VELOCITY OF EFFLUX. 



147 



Substituting this value of RO for x in (3) of Art. 151, 

 Anal. Mechs., and for v 2 its value 2gz, we have 



20 4- 3x , 



x a = - tan 30 



2\/3 



_ 2a 4- 3x (2a 



/2 

 " \ 



2 V3 



cos 2 30 C 



36z 



ivhich is the depth of the orifice from the vextex. (See 

 Eland's Hydrostatics, p. 142.) 



84. Velocity of Efflux through an Orifice of any 

 Size in the Bottom of a Cylindrical Vessel. Let 



AB be the upper surface of the liquid at a 

 height h above the orifice EF; consider any 

 lamina GH, at a height x above the orifice; 

 and as before, let k, K be the areas of the 

 orifice and the section GH, respectively. 



At the height x above the orifice, let p be 

 the pressure and p the density, and at a height 

 x + dx, let p 4- dp be the pressure. Then 

 the volume Kdx of liquid may be considered 

 as acted upon by the pressures pK, (p -\- dp) K, and its 

 weight, gpKdx. Hence the moving force will be 



pK (p -\- dp) K ypKdx = Kdp gpKdx ;* 



and since the moving force is measured by the mass into 

 the acceleration (Anal. Mechs., (3) of Art. 20), we have 



Kdp gpKdx = pKdx -^ , 



d*x _ dp + gpdx 

 d& pdx 



(1) 



* The moving force is here negative because x is positive upwards. 



