Mechanics of Fluids

620 Fluid machines
thousand times a second. The intense pressures, even though acting for only
a very brief time over a tiny area can cause severe damage to the surface. The
material ultimately fails by fatigue, aided perhaps by corrosion, so the surface
becomes badly scored and pitted. Parts of the surface may even be torn
completely away. Associated with cavitating flow there may be considerable
vibration and noise; when cavitation occurs in a turbine or pump it may
sound as though gravel were passing through the machine.
Not only is cavitation destructive: the large pockets of vapour may so
disturb the flow that the efficiency of a machine is impaired. Everything
possible should therefore be done to eliminate cavitation in fluid machinery,
that is, to ensure that at every point the pressure of the liquid is above the
vapour pressure. When the liquid has air in solution this is released as the
pressure falls and so air cavitation also occurs. Although air cavitation is less
damaging to surfaces than vapour cavitation, it has a similar effect on the
efficiency of the machine.
Since cavitation begins when the pressure reaches too low a value, it is
likely to occur at points where the velocity or the elevation is high, and
particularly at those where high velocity and high elevation are combined.
In a reaction turbine the point of minimum pressure is usually at the outlet
end of a runner blade, on the leading side. For the flow between such a point
and the final discharge into the tail race (where the total head is atmospheric)
the energy equation may be written
pmin
ϱg
v2
+
2g + z − hf = patm
ϱg
(13.14)
Here h f represents the head lost to friction in the draft tube, and the pressures
are absolute.
Equation 13.14 incidentally shows a further reason why the outlet velocity
v of the fluid from the runner should be as small as possible: the larger the
value of v the smaller is the value of pmin and the more likely is cavitation.
Rearranging the equation gives
v2 2g − hf = patm pmin
− − z
ϱg ϱg
For a particular design of machine operated under its design conditions, the
left-hand side of this relation may be regarded as a particular proportion,
say σc, of the net head H across the machine. Then
σc = patm/ϱg − pmin/ϱg − z
H
For cavitation not to occur pmin must be greater than the vapour pressure of
the liquid, pv, that is,
σ>σcwhere σ = patm/ϱg − pv/ϱg − z
(13.15)
H
The expression 13.15 is known as Thoma’s cavitation parameter, after the
German engineer Dietrich Thoma (1881–1944) who first advocated its use.