374 Hydrodynamics. 



2A _ 2A 2A 



~ s -* 



To find the time of completely emptying the vessel, we have 

 only to make x = s, in which case the preceding expression will 

 become 



* = s = - /4 s - 



But from what is above shown, we have Q or A s = tf 

 from which we obtain 



By comparing this result with the preceding, it will be seen 

 that when a vessel is suffered to exhaust itself, the time employed is 

 just double that required to discharge the same quantity when the 

 vessel is kept full. The same conclusion might indeed be drawn 

 from articles 266, 270. 



483. Let the vessel be any solid generated by the revolution 

 of a curve. The axis being vertical, A will be the area of a cir- 

 cle which has for its radius the ordinate y of the generating 

 curve, that is, if n 3,14159 &c., A = ny*. Substituting this 

 290 m> va ^ ue ^ or A in t ^ le ec l uat i on f article 282 we have 



7i f dxy 2 



= <2" " ^ V T^~x 



V* 



In any particular examples, it will be necessary to put for y 

 its value deduced, in terms of a?, from the equation of the gener- 

 ating curve. 



484. Let ABCD be the vertical side of a vessel, EFGH a 

 Fig.235. rectangular notch in it, and let IL i I be a rectangular parallelo- 

 gram whose breadth li is infinitely small compared with EG. 

 The velocity with which the fluid would escape at GH, is to the 

 velocity with which it would escape from IL i /, as \/EG to \SEL> 



