238
6 Fans and Flow Control Devices
Solution
R
32
250 Pa
250 Pa
27
m
3
s
First, we calculate the total resistance of the district without regulator (R dist ):
R dist =
Q
2
dist
=
250 Pa
32
m 3
s
2 = 0.244
N s
2
m 8
For airflow rate to be 27 m
3 s
−1 , the total resistance in the circuit with regulator
must be:
R eq =
Q 2
reg
=
250 Pa
27
m 3
s
2 = 0.343
N s
2
m 8
The regulator must provide the difference in resistance, thus:
R reg = R eq − R dist = 0.099
N s
2
m 8
The area of the regulator can be obtained as:
A =
1.2
√
Q =
1.2
R reg Q 2
Q =
1.2
R reg
And therefore:
A =
1.2
R reg
=
1.2
0.099
N s 2
m 8
= 3.81 m
2
Question 6.4 The system a of the figure represents a water tank, which is freely
discharged through a network of hoses. System a
is identical to system a except for
the fact that one of the hoses is constricted by means of a clamp. You are asked to
determine if the flow rate (Q) exiting the system a is greater or equal to that exiting
system a
(Q
). Use the mathematical expressions studied in this section in your reply.