876 
the piston is in motion, one should expect theee to be good 
approximaticns; it will be verified that they are. 
15. Consider the incompressive, non-central, approximation 
first. Let the gauge have a rigid piston and an immovable, in- 
finite baffle, as specified in (11.1). Thet is, the region B 
is infinite and z, = 0. Then by (9.3) and (11.1) 
(15.1) p = 2p, - &J om z, 4s 
where Zz, is not retarded, and A, 1s the mouth of the orifice. 
After integration (15.1) givee for the pressure at the point 
(b, @) 
(15.2) p=2p,- £8 2, E(%, = 
wrere E ; : ; 
E( =), k) = | [1 - x* sin’g] * ag 
fe an elliptic integral of the second kind. Equation (15.2) 
shows how the relief pressure according to the incompressive 
approximation decreases from the center (E(0) = 1.57) to the 
edge (E(1) = 1). To get the total force acting scroes Ass the 
mouth of the orifice, integrate (15.2) over this area. Let P, 
be the mean value of the incident wvressure, Py» over A: Then 
(15.3) J pas = 2Pa-S§ rp ¢ 
(A_) 
oO 
A 
since 
calor 
1 
J E(k) k ak = 
(0) 
In the terminology of paragraph 14. the approximation (15.3) is 
Shp No 
