150 



RECTANGULAR ORIFICE 



A VESSEL. 



flow from a rectangular orifice in the side of a vessel 

 which is kept constantly full. 



(1) When one side of the orifice coincides with the 

 surface of the liquid. 



Let h be the height and b the 

 breadth of the rectangular ori- 

 fice ALMD, through which the 

 efflux takes place ; let HK be 

 a horizontal strip at the dis- 

 tance x below AD, and of infin- 

 itesimal thickness dx, so that 

 the velocity of the liquid in 

 every part of the strip is the 

 same. 



Then the velocity of efflux through this strip is 

 [Art. 76, (2)],_and the quantity discharged in a unit of 

 time is MX Vfyz', hence, calling Q the whole quantity 

 discharged in a unit of time, we have 



Q = j MX \/2gx ; 



and integrating between x = and x = h, we have 



Q = 



(1) 



If we denote by v the mean velocity, i.e., the velocity 

 which would have to exist at every point of the orifice, in 

 order that the same quantity of liquid would flow through 

 the orifice with a uniform velocity as now flows through 

 with the variable velocity, we have 



which in (2) gives 



(3) 



Hence the mean velocity of a liquid flowing out 

 through a rectangular orifice in the side of a vessel 



