HVAC Cooling Tower Equations and Analysis in Excel

A cooling tower is a device that cools water by evaporating some of it and transferring heat to the surrounding air. The cooling tower efficiency is the ratio of the actual cooling to the maximum possible cooling. The maximum possible cooling is determined by the wet-bulb temperature, which is the lowest temperature that air can reach by evaporating water into it. The actual cooling is the difference between the inlet and outlet water temperatures.

The cooling tower capacity is the amount of heat that the cooling tower can remove from the water per unit time. It is usually measured in tons, where one ton of cooling is equal to 12,000 Btu/h. The cooling tower capacity depends on the water flow rate, the temperature difference, and a constant factor of 500. The water flow rate is the volume of water that passes through the cooling tower per unit time. The temperature difference is the difference between the inlet and outlet water temperatures.

The cooling tower also consumes water and energy. The water consumption is the amount of water that is evaporated and lost from the cooling tower per unit time. It depends on the cooling load, the range, the specific gravity, and the specific heat of the water. The range is the temperature difference between the inlet and outlet water temperatures. The specific gravity is the ratio of the density of the water to the density of pure water. The specific heat is the amount of heat required to raise the temperature of one unit mass of water by one degree.

The energy consumption is the amount of power that is used by the cooling tower fan and pump per unit time. It depends on the fan and pump efficiency, the air and water flow rates, the pressure drops, and the power factors. The fan and pump efficiency is the ratio of the useful work done by the fan and pump to the input power. The air and water flow rates are the volumes of air and water that pass through the cooling tower per unit time. The pressure drops are the losses of pressure due to friction and turbulence in the air and water passages. The power factors are the ratios of the real power to the apparent power in the electrical circuits.

The cooling tower performance can be improved by optimizing the design and operation parameters, such as the air and water flow rates, the fill type and area, the fan and pump speed, the water quality, and the maintenance schedule. The cooling tower performance can also be affected by the environmental factors, such as the ambient temperature, humidity, wind speed, and solar radiation. The cooling tower performance can be evaluated by measuring the inlet and outlet water temperatures, the wet-bulb temperature, the water flow rate, the fan and pump power, and the water consumption. The cooling tower performance can be calculated by using the cooling tower formulas and equations.

Basic Theory:

Cooling towers operate on the principle of evaporative cooling. Hot water from industrial processes or air
conditioning systems is pumped to the top of the tower and distributed over the tower fill or packing.
Simultaneously, air is drawn or forced through the fill, causing a portion of the water to evaporate. This
evaporation process removes heat from the remaining water, effectively cooling it down before it returns to the
system.

Procedures:

Approach:
- Understand the design parameters of the cooling tower, including water flow rate, temperature
  differentials, and the characteristics of the fill.
- Apply the appropriate equations to calculate the key performance indicators such as cooling capacity
  and approach.
Equations:
- Cooling Range (ΔT): $ΔT = T_{HotWaterIn} - T_{ColdWaterOut}$
- Approach (ΔT_approach): $ΔT_{approach} = T_{ColdWaterOut} - T_{WetBulbTemperature}$
- Cooling Capacity (Q): $Q = m \cdot c \cdot ΔT$ where $m$ is the mass flow rate
  and $c$ is the specific heat of water.
Excel Implementation:
- Utilize Excel to organize data and implement formulas.
- Create a table with columns for input parameters, calculations, and results.

Scenario:

Consider a cooling tower with the following parameters:

Hot Water Inlet Temperature ( $T_{HotWaterIn}$ ): 35°C
Cold Water Outlet Temperature ( $T_{ColdWaterOut}$ ): 25°C
Wet Bulb Temperature ( $T_{WetBulbTemperature}$ ): 20°C
Water Flow Rate ( $m$ ): 5000 kg/h
Specific Heat of Water ( $c$ ): 4.18 kJ/kg°C

Excel Table:

Parameter	Value
Hot Water Inlet Temp (°C)	35
Cold Water Outlet Temp (°C)	25
Wet Bulb Temperature (°C)	20
Water Flow Rate (kg/h)	5000
Specific Heat of Water (kJ/kg°C)	4.18

Excel Formulas:

ΔT: =B2 - B3
ΔT_approach: =B3 - B4
Q: =B6 * B7 * C2

Result:

Cooling Range (ΔT): 10°C
Approach (ΔT_approach): 5°C
Cooling Capacity (Q): 209,000 kJ/h

MATLAB Comparison:


% MATLAB Code
T_hot_water_in = 35;
T_cold_water_out = 25;
T_wet_bulb = 20;
m = 5000;
c = 4.18;

delta_T = T_hot_water_in - T_cold_water_out;
delta_T_approach = T_cold_water_out - T_wet_bulb;
Q = m * c * delta_T;

% Display results
disp(['Cooling Range (ΔT): ' num2str(delta_T) '°C']);
disp(['Approach (ΔT_approach): ' num2str(delta_T_approach) '°C']);
disp(['Cooling Capacity (Q): ' num2str(Q) ' kJ/h']);

MATLAB Result:

Cooling Range (ΔT): 10°C
Approach (ΔT_approach): 5°C
Cooling Capacity (Q): 209,000 kJ/h

HVAC Cooling Tower Equations and Analysis in Excel

Basic Theory:

Procedures:

Approach:

Equations:

Excel Implementation: