Page 37 - Advanced Mine Ventilation

20 Advanced Mine Ventilation

Table 2.1 Roughness for Various Pipes

Type of Pipe e, in.
Wrought iron pipe 0.0017
Well tubing/line pipe 0.0007
Cast iron 0.0050
Galvanized iron 0.0060
Uncoated cast iron 0.0100
Wood pipe 0.007 to 0.036
Concrete 0.012 to 0.12
Riveted steel 0.035 to 0.35

⎡ ⎤
1 = 2 log d 1.14 - 2 log 1 ⎢ + ⎢ 9.28 ⎥ ⎥ +
e
λ e ⎢ R ⎛⎞ λ ⎥ (2.4)
⎢ ⎣ ⎜⎟ ⎥ ⎦
d
⎝⎠
The value of l is obtained by several iterations. However, Eq. (2.4) has been made
user-friendly by the Moody [5] diagram that shows the value of l against varying Rey-

1
nold’s number and different e ratios ranging from 10 5 to 10 . Mostly, the l values
d
range from 0.01 to 0.09, representing very smooth to wholly rough pipes. For fully tur-
bulent flow in smooth pipes, Vennard [1] provides another equation for l that may be
easier to use.
1 = - 0.80 + 2.0 log R λ
λ (2.5)

When the flow becomes completely turbulentdthat is beyond the transition zoned
the frictional coefficient is no longer a function of Reynold’s number but becomes a
function of e/d only. The friction factor in this region of flow is completely indepen-
dent of the physical properties of the flowing fluid. For fully turbulent flow, the l factor
is expressed by an equation obtained experimentally by Nikuradse [6].
1 = 2 log d + 1.14
λ e (2.6)

00
Thus for a 6 diameter cast iron pipe with roughness of 0.005 in:
d 6
¼ ¼ 1200
e 0:005
Hence,
1 = 2 log 1200 + 1.14 = 7.3
λ