3.8 Exercises
147
4. Calculate the design flow rate of the rotor. Compare with Q = 4 m
3
/s.
5. Determine the velocity triangles just upstream of the rotor outlet (station 2
b
) and
just downstream of the rotor outlet (station 2).
6. Calculate the work transferred to the fluid.
7. Determine the degree of reaction.
8. Determine the rise of the total pressure rise across the rotor ignoring all losses,
except the incidence loss at the rotor entrance.
A: ζ = 0.592; q irr, inc1 = 46.52 J/kg; Q* = 5.59 m
3
/s; ΔW = 1772.04 J/kg; R = 0.749;
Δp 0,rot = 2070.6 Pa.
3.8.3 Number of Blades of a Rotor of a Centrifugal Fan
Verify with the Pfleiderer moment coefficient (Eq. 3.31) that with the dimensions in
Exercise 3.8.2, the number of blades is appropriate.
A: C M = 0.960; thus OK.
3.8.4 Volute of a Centrifugal Fan
Add a volute around the rotor of Exercise 3.8.2 with width b 3 = 375 mm and height
at the outlet h 3 = 375 mm. Assume a logarithmic spiral for the outer wall shape.
Remark that the outlet area of the volute is 88.4 % of the suction inlet area of the
fan ( d 0 = 450 mm). Thus with a diffuser downstream of the volute with an area ratio
1.131 the velocity at the discharge side of the fan becomes the same as at the suction side.
1. Calculate the loss due to the radial dump at the entrance of the volute. Take into
account that the complete rotor flow rate enters the volute during the dump.
2. Calculate the loss due to tangential deflection at the entrance of the volute.
Assume as attenuation coefficient of this loss µ def = 0.80.
3. Determine the rise of the total pressure across the resulting fan taking into
account the dump loss at volute entrance and the incidence losses at rotor inlet
and at volute inlet, neglecting all other losses.
A: q irr, dump = 27.68 J/kg; q irr, inc2 = 39.33 J/kg; Δp 0 = 1990.2 Pa.
3.8.5 Leakage Flow Rate with Centrifugal Fan
Assume in the previous Exercises 3.8.2–3.8.4 a 3 mm gap between the volute and
the rotor inlet. Assume a contraction coefficient 0.90 for the gap flow. Calculate the
leakage flow rate at the specified operating point and verify the estimated volumetric efficiency. Assume that the total pressure in front of the gap on the volute side is
the static pressure at volute entrance after the radial dump (station 2’) and that the
147
4. Calculate the design flow rate of the rotor. Compare with Q = 4 m
3
/s.
5. Determine the velocity triangles just upstream of the rotor outlet (station 2
b
) and
just downstream of the rotor outlet (station 2).
6. Calculate the work transferred to the fluid.
7. Determine the degree of reaction.
8. Determine the rise of the total pressure rise across the rotor ignoring all losses,
except the incidence loss at the rotor entrance.
A: ζ = 0.592; q irr, inc1 = 46.52 J/kg; Q* = 5.59 m
3
/s; ΔW = 1772.04 J/kg; R = 0.749;
Δp 0,rot = 2070.6 Pa.
3.8.3 Number of Blades of a Rotor of a Centrifugal Fan
Verify with the Pfleiderer moment coefficient (Eq. 3.31) that with the dimensions in
Exercise 3.8.2, the number of blades is appropriate.
A: C M = 0.960; thus OK.
3.8.4 Volute of a Centrifugal Fan
Add a volute around the rotor of Exercise 3.8.2 with width b 3 = 375 mm and height
at the outlet h 3 = 375 mm. Assume a logarithmic spiral for the outer wall shape.
Remark that the outlet area of the volute is 88.4 % of the suction inlet area of the
fan ( d 0 = 450 mm). Thus with a diffuser downstream of the volute with an area ratio
1.131 the velocity at the discharge side of the fan becomes the same as at the suction side.
1. Calculate the loss due to the radial dump at the entrance of the volute. Take into
account that the complete rotor flow rate enters the volute during the dump.
2. Calculate the loss due to tangential deflection at the entrance of the volute.
Assume as attenuation coefficient of this loss µ def = 0.80.
3. Determine the rise of the total pressure across the resulting fan taking into
account the dump loss at volute entrance and the incidence losses at rotor inlet
and at volute inlet, neglecting all other losses.
A: q irr, dump = 27.68 J/kg; q irr, inc2 = 39.33 J/kg; Δp 0 = 1990.2 Pa.
3.8.5 Leakage Flow Rate with Centrifugal Fan
Assume in the previous Exercises 3.8.2–3.8.4 a 3 mm gap between the volute and
the rotor inlet. Assume a contraction coefficient 0.90 for the gap flow. Calculate the
leakage flow rate at the specified operating point and verify the estimated volumetric efficiency. Assume that the total pressure in front of the gap on the volute side is
the static pressure at volute entrance after the radial dump (station 2’) and that the