Mechanics of Fluids

592 Fluid machines
derives essentially from changes of the volume occupied by the fluid within
the machine. This type is most commonly exemplified by those machines,
such as reciprocating pumps and engines, in which a piston moves to and fro
in a cylinder (a suitable arrangement of valves ensures that the fluid always
moves in the direction appropriate to either a pump or an engine). Also in this
category are diaphragm pumps, in which the change of volume is brought
about by the deformation of flexible boundary surfaces (an animal heart is an
example of this form of pump), and gear pumps in which two rotors similar
to gear wheels mesh together within a close-fitting housing. Although hydrodynamic
effects may be associated with a positive-displacement machine, the
operation of the machine itself depends only on mechanical and hydrostatic
principles. This is not to say that such a machine is easy to design, but since
few principles of the mechanics of fluids are involved our consideration of
positive-displacement machines in this book will be very brief.
13.1.4 Rotodynamic machines
All rotodynamic machines have a rotor, that is, a rotating part through
which the fluid passes. In a turbine this rotor is called the runner, for a
pump the term impeller is more often used. The fluid has a component of
velocity and therefore of momentum in a direction tangential to the rotor,
and the rate at which this tangential momentum is changed corresponds
to a tangential force on the rotor. In a turbine there is a reduction of the
tangential momentum of the fluid in the direction of movement of the rotor;
thus energy is transferred from the fluid to the rotor and hence to the output
shaft. In a pump, energy from the rotor is used to increase the tangential
momentum of the fluid; subsequent deceleration of the fluid produces a rise
in pressure.
Rotodynamic machines have several advantages over the positivedisplacement
type. The flow from most positive-displacement machines is
unsteady whereas, for normal conditions of operation, that from a rotodynamic
machine is essentially steady. Most positive-displacement machines
require small clearances between moving and stationary parts, and so are
unsuited to handling fluids containing solid particles; in general, rotodynamic
machines are not restricted in this way. If discharge from a
positive-displacement pump is prevented – for example, by the closing of
a valve – the pressure within the pump rises and either the pump stops or
some part of the casing bursts; if the discharge valve of a rotodynamic pump
is closed, however, the rotating impeller merely churns the fluid round, and
the energy consumed is converted to heat. Moreover, for dealing with a given
overall rate of flow a rotodynamic machine is usually less bulky than one of
positive-displacement type.
13.2 RECIPROCATING PUMPS
From the point of view of mechanics of fluids a positive-displacement
machine holds interest principally because of the unsteady nature of the