Page 249 - Introduction to Naval Architecture

234 PROPULSION

CAVITATION

The lift force on a propeller blade is generated by increased pressure
on the face and reduced pressure on the back, the latter making the
greater contribution, Figure 9.11. If the reduction in pressure on the
back is great enough cavities form and fill up with air coming out of
solution and by water vapour. Thus local pressures in the water are
important to the study of propellers. In deriving non-dimensional
parameters that might be used to characterize fluid flow, it can be
shown that the parameter associated with the pressure, p, in the fluid is
p/pV*. There is always an 'ambient' pressure in water at rest due to
atmospheric pressure acting on the surface plus a pressure due to the
water column above the point considered. If the water is moving with
a velocity V then the pressure reduces to say, p v, from this ambient
value, p 0, according to Bernoulli's principle.

Comparing ship and model under cavitating conditions
For dynamic similarity of ship and model conditions the non-
dimensional quantity must be the same for both. That is, using
subscripts m and s for model and ship:

If the propellers are to operate at the same Froude number, as they
would need to if the propeller-hull combination is to be used for
propulsion tests:

where A is the ratio of the linear dimensions. That is:

Assuming water is the medium in which both model and ship are run,
the difference in density values will be negligible. For dynamic
similarity the pressure must be scaled down in the ratio of the linear
dimensions. This can be arranged for the water pressure head but the
atmospheric pressure requires special action. The only way in which
this can be scaled is to run the model in an enclosed space in which the
pressure can be reduced. This can be done by reducing the air pressure
over a ship tank and running a model with propellers fitted at the