TIME OF DISCHARGE. 141 



orifice ; then the range CH will be determined by making 

 y = MC. Hence we have from (1) 



x = 2 Vfy = 2 \/BM x MC 



= 2MN ; (2) 



that is, the horizontal range of a liquid issuing hori- 

 zontally through a very small orifice in the side of & 

 vessel is equal to twice the ordinate at the orifice, in 

 a semicircle whose diameter is the vertical distance 

 from the surface of the liquid to the horizontal 

 plane. 



COR. When the orifice is made at the centre of the side 

 BC, the horizontal range is a maximum, and equal to the 

 height of the liquid above CH; at equal distances above 

 and below the centre, the range will be the same. 



78. Time of Discharge from a Cylindrical Tessel 

 when the Height is Constant When a cylindrical 

 vessel is kept constantly full, it is required to deter- 

 mine the time in ivhich a quantity of liquid equal in 

 volume to the cylinder will flow through a small 

 orifice in its base. 



Let h be the height of the surface, K the area of the base 

 of the vessel, and ~k of the orifice, V the velocity of descent 

 of the surface of the liquid, and v the velocity of efflux at 

 the orifice, and t the time necessary to discharge a volume 

 of liquid equal to that of the cylinder, which remains con- 

 stantly full. 



Then the quantity of liquid which flows through the 

 orifice in the unit of time is Ic Vfyh ; and since the velocity 

 of the surface is F, the quantity of liquid which passes 

 through the orifice in the unit of time must equal VK. 

 Hence we have 



VK 



