whereNis the rotational speed in revolutions per minute (rev min^1 ),Pis
the power developed (kW), and His the effective head (m).
The speed factor, , is the ratio of the peripheral speed, , of the
buckets or vanes at the nominal diameter, D, to the theoretical velocity of
water under the effective head, H, acting on the turbine:
/(2gH)1/2DN/(84.6H1/2). (12.3)Table 12.1 suggests appropriate values of which give the highest
efficiencies for any turbine. Also shown in the table are the head and spe-
cific speed ranges and the efficiencies of the three main types of turbine.
12.8.3 Turbine rating and performanceHydraulic turbines are generally rated under maximum, minimum, normal,
and design head. The runner is designed for optimum speed and maximum
efficiency at design head, which is usually selected as the head above and
below which the average annual generation of power is approximately equal.
However, in reality, head and load conditions change during operation and it
is extremely important to know the performance of the unit at all other
heads. Such information is usually furnished by the manufacturer in the form
of plots of efficiency versus various part-loading conditions (Fig. 12.10(a)).
The change of efficiency with specific speed is shown in Fig. 12.10(b).
For a given total plant capacity, total costs will generally increase
with an increase in the number of units. As efficiencies of large units
(turbine and generators) are higher than those of smaller ones of the same
type, if the power demand is reasonably uniform, it is good practice to
install a small number of large units.
On the other hand as the efficiency of the hydraulic turbine
decreases with the decreasing flow rate (e.g. when running under part-full-
HYDRAULIC TURBINES AND THEIR SELECTION 507
Table 12.1 Range of values, specific speeds and heads
Type of runner Ns H (m) Efficiency (%)
Impulse 0.43–0.48 008–17 85–90
017 250 90
017–30 90–82
Francis 0.60–0.90 040–130 90–94
130–350 25–450 94
350–452 94–93
Propeller 1.4–2.0 380–600 60 94
600–902 94–85