39
1.8 Performance Characteristics
ing curve. Figure 1.12 (axial pump) demonstrates that v 2u increases with flow rate
decrease. The characteristic of the axial pump is thus similar to that of the centrifugal pump with backward curved rotor blades.
From a didactical point of view (not really from a practical one), it is interesting
to derive the dependence of head on flow rate for a hydraulic turbine. Figure 1.20
shows the velocity triangles for the design flow rate and with flow rate increase (by
increasing the head) for an axial hydraulic turbine as sketched in Fig. 1.9.
In Fig. 1.20 we notice (* indicates the design flow rate):
Rotor work is
Figure 1.20 sketches the work and the head. The work increases linearly with
the flow rate. Due to friction losses and incidence losses, the energy extracted from
the flow exceeds the rotor work. The observation is that the head increases with the
flow rate. Of course, a more convenient reading of the graph is saying that the flow
rate increases with the head.
*
1u
1u
1u
*
Q
v
v (
) ; v
0,
Q
=
>
*
*
2u
2u
2u
2u
2u
2u
*
Q
w
w (
) ; w
0 ; w
u ; v
u w .
Q
=
<
= −
= +
*
*
2
1u
2u
1u
1u
*
*
*
Q
Q
Q
W (v
v )u [v (
) u u(
)]u (v
u)u(
) u .
Q
Q
Q
D
−
=
−
=
− +
=
+
−
u
u
*
1
v
1
v
1
w
*
1
w
2
w
*
2
w
2
v
*
2
v
)
kg
/
J
(
gH
,
W
m
∆
−
m
gH
W
∆
−
)
s
/
m
(
Q
3
2
u
−
Fig. 1.20 Change of the velocity triangles with flow rate increase in an axial hydraulic turbine;
full line: design (*); dashed line: increased flow rate; turbine characteristic: flow rate depending
on head with constant rotational speed and constant geometry