The cavitation characteristic of a hydraulic machine is defined as the
cavitation coefficient or plant sigma (), given by
(Ha Hv Ys)/H (12.5)whereHa HvHb, is the barometric pressure head (at sea level and 20 °C,
Hb10.1 m), and His the effective head on the runner.
From equation (12.5) the maximum permissible turbine setting Ys, max
(elevation above tailwater to the centreline of the propeller runners, or to
the bottom of the Francis runners) can be written as
Ys, maxHb cH (Thoma’s formula) (12.6)wherecis the minimum (critical) value of at which cavitation occurs
(usually determined by experiments). If Ysis negative the runner must be
set below the tailwater.
Typical values of cfor reaction turbines, versus their specific speeds,
are shown in Table 12.4.
Table 12.4 Critical plant sigma values, c
Francis runners Propeller runnersSpecific speed (Ns) 75 150 225 300 375 375 600 750 900
c 00.025000.10000.23000.40000.64000.43000.8 001.5 003.5
The above recommended limiting values of may also be approxim-
ated by
c0.0432(Ns/100)^2 for Francis runners (12.7)and
c0.280.0024(Ns/100)^3 for propeller runners (12.8)with an increase of cby 10% for Kaplan turbines (Mosonyi, 1987).
The preliminary calculations of the elevation of the distributor above
the tailwater level (Yt, Fig. 12.15) suggest the following empirical relation-
ships (based on knowledge of the existing plants (Doland, 1957)):
YtYs0.025DNs0.34 for Francis runners (12.9)and
YtYs0.41D for propeller runners (12.10)whereDis the nominal diameter of the runner.