114
3 Fans
The pressure difference between the pressure and suction sides of a blade follows
from the Bernoulli equation and is given by (Eq. 3.15). So, the velocity difference
at the trailing edge between suction and pressure sides may be estimated, using the
average pressure difference, by
(3.22)
from which:
The rotor work is
With Pfleiderer’s reasoning, there is a relation between rotor work with and without
slip according to
∆
∆
W
W
Pf
t
t
= +
∞
1
, with the Pfleiderer factor Pf
r b
Z M st
=
cos β π
2
2
2
2
2
.
A correction for using the mean value of the pressure difference is required and a
correction for friction as well. Further, to be manageable, the blade angle, and not
the flow angle, must be applied. Therefore Pfleiderer adapted the formula by comparing it to experimental results and defined a work reduction factor as
(3.23)
The coefficient ξ depends on the blade angle at the outlet and the rotor environment.
Adaptation to experimental results gives
(3.24)
The angle β 2
o
is the material blade angle, expressed in degrees (negative with backward curved blades), with
λ = 0.65 to 0.85 for a rotor followed by a volute;
λ ≈ 0.6 for a rotor followed by a vaned diffuser;
λ = 0.85 to 1 for a rotor followed by a vaneless diffuser.
In practice, we may approximate the integral for the determination of the static
moment by
(3.25)
∆
∆
Ω
p
w w w
M
Z M
v
rb
Z M
W
s
p
st
r
st
=
−
=
=
ρ
ρ
π
2
2
2
2 2
(
)
,
2
δ
π
β π
v
v
w
r b
Z M
W
r b
Z M
W
u
r
st
st
=
=
1
2
2
2
2
2 2
2
2 2
∆
Ω
∆
Ω
cos
.
∆
∆
W u v
u v
W
u v
t
u
u
t
u
=
−
=
−
∞
2 2
1 1
2 δ .
2
0,
2 2
0,
1
, with
and
.
1
t
t
st
p
r b
Pf
p
Pf
Z M
e
e
x
∞
∆
=
=
=
∆
+
ξ λ
β
=
+


 


 
2 5 60
2
.
.
o
M
b r b r r r
st =
+
−
2 2
1 1 2
1
2
(
).