the right temperature and pH conditions with calcium hardness to cause the precipitation of tricalcium phosphate. The pH of saturation of tricalcium phosphate can be estimated from the following equation.

pHs = [11.755 – log(CaH) – log(o-PO4) – 2log(T)]


Actual cooling water pH’s above the pH of saturation for tricalcium phosphate will cause phosphate precipitation in the absence of chemical treatment.

As a rule of thumb, follow these guidelines for phosphate and calcium hardness levels.



o-PO4, ppm

Calcium, ppm

< 110 F


5 to 10

750 to 800

110 to 129 F


5 to 10

650 to 700

130 to 149 F


5 to 10

550 to 600

Silica Deposition 

Silica reacts with magnesium to form adherent scale deposits in cooling water systems. Like other scales, silica solubility is influenced by temperature and pH. The solubility increases with increasing pH and decreasing temperature. As a general rule, maintain silica levels below 150 ppm in the recirculating water to guard against this deposit.

Chemical Treatment

Chemical additives such as organophosphonates (HEDP and AMP) have been shown to increase the solubility of the common cooling water scales at low, threshold dosages. The following chart summarizes the impact these additives have on the solubility of calcium carbonate, tricalcium phosphate and calcium sulfate.

Phosphate versus Scale Solubility

Dosage, ppm

LSI Value

RSI Value

Calcium Phosphate

Calcium Sulfate








































Determining the Water Balance

Open cooling water systems must maintain a proper balance between evaporation, bleed, windage and makeup to control the cycles of concentration within the desired range. Once the desired cycles of concentration have been determined, the mass flow of water in and out of the system can be calculated from a few additional operating parameters.


Cooling Range is a measure of the difference between the cold water in the tower basin and the warmer cooling water return. This temperature differential is normally between 10 and 20 degrees F.

Approach is the difference between the cold cooling water temperature and the wet bulb temperature of the air. A cooling tower cannot cool water below the wet bulb temperature. Normally, the approach is with 7 to 10 degrees of the wet bulb temperature.

Recirculation Rates:

Obtain the rated capacity of the recirculation pumps in the cooling system. For comfort cooling systems, using centrifugal or absorption chillers, the recirculation rate can be estimated based on the refrigeration capacity of the chiller.

Centrifugal Machines require 3 gpm per rated ton.

Absorption Machines require 4 gpm per rated ton.

Water Quality

Obtain water analyses for the recirculating cooling water and makeup.

Evaporation Rate Calculations

The amount of water evaporated from the cooling tower is a function of the recirculation rate and cooling range. Cooling towers cool water by evaporating a small percentage of the recirculating water flow. In general, 0.1% of the recirculating water is evaporated for every 1 degree of temperature drop across the tower. It takes approximately 1000 Btu’s to evaporate 1 pound of water. If 1 pound of water is evaporated from 1000 pounds of water (0.1%), 1000 Btu’s are removed from 999 pounds of water, or 1 Btu per pound. 1 Btu removed from 1 pound of water lowers the temperature by 1 oF. (A Btu is the amount of heat required to raise (or lower) the temperature of 1 pound of water by 1 oF.) Therefore:

Evaporation = 0.001 X R x dT X f


R = recirculation rate, gpm

dT = temperature range across tower or “delta T”

f = evaporative cooling factor

Not all of the temperature drop across the cooling tower is a result of evaporative cooling. Some of the heat loss occurs by convective cooling, whereby heat is transferred by direct contact between the cooler air and the warmer water. On average, convective cooling accounts for 25% of the heat loss in a cooling tower. This will vary seasonally, however. In the Midwest, for example, 15% convective cooling occurs in the summer months, increasing to 35% in the winter. For most areas of the US, an average of 25% is reasonable. The evaporation rate must be adjusted for the amount of convective cooling taking place. The “f” factor accomplishes this. Use 0.75 for most estimates.

For mechanical refrigeration machines, the evaporation rate can be estimated from the refrigeration capacity and the heat rejection factor of the machine using the following formulat

Evaporation = Tons X Hfr X 24



Evaporation = evaporation rate, gpm

Tons = refrigeration capacity, tons

Hfr = Heat rejection factor of the machine

Compression machines = 1.25

Absorption machines = 2.6

Hfg = Heat of vaporization of water, 1050 Btu/pound

Cycles of Concentrati

As water evaporates from the cooling tower, the mineral impurities in the makeup are concentrated in the recirculating water. The cycles of concentration or concentration ratio is determined by calculating the ratio between an impurity in the cooling water and the same impurity in the makeup. Normally, chlorides are used for this purpose since they are very soluble and unlikely to precipitate to form scale or sludge in the system. If sodium hypochlorite (bleach) is used, however, the chloride level in the tower will be artificially high. Other impurities such as magnesium hardness or conductivity may be used to check the concentration ratio.

Cycles = ClB = MgHB = CondB

                ClMU MgHMU CondMU

Cycles of concentration can also be determined by calculating the ratio between the makeup and bleed off rates. A water meter installed on the makeup and bleed off lines is helpful in determining the average gpm for each parameter.

Cycles = Makeup rate

               Bleed rate

Bleed Rate

Cycles of concentration are controlled by discharging a percentage of the recirculating water to drain and replacing this concentrated cooling water with fresh makeup. Increasing the bleed rate decreases the cycles of concentration. Decreasing the bleed increases cycles. The bleed rate required to maintain a desired cycle of concentration is determined by the following equation.

Bleed = Evaporation Rate

                (Cycles – 1)

The bleed rate can also be determined by measuring the makeup rate and dividing by the cycles of concentration.

Bleed = Makeup rate



The air passing through a cooling tower frequently blows small droplets of water out of the tower. This mist is called windage or drift. In some cooling systems windage can account for a significant amount of water loss from the system. These losses are reported as a percentage of the total recirculation rate. Although difficult to measure, the impact of windage can be estimated from the following chart.

Windage Losses


Windage Loss, %

Spray Pond

1.0 to 5.0

Atmospheric Tower

0.3 to 1.0

Mechanical Draft Tower

0.1 to 0.3

Evaporative Condenser

0.0 to 0.1

Windage = %Windage X Recirculation rate

Water lost by windage has the same effect on cycles of concentration as does bleed off. Water losses in cooling towers with excessive windage must be included in the total bleed off rate when calculating the cycles of concentration. Increased windage lowers cycles, whereas decreased windage increases cycles. For modern mechanical draft cooling towers with drift eliminators, the impact of windage on the overall bleed rate is minimal and often ignored in cooling tower calculations.

Theoretically, if the controlled bleed is shut off, the maximum cycles of concentration achievable in a cooling tower is limited by the percent evaporation and percent windage

Cycles max = %Evaporation + %Windage



Fresh makeup water is added to the cooling system to replace water lost by evaporation, bleed off, windage, and leaks. Unless systems leaks are significant, they are generally ignored altogether or included in the windage loss estimates. The makeup rate is then determined by adding all of the water losses from the system.

Makeup = Evaporation + Bleed + Windage

The makeup rate can also be estimated by rearranging the bleed off and cycles of concentration equations identified previously. Some useful formulas are:

Makeup = Evaporation + Makeup


Makeup = Evaporation + Evaporation 

                                           (Cycles – 1)                   

Makeup = Cycles X Evaporation

                     (Cycles – 1)



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