142 



TIME OF EMPTYING ANT VESSEL. 



and as the vessel is kept constantly full, we have 



(a) 





where Q denotes the whole quantity of liquid in the vessel. 



COR. If the liquid be kept at a height h' in a second 

 vessel, containing a quantity Q', which flows through an 

 orifice k', in the time t, we have from (1) 



and from (1) and (2) we have 



Q : Q' : : k Vh : k' 



Hence, the quantities discharged in the same time, 

 from, orifices of different sizes, and at different 

 depths, are as the areas of those orifices and the 

 square roots of their depths jointly. 



79. The Time of Emptying any Vessel through 

 a Small Orifice in the Bottom. Let EH be the upper 

 surface of the liquid at the time t, x and 

 y the distances OD and DH, h the depth 

 OC of the liquid when the vessel is full, 

 k the area of the orifice, and K the area 

 of the upper surface of the liquid at the 

 time t, which, when the figure of the 

 vessel is known, will be given in terms 

 of x and y. 



Then the quantity of liquid which flows through the 

 orifice in an element of time is k Vfyx dt ; and since in the 

 same time the surface EH descends a distance dx } the quan- 



