where r denotes distance from the source. The pressure at any point in the fluid, from the 

 usual pressure equation for incompressible frictionless fluid moving irrotationally or 

 Equation [9g], is 



ld<k 1 , 

 V = p I Q ] + constant = p ( 1 + v 



1 (lA A^ 

 2r'' 



[120c] 



where "p^ is the pressure at infinity. For, at a given point, only the factor A \r\ 4> varies, so 

 that 



ar6 1 dA 



dt ~ T dt 



The point source is an ideal abstraction that is useful in building up solutions of 

 practical problems. 



Consider, for example, a sphere whose radius R varies with the time; or, it may be simply 

 a spherical cavity in the fluid, or a bubble of gas. Let the fluid motion be spherically symmet- 

 rical about the center P of the sphere or cavity. Then it can be represented by the formulas 

 appropriate to a point source located at P; see Figure 200. 



Figure 200 - A spherical cavity of 

 variable radius R. 



At the sphere, r = ff and 7^ = dR/dt. Thus, from [120b], 



dR 



A^R^ 



dt 



[120d] 



and in the surrounding fluid 



ff2 dR 



7 It' '^^ 



RV dR 

 r dt 



[120e,f] 



P = P 



T dt \ dt I 2 \t I \dt I 



+ V^ 



[120g] 



304 



