23-24] LIMITING VELOCITY. 25 



of air or other dissolved gas have been eliminated can sustain a 

 negative pressure, or tension, of considerable magnitude, this is not 

 the case with fluids such as we find them under ordinary conditions. 

 Practically, then, the equation (7) shews that q cannot exceed 







If in any case of fluid motion of which we have succeeded 

 in obtaining the analytical expression, we suppose the motion 

 to be gradually accelerated until the velocity at some point reaches 

 the limit here indicated, a cavity will be formed there, and the 

 conditions of the problem are more or less changed. 



It will be shewn, in the next chapter, that in irrotational /?/./.// 

 motion of a liquid, whether steady or not, the place of least 

 pressure is always at some point of the boundary, provided the 

 extraneous forces have a potential II satisfying the equation 



This includes, of course, the case of gravity. 



The limiting velocity, when no extraneous forces act, is of course that with 

 which the fluid would escape from the reservoir into a vacuum. In the case 

 of water at atmospheric pressure it is the velocity due to the height of the 

 water-barometer, or about 45 feet per second. 



In the general case of a fluid in which p is a given function 

 of p we have, putting O = in (3), 



P 

 For a gas subject to the adiabatic law, this gives 



7 - 



= ;p 1 (co 2 -c 2 ) ........................... (10), 



if c, = (yp/p)*, = (dp/dp)*, denote the velocity of sound in the gas 

 when at pressure p and density p, and c the corresponding velocity 

 for gas under the conditions which obtain in the reservoir. (See 

 Chap, x.) Hence the limiting velocity is 



or, 2-214 c , if 7 =1-408. 



