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255 



THEORETICAL INVESTIGATION OF CAVITATION PHENOMENA 

 OCCURRING WHEN AN UNDERWATER PRESSURE PULSE 

 IS INCIDENT ON A YIELDING SURFACE: I. 



H. N. V. Temper ley 



. August 1944 



Summary . 



An account is given of the present position of the theory of the motion of a steel plate 

 when subjected to an explosion pulse. Two approximations are in use, the infinite plate, and the 

 piston in rijid wall. The former is considered to De a better approximation to a ship, the latter 

 to a box model or diaphrijm-jauae. Ships' plates of the thicknesses and strengths used in practice 

 Dehavi (towards .explosion pulsus) vor^ much like free surfaces ana nejative pressures are consequently 

 set up in the water. In certain circumstances cavitation occurs In the water, and sorne of the 

 enerjy of the explosion pulse is transformed into kinetic enerjy of this water, which eventually 

 collides with the plate. The plate thus receives energy which would Be radiated away as a tension 

 pulse if water were able to stand tension. Only a fraction of this kinetic enerjy is available to 

 cause damage, nevertheless the investigation shows that the effect makes an important contribution 

 to damage even if the plate is several inches thick. The theory is in qualitative agreement with 

 experiment, and the modifications which will be necessary in order to take account of the effect 

 of clamped edges or stiffeners are briefly discussed. Two effects which will have to be considered 

 are diffraction of positiv; pressure from the Immobile parts of the plate and impact of non-cavitated 

 water with the plate after the disappearance of cavitation. Both of these effects, however, vanish 

 for an infinite plate, which is the only case considered in the present report. 



L ist of Symbols . 



Pi^ = maximum pressure of incident pulse.- 



* time constant of incident pulse. 



C "^ velocity of sound. 



X = distance from origin of co-ordinates (also thickness of reconstituted layer of water) 



y = deflection of plate. 



p - density of plate, 



a = thickness of plate. 



p - density of *3ter. 



<^ (t - j) = pressure pulse reflected from plate. 



Ej = Taylor -.n-.rgy. 



J definea in sub. paragraph "Energy Cons idarat ion" 



