104
4 Mine Ventilation Networks
Solution
X =
1 −
3
5
2
2
= 0.4096
v 1 =
Q
A 1
=
100
m
3
s
π3 2
4
m 2
= 14.147
m
s
P v =
1
2
· 1.2
Kg
m 3 ·
14.147
m
s
2 = 120.08 Pa
P shock = 0.4096 · 120.08 = 49.18 Pa
4.6 Shock Resistance and Equivalent Length
The equivalent length is the length of a straight airway of the same cross section as
that of the airway in which the fitting is installed which produces the same pressure
losses as the fitting.
In order to express this mathematically, we can start from Eq. 1.30 and work it
out as follows:
P shock = Xρ
v
2
2
= Xρ
Q
A
2
2
=
Xρ
2 A 2 Q
2
= R shock Q
2
Therefore, the value of the shock resistance is (Eq. 4.14):
R shock =
X ρ
2 A 2
(4.14)
If, in addition, the Atkinson resistance equation (Eq. 4.9) is used and it is adapted
only for the case of shock losses through the equivalent length of shock (L eq ) one
has: (Eq. 4.15):
R shock =
K O L eq
A 3
⎛
⎝ ρ
1.2
kg
m 3
⎞
⎠
(4.15)
Then equalizing the two expressions of resistances and clearing the equivalent
length, we have Eq. 4.16: