 # Cooling Tower Calculations

In order to understand cooling tower calculations, you need to understand some basic terminology & formulas.

Let’s start…

## Cooling Tower Calculations & Terminologies:

### #1. Wet bulb temperature:

wet bulb temperature is measured by the thermometer which is wrapped in a cloth called soak. Wet bulb temperature of a cooling tower is measured by sling psychomotor.

### #2. Dry bulb temperature:

This the temperature of the atmosphere. It is also called ambient temperature. It doesn’t take account of relative humidity in the air. Relative humidity simply represents how much moisture could be at a given temperature compared to the actual moisture present in the air. If the humidity is 100% then no evaporation is possible because air is completely saturated with water.

### #3. Range or Delta T:

It is the difference between cooling water inlet temperature and outlet temperature.

Range or Delta T Calculation
Range or Delta T = Hot cooling water inlet temp – Cold cooling water outlet temp

### #4. Approach:

This is the difference between the cooling tower outlet cold water temperature and ambient wet bulb temperature.

Approach Calculation
Approach = Cold cooling water outlet – Wet bulb temperature

### #5. Cooling Tower Effectiveness:

This is the ratio of range to the ideal range

CT Effectiveness Calculation
CT effectiveness (%) = Range / (Range + Approach) *100

### #6. Hold up volume:

It is the total volume of water present in the whole circuit of the cooling tower including piping & equipment. Don’t confuse with circulation rate. The holdup volume is measured in m3

### #7. Circulation Rate or Re-circulation Rate:

It is the flow rate of water which is circulated in the cooling tower. Normally, the circulation rate is measured in m3/hr

### #8. Evaporation Loss:

Evaporation Loss: It is the loss of water from a cooling tower by evaporation. Theoretically, the evaporation quantity of water is 1.8 m3 for every 10,00,000 Kcal heat rejected.

Evaporation Loss Calculation
Evaporation Loss(m3/hr) = 0.00153 * Recirculation Rate (m3/hr)  * Delta T

### #9. Windage or Drift Loss:

It is very difficult to ignore the drift problem in a cooling tower. Drift or windage loss of cooling tower is normally provided by its manufacturer based on cooling tower design. If it isn’t available then you can assume based on below formula.

Drift Loss Calculation
Natural Draft Cooling Tower: 0.3 to 1.0 * Recirculation Rate / 100

Induced Draft Cooling Tower: 0.1 to 0.3 * Recirculation Rate / 100

Cooling Tower with drift eliminator: 0.01 * Recirculation Rate / 100

### #10. Cycle of concentration(COC):

cycle of concentration (COC): It is simply a ratio of the parameters of cooling water to the parameters of makeup water. It is a dimensionless number. It can be calculated by any of the below formulae.

COC Calculation
COC = Silica in cooling water / Silica in makeup water

COC = Calcium Hardness in cooling water / Calcium Hardness in makeup water

COC = Conductivity in cooling water / Conductivity in makeup water.

COC = Make up water quantity / Blowdown water quantity

The last formula gives you more accurate COC if you have flow measurement facility available for makeup & Blowdown water in the cooling tower. The cycles of concentration normally vary from 3.0 to 8.0 depending on the design of a cooling tower.

It is always advisable to maintain COC as high as possible to reduce make water requirement. It is ultimately saves the water. On other side higher COC increases dissolved solids concentration in cooling tower.

### #11. Blow down:

As you know when water evaporates it leaves solids & only pure water evaporates. It means as COC increases dissolved solids gets concentrate. This will lead to corrosion & scaling problem in the system if COC is not maintained as per design limit. So, to maintain design COC some quantity of water is discharged from the cooling tower. It is known as Blow down & calculated based on below formula

Blowdown Calculation
Blow down = Evaporation Loss / COC-1

### #12. Holding Time Index:

It is a measurement of time at which the concentration of the added chemical into the cooling water system decreases to 50% of its original value. This happens due to blowdown & drift loss of water from the system plus the addition of new makeup water in the system. The ideal value for HTI is 24 hours. High HTI (>48 hours) can result in chemical degradation.

HTI Calculation
HTI = 0.693 * Hold up Volume / Blowdown

### #13. Chemical dosing calculation based on blowdown:

Chemicals like corrosion and scale inhibitors are dosing on a continuous basis so the dosing of these chemicals is calculated based on blowdown rate. Basically, the purpose is to make up the chemical which is lost with blowdown to maintain desired concentration. This calculation is a very important part of any cooling tower calculations.

Chemical Calculation Based on Blowdown
Chamical Quantity (Kg/hr) = Blowdown (m3 /hr) * ppm / 1000

### #14. Chemical dosing calculation based on holdup volume:

Slug dosed chemicals like non-oxidising biocide calculated based on hold up volume of cooling tower. Generally, after dosing of biocide blowdown is closed for 24 hours to make it more effective.

Chemical Calculation Based on Holdup
Chamical Quantity (Kg) = Hold up volume (m3) * ppm / 1000

### #15. Langelier Saturation Index:

LSI calculation will indicate the calcium carbonate scaling tendency of the water. Calculating an LSI is very important because exceeding a treatment program’s LSI limit will likely lead to the formation of a calcium carbonate deposit.

### #16. Log Mean Temperature Difference(LMTD):

This calculates average temperature differential across heat exchangers. It compares the difference between temperatures of the “hot” and “cold” fluids in heat exchangers. The larger temperature difference between two fluids at either the exit or the entrance of the heat exchanger is designated as ∆T2 and the smaller temperature difference is designated as ∆T1

Counterflow heat exchanger design where hot fluid enters at the opposite side of cooling water. The LMTD of counterflow heat exchanger design calculated by using the below formula:

LMTD Calculation For Counter flow Heat Exchanger
LMTD = [(T1 – t2) – (T2 – t1)] / ln [(T1 – t2) – (T2 – t1)]

Parallel flow heat exchanger design where hot fluid & cooling water enters on the same side of the heat exchanger. The LMTD of parallel flow heat exchanger design calculated by using the below formula:

LMTD Calculation For Parallel flow Heat Exchanger
LMTD = [(T1 – t1) – (T2 – t2)] / ln [(T1 – t1) – (T2 – t2)]
Where;

T1 = Hot fluid inlet temperature

T2 = Hot fluid outlet temperature

t1 = Cold fluid inlet temperature

t2 = Cold fluid outlet temperature

### #17.Terminal Temperature Difference(TTD):

TTD is the difference in temperatures of hot fluid exiting (T hot-out ) and cold fluid exiting (T cold-out ) the heat exchanger.

TTD Calculation
TTD = T hot(out) – T cold(out)

### Why LMTD & TTD is important?

Increasing LMTD & TTD means there is reduced heat transfer occurring, and the system might be fouling on the process side or the cooling water side.

In Conclusion, above all cooling tower calculation are the most important part of any cooling water treatment program to monitor it very effectively.

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