456 



2 - 



A difficulty is encountered as water is compress idle. This question was attacked by 

 first considering the plat<? tc start at rest and secondly Dy considering the plate to be given an 

 impulsive velocity equivalent to the experimentally noasured impulse per unit area due to li lb. 

 of T.N.T. In this case the motion of the Box Kjde) plate was subject to the following 

 assumpt tons:- 



(a) The "skirt" of the Box Model was assumed to be an infinite wall. 



(ft) The tension of the plate, during the process of stretching, was assumed to be 



constant at the yield point, the plate being represented as a piston backed by a 

 spring closing hole in an infinite wall. This representation was deemed to 

 hold after the stretching when elastic recovery makes the plate move out again. 



It was concluded by Temperley that a deformable structure may act either as a free surface 

 or as a rigid surface, and also that the nature of the effect may Oe reversed during the interval 

 of the experiment. The valid objection has been made against tMs treatment that effectively 

 the whole infinite baffle is moving. »n alternative derivation of th3 oquations of motion, due 

 to Temperley is presented here, together with a discussion of the results of integrating the 

 equations in two cases. 



Theory , 



The taroet is treated as a fixed rigid plate and the motion of the target plate is allowed 

 for by introducing at its centre a simple source whose strength is cnoson so that the flow through 

 a hemisphere with centre at the source is equal to the volume actually swept out by the target. 



The conditions of ccntinuity of pressure and velocity at the gas-water interface give, 

 on equating terms independent of cos 5, and terms in cos 5, respectively. 



lis.-- 



a' - T U- 



(1) .^^^.J^U-^$1.U 



8 d' 2a dt 



3 aU 



. aL; * 2.41 . 1 ^ 



(2) . i° (a V t a V) 



2 a' 



where Taylor's units are used throughout. 



To aid in the computation we form a pseudo-energy equation. This is derived by 

 mult i ply ing (l) by 4 77 a a, and (2) by •, 77 a j. substract ing and integrat ing the resulting 



equation with respect to time. We obtain 



ill 



2d 3 3 2d 



2 77 aV (I . 2_) * ZLiTi! * !:JL^ - !L|: a i 



(a) . 477 0^ / v(£| . ^ii) 



\w' lid / 



dt = k - ca~ 



We may note in passing that (a) presents several interesting features. It is, in fact, 

 similar to equation (2) of the repurt "Vertical motion of a spherical bubble and the pressure 

 surrounding it". The radial kinetic energy is increased by a factor (l + ■^) due to the rigid 

 surface as pointed out by Conyers Herring. The cross product a z does not occur in equation (2) 

 of above mentioned report which is a true energy integral. k is not equal to unity, being 

 analogous to the total energy of the system, which includes an unknown amount of energy In the 

 moving target plate system. 



Putt ing 



