138 VELOCITY OF EFFLUX. 



we may equate these two quantities of work, and shall 

 have 



wv 2 



-, = wh, 



*g 



from which we find 



(1) 



v = &h', (2) 



that is, the velocity of efflux is the same as that of a 

 body which has fallen freely through the height h. 



From (2) we have h = , in which the height h, 



corresponding to the velocity v, is called the head due to the 

 velocity, or simply the head. The corresponding velocity is 

 called the velocity due to the head. 



COR. 1. If the orifice be made in the vertical face of 

 the vessel, and a tube be inserted so as to direct the current 

 obliquely, horizontally, or vertically upivard, the velocity of 

 efflux will be the same, since the pressure of fluids at the 

 same depth is the same in every direction (Art. 7), and 

 each particle of liquid having the same velocity will follow 

 the same path ; a parabola whose directrix, whatever be the 

 angle of elevation, is fixed, and lies in the surface of the 

 liquid (Anal. Mechs., Arts. 151 and 153). If the liquid 

 issue obliquely, its equation is given in (3) of Art. 151, 

 Anal. Mechs. If it issue horizontally, = 0, and this 

 equation becomes 



a? 



9 y ' 



COR. 2. If Aj be the depth of a second orifice below the 

 surface, and v^ the velocity, we have 



(3) 



therefore, from (2) and (3), we have 

 v i v :: Vh ' 



