Laws of Cavitation Bubbles
We consider a cone with height h and diameter d   which is moved horizontally
in direction of its axis of symmetry with the velocity v through water.
Its drag coefficient cw is found in the preceding figure.|
Gaining sufficiently high velocity flow separates from the base of the cone generating an approximate rotational ellipsoidal cavity the so called "cavitation bubble" with a contour given by the equation :
The ratio of maximum diameter of the bubble D versus its length L is given by the relation:
where σ is defined as:
with po pressure at location of motion
with pL pressure on the water surface,
By transformation results for the maximum bubble diameter D depending on cone diameter d , drag coeffcient cwo and cavitation number σ :
The force required to move the cone through water is given by the drag coefficient of the cone (Kegel), the cross section F of the cone, the density of water and the velocity v .
The normal force on a cone (Kegel) moving with an angle of attack α versus direction of motion is calculated by:
angle of attack
These 6 equations are sufficient for calculation of supercavitating objects.
For illustration we calculate an example:
A cylinder of diameter 25 cm is axially and horizontally moved through water in a depth of 5 m with velocity 100 m/s.
Let us assume a pressure within the bubble of 0 bar then the cylinder produces a cavity with length 15 m and maximum diameter
of 1.3 m.