45
1.9 Exercises
(1.35). Work may further be reduced by incorporating diffusion into the rotor (  w 2 <
w 1 ) and by reducing the kinetic energy in a diffuser downstream of the rotor. Incorporating some diffusion into the rotor is easy and typically applied. A diffuser is a
supplementary component and typically not implemented.
1.9.8 Consider the same problem as in the foregoing exercise, but with an axial
fan, as sketched in the figure. Determine the power required for the application.
Compare with the result from the foregoing exercise.
A: The figure sketches the velocity triangles at the inlet and the outlet. Note that,
at constant meridional velocity, diffusion within the rotor necessarily occurs.
The pressure balance is uv
v
v
u
u
2
2
2
1
2
2
2
−
=
.
So:
(1.37)
The first term in (1.37) is useful. The second term is the kinetic energy increase
within the rotor, useless but unavoidable. We note that the expressions with the
axial fan are not fundamentally different from those with the adapted radial fan in
the foregoing exercise. Since with the radial fan u 2 – u 1 = v 2u , the expressions for ΔE k
and ΔW are in principle the same for both fans.
2u
W uv ,
D =
2
2
2
2
2
2
2
2
2u
2u
2u
2
1
1
2
k
p
2u
v
( u v )
v
v
v
w w
u
E
, E
uv
.
2
2
2
2
2
2
2
D
D
−
−
=
−
=
=
=
−
=
−
2
2
2u
1
2u
v
v
W uv
.
2
2
D =
=
+