Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

Hydraulic Turbines 309
constant. The regulation at part load operation is achieved by varying the angle of the
guide vanes. The guide vanes are pivoted and, by means of a gearing mechanism, the
setting can be adjusted to the optimum angle. However, operation at part load causes
a whirl velocity component to be set up downstream of the runner causing a reduction
in efficiency. The strength of the vortex can be such that cavitation can occur along the
axis of the draft tube (see remarks on cavitation later in this chapter).
Example 9.3. In a vertical-shaft Francis turbine the available head at the inlet flange
of the turbine is 150m and the vertical distance between the runner and the tailrace is
2.0m. The runner tip speed is 35m/s, the meridional velocity of the water through the
runner is constant and equal to 10.5m/s, the flow leaves the runner without whirl and
the velocity at exit from the draft tube is 3.5m/s. The hydraulic energy losses estimated
for the turbine are as follows:
Determine
(i) the pressure head (relative to the tailrace) at inlet to and at exit from the runner;
(ii) the flow angles at runner inlet and at guide vane exit;
(iii) the hydraulic efficiency of the turbine.
If the flow discharged by the turbine is 20m 3 /s and the power specific speed of the
turbine is 0.8 (rad), determine the speed of rotation and the diameter of the runner.
Solution. From eqn. (9.20)
N.B. The head H3 is relative to the tailrace.
i.e. the pressure at runner outlet is below atmospheric pressure, a matter of some importance
when we come to consider the subject of cavitation later in this chapter. From
eqn. (9.18),
From eqn. (9.18),