146
3 Fans
3.8 Exercises
The list contains exercises on fans, but also on pumps and hydraulic turbines, as
with the theory developed up to now, basic problems on all kinds of machines with
constant density fluids can be analysed.
3.8.1 Centrifugal Pump (Idealised Flow)
A centrifugal pump has rotor internal diameter d 1 = 80 mm and external diameter
d 2 = 200 mm. Blades are simply curved with width b 1 = 30 mm at the inlet and
b 2 = 15 mm at the outlet. There is no pre-swirl, which results in a purely radial rotor
inlet flow. Relative velocity at the rotor inlet and outlet form the angle β 1 = β 2 = − 60°
with the radial direction. The pump runs at 1450 rpm and pumps water (ρ = 1000 kg/
m
3
). Assume idealised flow, i.e. no internal losses and an infinite number of infinitesimally thin blades, with flow aligned to the blades.
1. Determine the static pressure rise across the rotor Δp rot . First determine the velocity triangles and the rotor work ΔW. Verify that the sum of the pressure energy
rise and the kinetic energy rise in the flow is equal to the rotor work.
2. Determine the degree of reaction R.
3. Determine the volume flow rate Q through the pump.
4. Determine the rotor power or idealised internal power P i .
A: ΔW = 156.78 J/kg; (1/ρ)Δp rot = 105.69 J/kg; R = 0.674; Q = 26.44 l/s;
P i = 4146 W.
3.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades
and Internal Losses)
A centrifugal fan has rotor internal and external diameters d 1 = 500 and d 2 = 750 mm.
The diameter of the rotor eye is d 0 = 450 mm. The rotor has 10 blades with thickness t = 4 mm. Blades are simply curved with width b 1 = 180 mm at the inlet and
b 2 = 150 mm at the outlet. There is no pre-swirl. Blade angles at inlet and outlet are
β 1
60
b
= −
°
and β 2
45
b
= −
°
. The fan runs at 1450 rpm and delivers the volume flow
rate Q = 4 m
3
/s ( ρ air = 1.2 kg/m
3
). Assume that volumetric efficiency is η v = 0.95 and
the incidence loss coefficient at rotor inlet is µ def = 0.80. Apply Pfleiderer’s formulae
(3.23–3.25) to estimate the slip, with λ = 0.75.
1. Determine the velocity triangles just upstream of the rotor inlet (station 1) and
just downstream of the rotor inlet (station 1
b
).
2. Determine the deceleration ratio in the rotor eye ζ = v v
1
0
/ .
3. Determine the tangential deflection at the rotor inlet and the corresponding incidence loss.
3 Fans
3.8 Exercises
The list contains exercises on fans, but also on pumps and hydraulic turbines, as
with the theory developed up to now, basic problems on all kinds of machines with
constant density fluids can be analysed.
3.8.1 Centrifugal Pump (Idealised Flow)
A centrifugal pump has rotor internal diameter d 1 = 80 mm and external diameter
d 2 = 200 mm. Blades are simply curved with width b 1 = 30 mm at the inlet and
b 2 = 15 mm at the outlet. There is no pre-swirl, which results in a purely radial rotor
inlet flow. Relative velocity at the rotor inlet and outlet form the angle β 1 = β 2 = − 60°
with the radial direction. The pump runs at 1450 rpm and pumps water (ρ = 1000 kg/
m
3
). Assume idealised flow, i.e. no internal losses and an infinite number of infinitesimally thin blades, with flow aligned to the blades.
1. Determine the static pressure rise across the rotor Δp rot . First determine the velocity triangles and the rotor work ΔW. Verify that the sum of the pressure energy
rise and the kinetic energy rise in the flow is equal to the rotor work.
2. Determine the degree of reaction R.
3. Determine the volume flow rate Q through the pump.
4. Determine the rotor power or idealised internal power P i .
A: ΔW = 156.78 J/kg; (1/ρ)Δp rot = 105.69 J/kg; R = 0.674; Q = 26.44 l/s;
P i = 4146 W.
3.8.2 Rotor of a Centrifugal Fan (Finite Number of Blades
and Internal Losses)
A centrifugal fan has rotor internal and external diameters d 1 = 500 and d 2 = 750 mm.
The diameter of the rotor eye is d 0 = 450 mm. The rotor has 10 blades with thickness t = 4 mm. Blades are simply curved with width b 1 = 180 mm at the inlet and
b 2 = 150 mm at the outlet. There is no pre-swirl. Blade angles at inlet and outlet are
β 1
60
b
= −
°
and β 2
45
b
= −
°
. The fan runs at 1450 rpm and delivers the volume flow
rate Q = 4 m
3
/s ( ρ air = 1.2 kg/m
3
). Assume that volumetric efficiency is η v = 0.95 and
the incidence loss coefficient at rotor inlet is µ def = 0.80. Apply Pfleiderer’s formulae
(3.23–3.25) to estimate the slip, with λ = 0.75.
1. Determine the velocity triangles just upstream of the rotor inlet (station 1) and
just downstream of the rotor inlet (station 1
b
).
2. Determine the deceleration ratio in the rotor eye ζ = v v
1
0
/ .
3. Determine the tangential deflection at the rotor inlet and the corresponding incidence loss.