Cooling Tower's equation of humidity derivation

In summary, the equation Hs = (Mw/Ma){Ps/(P-Ps)} is derived from the ideal gas law and the concept of partial pressure. It represents the ratio of water vapor to dry air in a saturated mixture, taking into account the total pressure and saturation pressure.
  • #1
Rathy Cato
11
0
Humidity is known as mass of water vapor/mass of dry air

Hs (saturation) = (Mw/Ma){Ps/(P-Ps)}

P is total pressure
Ps is saturation pressure

what is the derivation for this equation?
 
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  • #2
For an ideal gas mixture, the partial pressure of a substance is equal to the total pressure times the mole fraction of the substance. If the air is saturated with water vapor, then the partial of water vapor is equal to the equilibrium vapor pressure of water at the temperature of the mixture ps. Therefore, the number of moles of water vapor per mole of all other gasses in the air (i.e., per mole of dry air) is ps/(P - ps), where P is the total pressure. Multiplying by the ratio of the molecular weights give the mass of water vapor per unit mass of dry air.
 

1. What is the Cooling Tower's equation of humidity derivation?

The Cooling Tower's equation of humidity derivation is a mathematical formula used to calculate the change in humidity of air as it passes through a cooling tower. It takes into account factors such as the temperature and moisture content of the air and the cooling water flow rate.

2. Why is the Cooling Tower's equation of humidity derivation important?

The Cooling Tower's equation of humidity derivation is important because it allows us to predict how much moisture will be removed from the air as it passes through a cooling tower. This information is crucial for designing and operating efficient cooling towers, which are used in various industrial and commercial processes.

3. How is the Cooling Tower's equation of humidity derivation derived?

The Cooling Tower's equation of humidity derivation is derived from the principles of psychrometrics, which is the study of the physical and thermodynamic properties of air and water vapor mixtures. It involves using the laws of thermodynamics and mass and energy balances to describe the behavior of air and water vapor in a cooling tower.

4. What are the assumptions made in the Cooling Tower's equation of humidity derivation?

The Cooling Tower's equation of humidity derivation makes several assumptions, including: constant total pressure, steady state conditions, ideal gas behavior of air and water vapor, and no heat or mass transfer between the air and the surrounding environment. These assumptions allow for a simplified and practical solution to the problem.

5. Can the Cooling Tower's equation of humidity derivation be used for all types of cooling towers?

The Cooling Tower's equation of humidity derivation is applicable for most types of cooling towers, including both crossflow and counterflow designs. However, it may not accurately predict the performance of cooling towers with complex geometries or those that use specialized cooling media, such as evaporative media or sprays. In these cases, more advanced models may be needed.

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