TRIANGULAR ORIFICE IN THE SIDE OF A VESSEL. 151 



is | the velocity at the lower edge of the orifice ; and 

 the quantity of liquid flowing out through this orifice 

 in any given time is the quantity that would flow 

 through an orifice of equal area placed horizontally 

 at the whole depth, in the same time, the vessel being 

 kept constantly full. 



(2) When the upper surface of the rectangular ori- 

 fice is below the surface of the liquid. 



Let SR be the upper edge of the orifice at the depth 7^ 

 below the surface AD. Then, integrating (1) between the 

 limits x = //! and x = h, we have 



h (4) 



If the mean velocity of efflux is v, we have 



Q = b(h-h l )v, 

 which in (4) gives 



86. Triangular Orifice in the Side of a Vessel. 



(1) When the vertex of the triangle is in the surface 

 of the liquid. 



E D 

 Let h be the height EF, and b the breadth 



HF of the triangular orifice EHF, through 

 which the efflux takes place; let LM be a 

 horizontal strip at the distance x below AD, 

 and of infinitesimal thickness dx, so that the 

 velocity of the liquid in every part of the strip 

 is the same. 



Then LM = -- x, and calling Q the quantity of liquid 

 discharged in a unit of time, we have 



