M

Where:

Mv = Mass of water vapor Ma = Mass of dry air

A typical humidity ratio is 0.00785 lbm (kg) of water per lbm (kg) of dry air. That is the amount of water in air at 70°F (21°C) and 50% RH at standard atmospheric pressure. In order to work in whole numbers, AC engineers commonly use the English system of measurement, which defines a lbm as consisting of 7,000 grains. So a humidity ratio of 0.00785 lbm of water/lbm of dry air is converted to whole numbers by multiplying by 7,000 grains/lbm of water. Thus,

000785 lbmwater/lbmairx 7,000 grains/lbmwater

= 55 grains/lbmatr

For conversions to SI units, there are 15,432 grains/kg, so a humidity ratio of 0.00785 would be equivalent to 121 grains/kg air. For example, assume that air at 90°F (32°C) and 70% RH is cooled and dehumidified so that the final state is 80°F (27°C) and 40% RH. The amount of water per lbm (kg) of dry air (w) is reduced from 0.0214 to 0.0087. The 0.0127 lbm (kg) of water removed per lbm (kg) of dry air corresponds to (7,000 x 0.0127) 88.9 grains/lbm (196 grains/kg) of dry air.

The air cooling process consists of removing sensible and latent heat, so that the enthalpy, or the total energy, in the air is reduced. When air is hot, its enthalpy is high. When air is moist, its enthalpy is also high because additional heat was required to evaporate moisture into the air. The total enthalpy (hm) of a mixture is equal to the enthalpy of the dry (ha) air plus the enthalpy of the water vapor (hv) times the humidity ratio (w). Thus, hm = ha + hvW

The amount of heat that must be removed to make this change, or enthalpy reduction, may be expressed as:

+ (Mcondensate x heat of vaporization)

Where:

SH = Specific heat in Btu/lbm • °F (kJ/kg • °C)

The enthalpy of the air is expressed as the number of Btu/lbm (kJ/kg or kW/kg) of dry air. Typical values range between 0 Btu/lbm (0 kJ/kg) at 0°F (-18°C) if the air is perfectly dry and 63 Btu/lbm (147 kJ/kg) if air is saturated at 95°F (35°C).

The heating and cooling requirements of AC loads are characterized by their sensible and latent components. The ratio of the sensible load component to the total heat load is sometimes referred to as the sensible heat fraction (SHF) or sensible heat ratio (SHR). The ratio of the latent component to the total load is sometimes referred to as a the latent heat fraction (LHF) or latent heat ratio (LHR).

Generally, the more water vapor that must be removed from the air stream to be conditioned, the more work a mechanical refrigeration compressor (or absorption chiller) must do to achieve a low enough cooling coil temperature to condense the water vapor. The cooling coil must be much colder simply to lower the (sensible) temperature of the air to the desired level. Thus, just as with other lower temperature refrigeration applications, the compressor must operate at a higher compression ratio, requiring more shaft power per ton (kW^ or kJ/h), if there is a high LHR or if a low RH is desired.

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