EFFLUX FROM A VESSEL IN MOTION. 159 



entire accelerating force pressing against every point in the 

 base is 



[from(l)] 



2P 



Let HO = h, and v = the velocity of efflux ; then we 

 have 



2Ph 



COR. 1. If the vessel is allowed to empty itself through 

 the orifice 0, without receiving any liquid, let x = the 

 variable altitude OH, K the horizontal section of the vessel, 

 which is a function of x, and k the section of the orifice. 

 Then we have 



Q = /Kdx ; 



which in (4) gives for the quantity discharged in an element 

 of time, 



2Px 



-- dt = 



+ fEdx 



COR, 2. If / = g, (3) becomes 



v = 



and the velocity of efflux is 1.414 times as great as it would 

 be if the vessel stood still. 



