4.9 Resistances in Parallel
125
1
R eq
=
1
√
R 1
+
1
√
R 1
+
1
√
R 1
1
R eq
=
3
√
R 1
→
1
R eq
=
9
R 1
Generalizing this expression for a system with n parallel airways each of resistance
R i , the equivalent resistance for the network (R eq ) can be expressed as:
1
R eq
=
n
2
R i
Rearranging this we have (Eq. 4.21):
R eq =
R i
n 2
(4.21)
It follows that the greater the number of parallel airways, the lower the equivalent
resistance of the complete circuit, and therefore the more economic it is to ventilate.
9
Question 4.5 A ventilation system is changed from one comprising a single inlet
to another comprising five parallel airways each identical to the original inlet. How
does the equivalent resistance of the system change?
Answer
Using the expression deduced above:
R eq =
R i
n 2
Substituting:
R eq =
R i
25
So the resistance turns out to be 25 times smaller.
Question 4.6 The resistance of a ventilation system with three identical inlets is 15
N s
2
m 8 . What would be the resistance of the system if it had 8 parallel inlets of analogous
characteristics to the three original inlets?
Answer
R i is the resistance of an individual airway in both systems so, calculating for the
initial 3-inlet system:
9 Note that shock losses are ignored in these calculations.
125
1
R eq
=
1
√
R 1
+
1
√
R 1
+
1
√
R 1
1
R eq
=
3
√
R 1
→
1
R eq
=
9
R 1
Generalizing this expression for a system with n parallel airways each of resistance
R i , the equivalent resistance for the network (R eq ) can be expressed as:
1
R eq
=
n
2
R i
Rearranging this we have (Eq. 4.21):
R eq =
R i
n 2
(4.21)
It follows that the greater the number of parallel airways, the lower the equivalent
resistance of the complete circuit, and therefore the more economic it is to ventilate.
9
Question 4.5 A ventilation system is changed from one comprising a single inlet
to another comprising five parallel airways each identical to the original inlet. How
does the equivalent resistance of the system change?
Answer
Using the expression deduced above:
R eq =
R i
n 2
Substituting:
R eq =
R i
25
So the resistance turns out to be 25 times smaller.
Question 4.6 The resistance of a ventilation system with three identical inlets is 15
N s
2
m 8 . What would be the resistance of the system if it had 8 parallel inlets of analogous
characteristics to the three original inlets?
Answer
R i is the resistance of an individual airway in both systems so, calculating for the
initial 3-inlet system:
9 Note that shock losses are ignored in these calculations.