A flow enters this regime when the ambient pressure is very low thus making the flow independent of the Reynolds number and purely dependent on the cavitation number. Andriotis et al.
Fifth, the cavitation number defined as difference between fuel injection pressure and vapor pressure divided by the difference between fuel injection pressure and ambient pressure.
To measure vibration characteristics induced by cavitating flow, a model pump made of stainless steel is designed; besides a transparent model pump of Plexiglass is also made to visualize the cavitating flow versus cavitation number decreasing.
The corresponding cavitation number is defined as in
In study of cavitating flow, a dimensionless parameter [sigma] is often used to characterize the extent of cavitation, namely, cavitation number, defined as [sigma] = 2 ([p.sub.[infinity]] - [p.sub.c)]/[rho][V.sup.2], where [rho] is the density of water, [p.sub.[infinity]] is the ambient pressure at infinity, [p.sub.c] is the cavity pressure, and V refers to the velocity of vehicle .
According to fluid dynamics exerted on different parts of supercavitating vehicle, the dynamic model  can be established with cavitation number [sigma] and feedback control gain of fin deflection angle k as variable parameters:
The transition into cavitation is defined by a critical cavitation number
and the discharge coefficient will be a constant value for no cavitation and calculated based on the cavitation number
in cavitating regime.
As a result, a constant velocity of [U.sub.[infinity]] [square root of 1 + [sigma]] may be obtained for the flow on the cavity surface by using the Bernoulli equation, in which [sigma] is the cavitation number
and is defined as follows:
The cavitating flow regimes related to the cavitation number
, [sigma] = 0,59, and [sigma] = 0,64 defined the value of the saturation pressure [P.sub.c].
where: K = cavitation number
, [P.sub.w] = pressure at the cylinder wall, [P.sub.v] = vapor pressure of the coolant, ??
There are different expressions that relate cavitation to a cavitation number
. For example, the cavitation number
can be expressed as:
In view of the desired and anticipated range of cavitation numbers
and with the selected range of test section flow velocities, the range of test section static pressure was chosen to be 0.5 to 60 psia (3.5 to 415 kPa, 0.03 to 4 atmospheres), specified to apply at a point at the top of the downstream end of the test section.