Page 26 - Advanced Mine Ventilation

Underground Coal Mine Atmosphere 9

Calculate the density of dry air if the temperature was 70 F
P a ¼ P e P v ¼ 30e0.5 ¼ 29.5 inch Hg
Or P a ¼ 2085.8 lb/ft 2

53:35ð460 þ 70Þ 3
Va ðspecific volume of airÞ¼ ¼ 13:556 ft lb
2085:8
1 3
Hence density of dry air; ¼ r a ¼ ¼ 0.0738 lb/ft
V a
Density of the moist air is also calculated by using another equation:
DðP 0:378 P v Þ
r ¼ (1.5)
a
T
where D is 1.3258 if pressure is measured in inches of mercury; P 1 ¼ barometric
pressure; P v ¼ vapor pressure; T ¼ dry-bulb temperature in Rankine.
3
This yields the density of dry air in the above example as 0.0743 lb/ft , which is
3
quite close to the previous volume of 0.0738 lb/ft .
1.3.1.4 Graham’s Law of Diffusion

It states that the rate of diffusion of a gas is adversely proportional to the square root of
the ratio of the densities (specific gravity) of the gas, r and air, r .
a
g
r a
r ffiffiffiffiffi
Diffusion rate is proportional to (1.6)
r
g
In other words, a gas lighter than air will diffuse faster than one heavier than air.
For example, methane has a specific gravity of 0.55 and carbon dioxide has a spe-
cific gravity of 1.5 compared with air, hence methane will diffuse 1.65 times faster than
carbon dioxide.

1.3.1.5 Air Density at Higher Altitude

The air density is normally measured at sea level, and it decreases as the altitude in-
creases. The temperature also normally goes down as the altitude increases. Madison
[5] provides a mathematical relationship as follows:

4:526
W 2 288 0:00198 H
¼ (1.7)
W 1 288
where W 2 is the density at height, H over the sea level; W 1 is the density at the sea
level.