Mechanics of Fluids

596 Fluid machines
The (approximately) simple harmonic variations of flow during the delivery
strokes of the individual cylinders here combine to produce only a ripple on
an otherwise steady total discharge. In the example illustrated, there are three
cylinders with cranks at 120 ◦ to one another. For 60 ◦ of rotation (between
90 ◦ and 150 ◦ , for example) one cylinder gives nearly its maximum delivery
while the other two are open to suction. Then for the next 60 ◦ the falling
output of the first cylinder is augmented by the increasing output of one of
the others.
The benefits resulting from the much smaller fluctuations of velocity in
both delivery and suction pipes of a multi-cylinder pump are thus similar to
those derived from the use of a large air vessel, and so this is then unnecessary.
In practice the discharge for each working stroke of a reciprocating pump
differs slightly from the volume displaced by the piston movement. This is a
consequence of leakage and the imperfect operation of the valves. A coefficient
of discharge is thus introduced (equal to the ratio of the actual discharge
per working stroke to the swept volume). The discrepancy is alternatively
expressed as a percentage slip where
% slip = (1 − C d) × 100
Reciprocating pumps, and positive-displacement pumps generally, are
most suitable for low rates of flow and particularly for high pressures. For
greater rates of flow and lower pressures rotodynamic machines are usually
more satisfactory.
13.3 TURBINES
We now turn attention to those machines that are distinguished from
positive-displacement machines in requiring relative motion between the
fluid and the moving part of the machine. The latter consists of a rotor having
a number of vanes or blades, and there is a transfer of energy between
the fluid and the rotor. Whether the fluid does work on the rotor (as in a
turbine) or the rotor does work on the fluid (as in a pump), the machine may
be classified in the first instance according to the main direction of the fluid’s
path in the rotor. In a radial-flow machine the path is wholly or mainly in
the plane of rotation; the fluid enters the rotor at one radius and leaves it at
a different radius. Examples of this type of machine are the Francis turbine
and the centrifugal pump. If, however, the main flow direction is parallel
to the axis of rotation, so that any fluid particle passes through the rotor at
a practically constant radius, then the machine is said to be an axial-flow
machine. The Kaplan turbine and the axial-flow pump are examples of this
type. If the flow is partly radial and partly axial the term mixed-flow machine
is used.
There are considerable similarities between turbines and pumps, and several
of the formulae we shall derive are applicable to both types of machine.
Indeed, a pump, for example, may be operated in reverse as a turbine;
dual-purpose machines having this facility are used in hydraulic pumped
storage schemes. (These are arrangements whereby, during periods of small