- ' - 139 



pressure at distance r from the explosion till a time which is approximately r/c secomls after the 

 explosion, c being the velocity of sounfl in water. Till some better method is discovered a fairly 

 good approximation can be made by Imagining that at time r/c after the explosion the pressure pulse 

 arrives at radius r and that the pressure jumps to p and then falls according to the empirical law 

 (31) till it reaches the pressure which would exist at that time .ind radius if the water had been 

 Incompressible. The subsequent pressure is then calculated by the methods described above. 



This proposed method is shown in Figure 3, where the pressure pulse and the subsequent slow 

 fall due to the radial flow are both shown on the correct scale for a radius r = lU feet from the 

 charge. It will oe seen that the two curves cross. It is assumed that the actual pressure 

 distribution is simply determined by whichever is the greater of the two. This method, though 

 necessarily inaccurate near the time when the two curves cut, is possibly not far from the truth 

 over the main part of the range. The virtual parts of the curves where the shock wave pressure 

 is small compared with that due to the radial flow and vice versa are shown dotted in Figure 3. 



The results of using the step-by-step process and calcufcting pressure from (30) are shown 



in Figure 3. This calculation must ba regarded as provisional and liable to modification when 



better methods have been developed, It is included here in order to show the order of magnitude 



of the pressures to be expected at l* feet from the ^i-es lb. charge after the pressure pulse has 

 passed. 



Effect of calculated pressure on plate rig idly held at its edges. 



Pressure wave . 



The effect of the pressure wave of the form p = p e~" on a steel plate which is free or 

 elastically supported has been discussed in my note "The pressure and impulse of submarine explosion 

 waves on plates". It depends on a non-dimensional number e = pc/mn, where m is the mass of the 

 plate per sq.cm., c the velocity of sound in water, p the density of water. For plates of thickness 

 0.173 inches m = .173 x 2.51 x 7.8 = 3. 43. For a charge of 4.65 lb. T.N.T. n = 5.86 x 10"^ and 

 c = l.UU X 10^ cm. /second so that e = 7.2. 



In the above mentioned report the case where water will not sustain tension is worked out. 

 It is found that with the above values of £ and n the plate will part from the water after time 



5.5 X 10 ^ seconds (38) 



2(1.385 X lo" ) , ,-1.161 , -.o ,r^ / 



'—, ^-T- 7.2 = 1.38 X 10^ cm. /second 



mn (3.43) (5.86 x 10"^) j^^j 



The kinetic energy per c.c. of the plate is then 



^Pjteel^^ = .^ (7.83)(1.38)^ X lo' = 7.45 x 10* ergs/c.c. (40) 



If the water can sustain some tension at the surface of the plate this energy would be 

 reduced. If the water could sustain internal tension though not at the surface of the plate, no 

 further energy would be communicated to the plate. If, however, the water could sustain no 

 internal tension, drops would be projected from the water on to the plate and further energy might 

 be cormiunicatod to it. 



Dtskirig of plate . 



The time during which the high pressure (initially 2 x 133.5 = 277 atmos.) is acting on the 

 plate is short compared with the time taken By the plate to come to rest in its displaced position 

 under the action of plastic and elastic stresses. For this rtason tne oynaiiiita uf tnt: >jldlc can bt 

 treated separately from that of the water on the assumption th?.t a velocity of 1.38 x 10^ cm. /second 

 is instantaneously given to the plate. In -jn analysis in which I hope to publish shortly the dishing 



of a 



