148
3 Fans
static pressure on the side of the rotor is the static pressure at the inlet of the rotor
(station 1).
A: Q leak = 0.217 m
3
/s; η v = 0.948.
3.8.6 Centrifugal Pump (Finite Number of Blades and Internal
Losses)
A centrifugal pump has rotor internal diameter d 1 = 100 mm and external diameter
d 2 = 180 mm. The rotor has 8 blades with thickness t = 2 mm. Blades are simply
curved with width b 1 = 15 mm at the inlet and b 2 = 10 mm at the outlet. There is no
pre-swirl. The blade angles at the inlet and outlet are β 1
70
b
= −
°
and β 2
60
b
= −
°
. The
pump runs at 1800 rpm and supplies the volume flow rate Q = 17.0 l/s ( ρ = 1000 kg/
m
3
). The manometric head is H m = 12 m. Ignore leakage flow. Assume as mechanical efficiency η m = 0.95 and as rotor incidence loss coefficient µ def = 0.80. Apply Wiesner’s formula for the slip (3.20–3.21).
1. Determine the power transferred to the fluid by the rotor, the internal efficiency
and the shaft power.
2. Determine the flow rate and the manometric head with an incidence-free rotor
inlet, with the assumption that all internal losses, except for the incidence loss at
the rotor inlet, are proportional to the flow rate squared.
A: P rot = 2494.1 W; η i = 0.802, P shaft = 2625.3 W; Q
*
= 13.76 l/s; H m
*
= 14.97 m.
3.8.7 Axial Fan (Idealised Flow): Analysis on Average Diameter
The rotor of an axial fan has a hub diameter d h = 0.24 m and a tip diameter d t = 0.48 m.
There is no pre-swirl. The inlet flow is purely axial on the quadratic average radius
r m = 0.19 m
2
2
2
2
1
m
t
h
r
)
r r
(
=
+
. The relative velocity forms the angle β 1 = −55° to
the axial direction at the rotor inlet and the angle β 2 = −35° at the outlet. Rotational
speed is 2500 rpm and the air has density ρ = 1.2 kg/m
3
. Assume idealised flow, i.e.
no internal losses. Assume as well that the flow on the average radius is characteristic for the entire machine.
1. Determine the velocity triangles of the flow on the average radius.
2. Determine the rotor work ΔW, the static pressure rise across the rotor Δp rot and
the degree of reaction R.
3. Determine the volume flow rate Q through the fan.
4. Determine the rotor power or internal idealised power P i at design flow rate.
A: ΔW = 1261.2 J/kg; Δp rot = 1127.7 Pa; R = 0.745; Q = 4.73 m
3
/s; P i = 7154 W.
3 Fans
static pressure on the side of the rotor is the static pressure at the inlet of the rotor
(station 1).
A: Q leak = 0.217 m
3
/s; η v = 0.948.
3.8.6 Centrifugal Pump (Finite Number of Blades and Internal
Losses)
A centrifugal pump has rotor internal diameter d 1 = 100 mm and external diameter
d 2 = 180 mm. The rotor has 8 blades with thickness t = 2 mm. Blades are simply
curved with width b 1 = 15 mm at the inlet and b 2 = 10 mm at the outlet. There is no
pre-swirl. The blade angles at the inlet and outlet are β 1
70
b
= −
°
and β 2
60
b
= −
°
. The
pump runs at 1800 rpm and supplies the volume flow rate Q = 17.0 l/s ( ρ = 1000 kg/
m
3
). The manometric head is H m = 12 m. Ignore leakage flow. Assume as mechanical efficiency η m = 0.95 and as rotor incidence loss coefficient µ def = 0.80. Apply Wiesner’s formula for the slip (3.20–3.21).
1. Determine the power transferred to the fluid by the rotor, the internal efficiency
and the shaft power.
2. Determine the flow rate and the manometric head with an incidence-free rotor
inlet, with the assumption that all internal losses, except for the incidence loss at
the rotor inlet, are proportional to the flow rate squared.
A: P rot = 2494.1 W; η i = 0.802, P shaft = 2625.3 W; Q
*
= 13.76 l/s; H m
*
= 14.97 m.
3.8.7 Axial Fan (Idealised Flow): Analysis on Average Diameter
The rotor of an axial fan has a hub diameter d h = 0.24 m and a tip diameter d t = 0.48 m.
There is no pre-swirl. The inlet flow is purely axial on the quadratic average radius
r m = 0.19 m
2
2
2
2
1
m
t
h
r
)
r r
(
=
+
. The relative velocity forms the angle β 1 = −55° to
the axial direction at the rotor inlet and the angle β 2 = −35° at the outlet. Rotational
speed is 2500 rpm and the air has density ρ = 1.2 kg/m
3
. Assume idealised flow, i.e.
no internal losses. Assume as well that the flow on the average radius is characteristic for the entire machine.
1. Determine the velocity triangles of the flow on the average radius.
2. Determine the rotor work ΔW, the static pressure rise across the rotor Δp rot and
the degree of reaction R.
3. Determine the volume flow rate Q through the fan.
4. Determine the rotor power or internal idealised power P i at design flow rate.
A: ΔW = 1261.2 J/kg; Δp rot = 1127.7 Pa; R = 0.745; Q = 4.73 m
3
/s; P i = 7154 W.