52 



38 



behavior of the material of the plate. All complications due to the material 

 of the plate have been hidden in the present treatment under the symbol ^ or 

 4> and no detailed consideration of them will be attempted in this report. 



In the absence of exact solutions, semiquantitative results of some 

 utility may be obtained by assuming a convenient or plausible type of propor- 

 tional constraint and applying the corresponding results of analysis. A 

 principle equivalent to the reduction principle may be expected to hold, al- 

 though, as has been stated, it is not easy to prove or even to formulate in 

 the general case. The velocities generated by a short impulse of pressure, 

 for example, should be relatively large at first, but they should decrease, 

 within a time less than the diffraction time, approximately to the velocities 

 that would have been generated if the water had been incompressible. 



CAVITATION AT A PLATE OR DIAPHRAGM 



The analysis is readily extended to cover the occurrence of cavita- 

 tion at the interface between a liquid and a plate or diaphragm that remains 



approximately plane, provided suffi- 

 ciently simple assumptions are made 

 concerning the laws of cavitation. Let 

 it be assumed that cavitation sets in 

 wherever the pressure at the interface 

 sinks below a fixed breaking-pressure 

 Pj, and let all complications due to 

 surface tension or to the projection of 

 spray from the free surface of the liq- 

 uid be ignored. The cavitated region 

 will thus be assumed to have a sharp 

 bounding edge on the diaphragm, as il- 

 lustrated in Figure 22. The results 

 obtained on these assumptions will be 

 described here, with reference for fur- 

 ther details to the Appendix; they 

 should find at least qualitative appli- 

 cation to actual cavitation at an in- 

 terface, unaccompanied by cavitation in 

 the midst of the liquid. 

 In practical cases the cavitation should usually begin, if at all, 

 during the initial phase of the motion, and at a central point where the in- 

 cidence of the waves is nearly normal. For this phase, therefore, the formu- 

 las for the free plate should hold approximately, as discussed on page U. 



Figure 22 - Illustration of the 

 Edge of a Cavitated Area 



In the left-hand figiire the edge is advancing at 

 speed U over the face of the diaphragm. In the 

 right-hand figure it is receding; at the edge, 

 the tangent to the liquid surface makes an angle 

 » with the tangent to the diaphragm, and, as the 

 edge passes, each point of the liquid surface 

 changes its normal velocity from z^ to the 

 normal velocity ip of the plate. 



