572 



There appears to be about a 30y& increase in the weight exponent for the 

 water-backed diaphragms over the air-backed diaphragms, however. 



The shape of the damage of the water-backed diaphrar^m was distinctly 

 different from the usual parabolic profile. This was noticed particularly 

 on the thin diaphragms when the damage exceeded half an inch. On these 

 diaphragms there was an additional dent in the center of the diaphragm 

 which also showed excessive thinning. This may in part explain the 

 higher weight exponents since damage is meastired in terms of maximum 

 central deflection. Profiles of air-backed and water-backed diaphragms 

 are shown in Figure 23, A and B, respectively. The unusual shape of B 

 may perhaps be qualitatively explained by assuming that the time of damage 

 of the diaphragms is of the same order of magnitude as the time required 

 for the shock wave to pass from the front face of the gauge around to the 

 central region in the back of the diaphragm. Then the diffracted wave in 

 the rear of the diaphragm will cause a 'disproportionate damage, acting 

 more near the edge than at the center. . This explanation has been tested 

 by mounting the gauge against one end of a 2-l/2 ft. pipe, leaving the 

 other end of the pipe open to the water. The profile of the resvilting 

 damage is shown in Figure 23, C. The appearaxice of the diaphragm 

 qualitatively verified this hypothesis in that the additional central 

 dent is removed and the shape is more nearly the usual one. 



(e) Cavitation , (i) Effect of cavitation on damage . In the deforma- 

 tion of a diaphragm by an "explosioni2/ wave, large negative pressures 

 may under some circumstances develop at the surface of the diaphragm due 

 to the reflected rarefaction wave emitted in the geometrical acoustical 

 phase of the motion. Since water cannot support a tension of great 

 magnitude, it has been suggested that cavitation will occur if the 

 pressure in the wave falls to zero or less". The chief role of cavitation 

 is to prevent loss of kinetic energy from the diaphragm by radiation in 

 the reflected rarefaction wave. Neglect of cavitation in cases where it 

 occurs therefore leads to the theoretical prediction of too little damage. 



(ii) Conditions required for the formation of cavitation . "Pori^'an 

 exponential wave impinging on a free plate with damping time 

 9^ = /^Blq/ /^ qCq, the pressure will fall to zero at a time 9^ given by 



0, = !!l. log^ §-" (35) 



^1 ®1 



9-9, 



The derivation of this equation is given in reference 21. The terms are 

 described below. £2/ "This time (9c) will be lengthened somewhat by the 



19/ Quoted sections have been taken from OSRD No. 1115, 

 J. G. Kirkwood, Dec. 19^2. 



20/ /^ and /i are the densities of the diaphragm material and 

 the water, respectively; a^ is the thickness of the diaphragm; c^ is the 

 velocity of sound in water; and 9 is the time constemt of the shock wave 

 (Section III). 



