43
1.9 Exercises
A: M
N mm n
r pm
friction
n ew
= =
71 66
148 1
.
,
.
.
1.9.7 The figure sketches an extraction fan with radial blades. The sucked flow
gets pre-swirl by a guide vane ring, so that the flow entering the rotor is tangent to
the blades. Inlet and outlet width are such that the relative velocity within the rotor
is constant. Determine the formula for work done on the flow. What is the part of the
kinetic energy increase and of the enthalpy increase? What is the degree of reaction?
The fan is intended to remove air through the suction pipe. The velocity in the pipe
generates a pressure drop. Sketch the pressure evolution through the suction pipe
and the fan. Derive the required pressure rise over the fan from a pressure balance.
Ignore friction losses. Analyse that there are two essential loss mechanisms with the
considered application: one at the rotor inlet and another at the rotor outlet. Derive
from that how the rotor shape can be made more efficient. Consider a rotor with
constant meridional velocity and constant relative velocity (no internal diffusion).
A: The figure sketches the velocity triangles at the rotor inlet and the rotor outlet.
So:
and
p
k
E
E
R 0.5
D
D
=
=
.
2
2
2 2u
1 1u
2
1
W u v
u v
u u ,
D =
−
=
−
2
2
2
2
2
2
2
2
2
2
2
1
2
1
2
1
1
2
2
1
k
p
v
v
u
u
u
u
w
w
u
u
E
,
E
.
2
2
2
2
2
2
2
2
2
2
D
D
=
−
=
−
=
−
+
−
=
−