70
3 Flow Rates and Pressure Measurements
Then, we can calculate D, as:
D = 300 m − 200 m = 100 m
Thus:
P B calc = 104,712
N
m 2
2 · 103,690
N
m 2 + 100
N
m 2 · 9.81
N
kg
· 1.245
kg
m 3
2 · 104,712
N
m 2 − 100
N
m 2 · 9.81
N
kg
· 1.250
kg
m 3
= 104,915 Pa
Therefore, the frictional pressure drop is:
AB = P B calc − P B = 104,915 Pa − 104,712 Pa = 203 Pa
(b) Given that the average airflow rate in the airway (20 m
3 s
−1 ) is provided, the
frictional resistance (R) can be approximated as:
R =
AB
Q 2 =
203
N
m 2
20
m 3
s
2 = 10.15
N s
2
m 8
3.5 Estimating the Section of a Gallery
The area of a cross section of a mine gallery can be found very precisely by laser
scanning. If this technique is not available, the area can be estimated according to its
approximate geometry, as shown in Fig. 3.5 (Luque Cabal 1988).
Hence, for the case of a steel straight walls semicircular arch (Fig. 3.5a), Eq. 3.3
would apply:
A = 0.83 B H
(3.3)
B
H
H
B
T
a)
b)
Fig. 3.5 Geometry of a section with: a a steel semicircular arch and b timber support