Page 100 - Advances In Productive, Safe, and Responsible Coal Mining

84 Advances in Productive, Safe, and Responsible Coal Mining

Air flow through mine ventilation networks follows a quadratic mathematical rela-
tionship similar to Ohm’s law in electricity:

∗
H ¼ R Q 2 (6.1)
where
H¼pressure difference between two points in the network. Units are Pa or inches water
gauge (in-WG). It is analogous to voltage in electrical networks.
R¼airflow resistance. It is a function of the number and size of the air ways. Units are
6
2
2
Ns m 8 or in-WGmin ft . It is analogous to resistance in electrical networks.
3
Q¼airflow quantity. Units are m /s or cubic feet per minute (CFM). It is analogous to cur-
rent in electrical networks.
Similar to electric current, ventilation flow and pressure also follow the basic laws of
all networks known as Kirchhoff’s laws. Kirchhoff’s first law provides for the conser-
vation of mass. At any junction or node connecting two or more airway branches or
paths within the network, the sum of mass flows of air going into the junction must be
equal to that going out. Kirchhoff’s second law requires that, in any closed loop
through a ventilation network, the sum of all pressure differentials across each branch
is zero.
A large variety of computer programs exist to calculate air flows and pressures in
mine ventilation networks. These programs use iterative methods, which are neces-
sary due to the quadratic relationship in Eq. (6.1). A well-known and frequently used
iteration method is the Hardy Cross Method, but with modern computers, other math-
ematical iteration methods may be used as well. Some computer programs can sim-
ulate dust and contaminant flow in mine airways, while others can be used to calculate
air temperatures and cooling or heating requirements. Some programs can also assess
the influence of a mine fire on ventilation.
Airflow resistance, R, can be calculated using the following equations:
∗
∗
For SI units, R ¼ k L O=A 3 (6.2)
∗
∗

For Imperial units, R ¼ k L O= 5:2A 3 (6.3)
where
2
4
4
2
3
k¼airway resistance coefficient or k-factor. Units are Ns /m (kg/m ) or in-lb*min /ft .
L¼airway length, including the equivalent length added for shock losses. Units are m or ft.
O¼perimeter of the airway cross section. Units are m or ft.
2
2
A¼cross-sectional area of the airway. Units are m or ft .
4
2
3
The k-factor conversion between unit systems is 1kg/m ¼1Ns /m ¼5.4 10 7 lb.
4
3
2
min /ft . The k-factor typically ranges between 3 and 40 10 3 kg/m (20 and
4
2
200 10 10 lb. min /ft ). Smooth, straight, circular airways tend to have k-factors
at the lower end, while curvy, irregular, and obstructed airways have higher k-factors.
For more information and a representative table of typical k-factors in Imperial units,
see United States (US) Bureau of Mines Bulletin 589 [1].