596 - 2 - 



and the experimental date in Table 1 have been fitted to this tomuta by the method of least 

 squares. In Table 1 it will be seen that there are several groups of repeat shots. In 

 applying the method of least squares the average value of V for each group has been used, being 

 weighted according to the number of shots in the group. No allotence has been made for 

 variations in the thickness of the diaphragms wihich deviate by 6J at most from the nominal value 

 of 0.1956 Inch. 



The formula resulting from this analysis is 



Log V = l.it09 + 0.«5e Log W - 0.791 Log (3) 



which expressed in power-law form is 



V = 25.63 */'-'»56/ (,0.791 ,„ 



differing little from that most recently published by S.M.D. viz, 



V - 27.3 wO-^S/dO-SO (5) 



The fact that the probable errors in V resulting from the use of formula (u) and (5) are 

 ± 2.5? and ± 2.B!i respectively shows that the difference between these two formulae is 

 instgni f icant. 



In figure 1 the experimental dita of Table I is fitted to the empirical formula (») 

 and in figure 2 a nanogram is given connecting w, and V using this formula. 



Theoretical analysis. 



(i ) Basic assumptions . 



(a) For the practical range of distance from charge to gauge in the trials considered 

 in this report, varying from about 25 to X> charges radii, the dishing of the 

 diaphragns is assumed to be caused by the primary pressure pulse behaving as a 

 small amplitude pl^ne wave. The pressure pulse is assumed to decay exponentially 

 with time, 



(b) The gauge is assumed sufficiently small relative to the effective length of pulse 

 for diffraction to be complete so that the gauge experiences no bodily motion, 



(c) The diaphragm is assumed to defom into a parabolic shape and to absorb energy 

 plastically. For a givjn mean deflection the amount of energy is assumed to be 

 the same as that measured statically under uniform lateral pressure. For an 

 amended form of assumption to take Into account the effect of dynamic loading 

 see paragraph (i i i ). 



( i i ) Solution assLBTiing incompressible flow and Wood's formulae. 



Neglecting the conpressibil i ty of water the equation of motion connecting the mean 

 deflection -i of the diaphragm and time T both expressed in non-dimensional units is shown In 

 the Appendix to be 



4 i^ . FU) = ^ e-'T (4.37) 



y being a numerical coistant depending upon the effective dimensions of the diaphragm allowing 

 for the increase in inertia due to the layer of witer following the motion of the diaphragm 

 whilst P| F(-i) is the static pressure required to produce a non-dimensional mean deflection i. 



It was found from the static pressure-volume calibration curve reproduced in figure 3 

 that a good approximation for the function F(-i) is given by the simple linear expressions 



F{4) = J for « -J < 0.5 



= 2 -J - 0.5 for ^ 5 0.5 



( 



