Page 200 - Advanced Mine Ventilation

180 Advanced Mine Ventilation

Figure 11.6 Plot of turbulent dispersion coefficient against Reynold’s number.

Eq. (11.41), have been recorded [14]. A summary of the most relevant data available
on this coefficient is given in Fig. 11.6 [12,15e18].
E x
The results are plotted as a graph of normalized value of E x as p ffiffiffiffiffiffiffi
4
D$Sc Sc t $ l=l r
against the Reynold’s number, Re ¼ (ud/nv)bothonlogarithmicscales. Here, l, l r
are the coefficients of friction for smooth and rough pipes, respectively, D is the
coefficient of molecular diffusion, n is the coefficient of kinematic viscosity,
Sc ¼ (n/D) is the molecular Schmidt number, Sc t ¼ (E u /E c )isthe turbulent
Schmidt number, E u is the coefficient of turbulent viscosity, E c is the coefficient
of turbulent diffusion, and d is a characteristic length; for pipes, it is the diameter.
For values of Re between 30,000 and 200,000, E x can be approximated within
10% by

4 p ffiffiffiffiffiffiffiffiffi
E x ¼ 15:8 D Re Sc Sc t l=l r
(11.42)
p
ffiffiffiffiffiffiffiffiffi
¼ 15:8 ud Sc 6 Sc t l=l r
Under normal atmospheric conditions, Sc ¼ 0.72 and Sc t ¼ 0.75. On substitution
Eq. (11.42) reduces to

p ffiffiffiffiffiffiffiffiffi
E x ¼ 14:4 ud l=l r (11.43)