Mechanics of Fluids

656 Fluid machines
than unity and falls off rapidly as the speed ratio approaches unity. This
characteristic is a serious disadvantage in many applications.
One way of meeting the difficulty is this. At the higher speed ratios T2/T1
falls below unity, that is, the reaction torque becomes negative (eqn 13.31).
If a ratchet device is fitted whereby the reaction member may rotate, but only
in a forward direction, the reaction blades automatically begin to turn as the
reaction torque changes sign. The entire device then behaves as a simple
coupling; the efficiency is equal to the speed ratio, and the torque ratio
remains at unity. Thus a combination of torque converter and coupling is
obtained in which each is used in its best operating range. An alternative
solution is to substitute a direct drive when the speed ratio reaches a certain
value; this is achieved by a clutch that is required to slip until the speeds of
the primary and secondary rotors are equalized.
The flow in torque converters may be studied by the use of the fundamental
relations derived for pumps and turbines. For further details, however, more
specialist works should be consulted.
13.6 THE EFFECT OF SIZE ON THE EFFICIENCY OF FLUID
MACHINES
If the requirements laid down in Section 13.3.5 were exactly satisfied,
all fluid machines in the same homologous series would have the
same efficiency when running at dynamically similar conditions. In practice,
however, small machines, no matter how well designed and made,
have lower efficiencies than larger members of the same homologous
series.
The main reason is that exact geometric similarity cannot be achieved. The
actual roughness of surfaces in a small machine may differ little from that in
a large machine; thus the relative roughness in the small machine is greater
and the frictional losses are consequently more significant. The blades in the
smaller machine may be relatively thicker. Clearances in the small machine
cannot be reduced in the same proportion as other length measurements, and
so leakage losses are relatively higher. Further departures from strict geometric
similarity may be found in commercial pump impellers of nominally
the same design.
All these effects reduce the hydraulic efficiency of the small machine.
The overall efficiency is often reduced still further because the mechanical
losses such as bearing friction and windage are relatively larger for the small
machine.
Not all types of machine are affected similarly by changes of size. For
example, a Pelton wheel does not suffer from leakage losses, so the effect of
a reduction in size for such a machine is somewhat less than for a reaction
machine.
When the results of tests on model machines are scaled up for the prototype
machine, empirical formulae are used to account for these differences of
efficiency. A simple formula is that proposed by L. F. Moody (1880–1953)