Page 38 - Advanced Mine Ventilation

Air Flow in Mine Airways 21

or 2
1
l ¼ ¼ 0:0188
7:3

An example:
For a flow rate of 75 gpm water, calculate the head (pressure) loss for 3000 feet of
00
3 diameter drill pipe. The roughness of pipe, e is 0.006.
Step 1. Calculate the fluid velocity.
3 3
Q; fluid flow rate ¼ 75 gpm ¼ 10 ft min ¼ 0:167 ft s
2
p 3 2
A; cross section of pipe ¼ ¼ 0:049 ft
4 12
Q 0:167
Hence velocity; V ¼ ¼ ¼ 3:41 ft=s
A 0:049
Step 2. Calculate the Reynold’s number, R.

Vd 3:41 0:25
R ¼ ¼ ¼ 70; 000
ðm=rÞ 1:217 10 5
5 2
ðm=r is the kinematic viscosity of water ¼ 1:217 10 ft =s
Hence the flow is fully turbulent.

Step 3. Calculate l from Eq. (2.6).
1 = 2 log ⎛ 3 ⎞ + 1.114
λ ⎜ ⎝ 0.006 ⎠ ⎟

This gives l ¼ 0.0234.
Step 4. Calculate head loss using Eq. (2.1).

2
0:0234 3000ð3:41Þ
h ¼ feet of water
2 32 0:25
¼ 51 ft ¼ 22:2 psi

2.3 Traditional Equations for Pressure Loss Calculation
in Mines

Eq. (2.1) works well for circular pipes and ventilation tubing made of steel or fiber-
glass, but it is not directly usable for mine airways that are actually rectangular in shape
and have uncertain degree of roughness.