Cooling Tower's equation of humidity derivation

[Rathy Cato]

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?

 

[Chestermiller]

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 p_s. 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 p_s/(P - p_s), 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.