Here is a detailed explanation of key formulas used in HVAC cooling tower calculations:
1. Cooling Tower Range
The range of a cooling tower is the difference between the cooling water entering temperature and the cooling water leaving temperature.
Formula:
- T_hot: Temperature of water entering the cooling tower (°C or °F)
- T_cold: Temperature of water leaving the cooling tower (°C or °F)
Explanation:
This measures the ability of the cooling tower to cool down the water. A higher range indicates the cooling tower is effectively removing heat.
2. Cooling Tower Approach
The approach is the difference between the temperature of water leaving the cooling tower and the wet-bulb temperature of the air entering the tower.
Formula:
- T_cold: Temperature of water leaving the cooling tower (°C or °F)
- T_wet-bulb: Wet-bulb temperature of incoming air (°C or °F)
Explanation:
Approach reflects how close the cooling tower can cool water to the wet-bulb temperature. A smaller approach value indicates better cooling performance.
3. Cooling Tower Effectiveness
Effectiveness measures the cooling tower's ability to cool water compared to the maximum possible cooling (approach and range combined).
Formula:
Explanation:
Effectiveness is expressed as a percentage, showing how well the cooling tower operates relative to its theoretical capacity.
4. Heat Load (Heat Rejection)
This calculates the total heat rejected by the cooling tower, typically in BTU/hr or kW.
Formula (in kW):
- : Heat load (kW)
- : Mass flow rate of water (kg/s or GPM)
- : Specific heat capacity of water (typically 4.186 kJ/kg·°C)
- : Hot water temperature (°C)
- : Cold water temperature (°C)
Explanation:
This formula determines the energy the cooling tower removes from the circulating water.
5. Water Circulation Rate
This calculates the required water flow rate for heat rejection in the cooling tower.
Formula:
- : Water flow rate (kg/s or GPM)
- : Heat rejection (kW or BTU/hr)
- : Temperature difference (°C or °F)
Explanation:
This measures the flow rate of water necessary to achieve the desired cooling performance.
6. Drift Loss
Drift loss accounts for water lost as droplets carried away by the airflow in the cooling tower.
Formula:
- Drift Factor: Typically 0.001% to 0.02%, depending on the cooling tower's design.
Explanation:
This loss must be minimized to conserve water and reduce operational costs.
7. Evaporation Loss
This calculates the water evaporated during the cooling process.
Formula:
- Latent heat of vaporization is typically 2,257 kJ/kg or 970 BTU/lb at 25°C.
Simplified Formula for Approximation:
Explanation:
Evaporation loss occurs as water absorbs heat to change into vapor, removing heat from the system.
8. Blowdown Loss
Blowdown is the water drained from the system to control the concentration of dissolved solids.
Formula:
- Cycles of Concentration (COC): Ratio of dissolved solids in circulating water to makeup water.
Explanation:
Blowdown prevents scaling and fouling by maintaining water quality.
9. Makeup Water Requirement
This is the total water required to replenish losses due to evaporation, drift, and blowdown.
Formula:
Explanation:
It ensures the system has enough water to operate efficiently without interruptions.
These formulas are crucial for designing, operating, and maintaining an HVAC cooling tower to optimize its performance and energy efficiency.
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