Page 39 - Advanced Mine Ventilation

22 Advanced Mine Ventilation

A new term, hydraulic radius, R h , is introduced as the ratio of area to perimeter.

A
R h ¼ (2.7)
P

where A is the area of the airway and P is the perimeter.
For a circular pipe of diameter, D:

A pD 2 D
R h ¼ ¼ ¼ (2.8)
P 4pD 4
Substituting Eq. (2.8) in Eq. (2.1),

l lv 2
h ¼ (2.9)
4R h 2g
Atkinson [7] used mining engineering units to further modify Eq. (2.9) such that:

KPLQ 2
H ¼ 3 (2.10)
5:2A
Q
where H is expressed in inches of water. L is in feet. V was replaced by where Q was
A
2
the air quantity in cubic feet/minute and A is the cross-sectional area in ft . g was
2
replaced by 32 ft/s .
3
Density of air was 0.075 lb/ft at standard temperature and pressure.
Where
lb min 2
10
K ¼ l 810 10
ft 4
Because K is a very small number, it is multiplied by 10 10 to get whole numbers
such as 10, 20, or 100.
Thus:

lb min 2
K ¼ 810 l (2.11)
ft 4
It should be noted that K must be corrected if the air density is different from
3
0.075 lb/ft by using Eq. (2.12).
W

Corrected K ¼ K (2.12)
0:075
3
where W is the actual density of air in lb/ft .
Eq. (2.10) is commonly used in mining engineering and is known as Atkinson’s
equation [7].