204
6 Fans and Flow Control Devices
as the quantity through gallery A is zero. In this way, as the resistance of gallery B
is also known, we have:
P
B = R B Q
T = 2.22
N s
2
m 8
42.87
m
3
s
2
= 4080 Pa
Exercise 6.2 The main fan of the mine shown in the figure communicates an airflow
rate of 50 m
3 s
−1 operating at a pressure of 6 kPa. The airflow rate which circulates
through gallery A is 35 m
3 s
−1 and through gallery B is 15 m
3 s
−1 . Determine the
pressure at which a booster fan located in gallery B should operate to increase its
airflow rate to 25 m
3 s
−1 . Assume that the pressure supplied by the main fan does
not change after installing the booster fan.
R = 1
R = 1
Solution
Prior to the installation of the booster fan, have for branch A:
6000 Pa =
R s 1 + R s 2
Q
2
T + R A Q
2
A = (1 + 1)
N s
2
m 8
50
m
3
s
2
+ R A
35
m
3
s
2
Solving for R A :
R A = 0.816
N s
2
m 8
Similarly, for branch B:
6000 Pa =
R s 1 + R s 2
Q
2
T + R B Q
2
B = (1 + 1)
N s
2
m 8
50
m
3
s
2
+ R B
15
m
3
s
2
6 Fans and Flow Control Devices
as the quantity through gallery A is zero. In this way, as the resistance of gallery B
is also known, we have:
P
B = R B Q
T = 2.22
N s
2
m 8
42.87
m
3
s
2
= 4080 Pa
Exercise 6.2 The main fan of the mine shown in the figure communicates an airflow
rate of 50 m
3 s
−1 operating at a pressure of 6 kPa. The airflow rate which circulates
through gallery A is 35 m
3 s
−1 and through gallery B is 15 m
3 s
−1 . Determine the
pressure at which a booster fan located in gallery B should operate to increase its
airflow rate to 25 m
3 s
−1 . Assume that the pressure supplied by the main fan does
not change after installing the booster fan.
R = 1
R = 1
Solution
Prior to the installation of the booster fan, have for branch A:
6000 Pa =
R s 1 + R s 2
Q
2
T + R A Q
2
A = (1 + 1)
N s
2
m 8
50
m
3
s
2
+ R A
35
m
3
s
2
Solving for R A :
R A = 0.816
N s
2
m 8
Similarly, for branch B:
6000 Pa =
R s 1 + R s 2
Q
2
T + R B Q
2
B = (1 + 1)
N s
2
m 8
50
m
3
s
2
+ R B
15
m
3
s
2