908 
an ordinary, linear differential equation readily soluble for various types of 
driving functions. 
A brief discussion of the experimental determination of k will be found 
in the reference listed in footnote b of the preceding page. 
Finkelstein®) shows that for a rigidly mounted gauge? ) the essociated mass 
M = masa of piston + 1/3 mass of ball + = pr (1-4) 
where: 
density of fluid medium 
— 
" 
kK 
ii] 
radius of piston. 
The last term in Eq. (I-4) represents the mass of fluid which becomes 
associated with the motion of the piston, thus adding to the inertia of the 
systeme In the case of the NOL design of ball crusher gauge®), used under 
water, this term constitutes about 4.5% of the total magnitude of Me When the 
gauges are used in air, the term is negligible. 
The sensitivity of the gauge (iee., the value of k) can be controlled by 
varying the size of the deformable copper bail- Two sizes, diameters 3/8 in. 
and 5/32 ine, respectively, have become standard. Various numerical parameters 
pertinent to the two types of gauge are given in Section 13. 
3- General Properties of the Equation of Motion 
1/2 
Letting w = (k/M) » Eqe (I-3) may be rewritten: 
oe 2 1 
x+o" x meres (I-5) 
This is familiar as the equation of motion of a spring obeying Hooke's 
law, and having a natural period 
T= an Vii/k = 2n/o 
a) The Theory of Piston Gauges, by Re Finkelstein, Explosives Research Report 
Noe 5, Navy Dept» BuOrd, April, 1944. 
b) When the body of the gauge is free to move, correction must be made for the 
relative accelerations of piston and gauge body (see reference listed in 
footnote c of the preceding page). 
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