1.3 Fluid Dynamics
29
Exercise 1.9 A fan 1.5 m in diameter moves a flow rate of 100 m
3 s
−1 . Determine
the pressure losses that occur in the inlet, if:
(a) It has a bell-mouth shape (X = 0.05).
(b) Its flank is plain (X = 0.9).
Air density: 1.2 kg m
−3 .
Solution
First, the velocity is calculated:
v =
Q
A
=
100
m
3
s
π (0.75 m)
2
= 56.59
m
s
Then the dynamic pressure is:
P v =
1
2
ρv
2
P v =
1
2
· 1.2
kg
m 3 ·
56.59
m
s
2 = 1921.46 Pa
Taking into account the expression for calculating shock losses:
P shock = X P v
(a) In the case of a flared inlet:
P shock (flared) = 0.05 · 1921.46 Pa = 96.07 Pa
(b) In the case of a plain inlet:
P shock (flat) = 0.9 · 1921.46 Pa = 1729.31 Pa.
29
Exercise 1.9 A fan 1.5 m in diameter moves a flow rate of 100 m
3 s
−1 . Determine
the pressure losses that occur in the inlet, if:
(a) It has a bell-mouth shape (X = 0.05).
(b) Its flank is plain (X = 0.9).
Air density: 1.2 kg m
−3 .
Solution
First, the velocity is calculated:
v =
Q
A
=
100
m
3
s
π (0.75 m)
2
= 56.59
m
s
Then the dynamic pressure is:
P v =
1
2
ρv
2
P v =
1
2
· 1.2
kg
m 3 ·
56.59
m
s
2 = 1921.46 Pa
Taking into account the expression for calculating shock losses:
P shock = X P v
(a) In the case of a flared inlet:
P shock (flared) = 0.05 · 1921.46 Pa = 96.07 Pa
(b) In the case of a plain inlet:
P shock (flat) = 0.9 · 1921.46 Pa = 1729.31 Pa.