grain per pound of dry air
Humidity ratioexact by definition
The grain of moisture per pound of dry air is the North American psychrometric unit, equal to exactly 1/7000 on a mass basis because there are exactly 7000 grains in a pound. The factor of 0.00014285714 is that exact seven-thousandth, rounded here only in its decimal display. Typical conditioned indoor air runs 50 to 65 gr/lb, and outdoor design conditions in humid climates reach 130 or more.
Watch out: Do not confuse the grain of moisture per pound with the grain per gallon of water hardness. Both use the same 64.79891 mg grain and both are common in North American trades, but one is a moisture content in air and the other a dissolved solids concentration in water.
| 1 gr/lb | 0.14285714 g/kg |
The grain arrived in psychrometrics from the same place it arrived in water hardness: it is a small enough unit that ordinary values come out as convenient whole numbers. Expressing indoor humidity as 60 gr/lb rather than 0.0086 lb/lb is the entire justification.
About the grain per pound of dry air
Grains per pound is how North American HVAC counts moisture, and its value is that it makes latent load arithmetic easy. The standard equation for latent heat removal is \(Q_L = 0.68 \times \text{cfm} \times \Delta W\), giving BTU per hour when \(\Delta W\) is in grains per pound. That 0.68 packs together the density of standard air, the latent heat of vaporisation of water, and the 7000 grains in a pound, in the same way the 1.08 in the sensible-heat equation packs density and specific heat.
The reason humidity ratio rather than relative humidity belongs in that equation is that it is conserved. Heat a sample of air and its relative humidity falls, though not a single molecule of water has left; cool it and the relative humidity rises. The grains per pound stays exactly where it was until the air reaches its dew point and starts dropping water out. So a coil that takes air from 78 gr/lb to 58 gr/lb has removed 20 grains from every pound of dry air passing through it, and at 2000 cfm that is \(0.68 \times 2000 \times 20 = 27\,200\) BTU/h of latent load, or about 2.3 tons, on top of whatever sensible cooling it is doing.
For orientation: 7000 gr/lb would be air made entirely of water, which is why real numbers are small. Comfortable indoor conditions of 75 °F and 50 percent RH are 65 gr/lb. Miami's summer design condition is around 130 gr/lb, Phoenix's around 60 despite being much hotter, and that difference is exactly why one city's cooling load is dominated by latent heat and the other's is not. Converting to metric, divide by 7 to get grams per kilogram: 65 gr/lb is 9.3 g/kg.