Mechanics of Fluids

644 Fluid machines
loss occurring past these devices, in addition to losses caused by pipe friction
and by bends in the pipe.
For a given design of pump operating under specified conditions, v 2 1 /2g
may be taken as a particular proportion of the head developed by the pump,
say σcH. Then rearranging eqn 13.25, we have
σc = p0/ϱg − pmin/ϱg − z1 − h f
H
For cavitation not to occur pmin must be greater than pv, the vapour pressure
of the liquid that is, σ>σc where
σ = p0/ϱg − pv/ϱg − z1 − h1
(13.26)
H
and σc is the critical value of this parameter at which appreciable cavitation
begins. Experiments show the σc is related to the specific speed of the pump.
The numerator of the expression 13.26 is known as the Net Positive
Suction Head (NPSH). (Suction is here simply a synonym for inlet.)
In order that σ should be as large as possible, z1 must be as small as
possible. In some installations it may even be necessary to set the pump
below the reservoir level (i.e. with z1 negative) to avoid cavitation.
Conditions in axial-flow pumps are even more conducive to cavitation
than those in centrifugal pumps. Since, however, the liquid does not enter
an axial-flow machine at a single radius, the overall parameter of eqn 13.26
is not suitable for this type of pump, and more complicated analysis is necessary.
Cavitation in an axial-flow pump usually begins on the backs of the
blade-tips because that is where the pressure is least. However, breakaway
of the flow from a blade may induce cavitation at other radii.
Recently, super-cavitating machines have been developed in which the
minimum pressure is unusually low, so the cavitation takes the form, not of
small bubbles which collapse violently against the blade surfaces, but of large
bubbles which are carried away from the surfaces. Without the restriction
on speed that cavitation ordinarily imposes, a super-cavitating machine may
be made smaller for a given flow rate. Also, since a lower minimum pressure
is allowable, restrictions on the positioning of the machine are less severe.
On the other hand, for conditions under which a conventional machine
would be satisfactory, a super-cavitating one has a lower efficiency. Such
machines are thus likely to find favour only in specialized applications where
the advantages over-ride the reduction of efficiency.
13.4.7 The performance characteristics of pumps
Pumps are normally run at constant speed. Interest therefore attaches to
the variation of head H with discharge Q and also to the variations of efficiency
and power required with Q. The results of a particular test may
be made available for a different speed – or for a homologous pump of
different diameter – by plotting the results in dimensionless form, that
is, using the dimensionless parameters CQ = Q/ωD 3 , CH = gH/ω 2 D 2