Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

308 Fluid Mechanics, Thermodynamics of Turbomachinery
where p3 is the absolute static pressure at runner exit.
By differencing eqns. (9.17) and (9.18), the specific work is obtained
(9.18)
(9.19)
where p02 and p03 are the absolute total pressures at runner inlet and exit.
Figure 9.15 shows the draft tube in relation to a vertical-shaft Francis turbine. The
most important dimension in this diagram is the vertical distance (z = z3) between the
exit plane of the runner and the free surface of the tailrace. The energy equation between
the exit of the runner and the tailrace can now be written as
where DHDT is the loss in head in the draft tube and c4 is the exit velocity.
The hydraulic efficiency is given by
and, if cq3 = 0, then
(9.20)
(9.21)
(9.21a)
The overall efficiency is given by h0 = hmhH. For large machines the mechanical losses
are relatively small and hm ª 100% and so h 0 ª h H.
For the Francis turbine the ratio of the runner speed to the spouting velocity, =
U/c0, is not as critical for high efficiency operation as it is for the Pelton turbine and,
in practice, it lies within a fairly wide range, i.e. 0.6 0.9. In most applications
of Francis turbines the turbine drives an alternator and its speed must be maintained
c 3
Z
Draft tube
Tailwater
FIG. 9.15. Location of draft tube in relation to vertical shaft Francis turbine.
c 4