154 



ORIFICE IN THE STDK OF A VESSEL. 



Otherwise thus : Let ODC be a vertical orifice, formed by 

 a plane curve, whose vertex is 0, at the 

 depth AO below the surface of the liquid. 



Let AB = h, AO = 7^, OE = x, EQ = 

 y ; then the area of the horizontal strip PQ, 

 of infinitesimal thickness dx^ = %y dx ; and 

 therefore the quantity discharged in a unit 

 of time through this elemental strip is 



and hence we have 



Q = 



(9) 



(1) When the orifice is a rectangle. 



Here y is constant, which put = %b, and integrating (9) 

 between the limits x = and x = h Jt 1 , we have for 

 the discharge through the whole orifice ODC, 



hA (10) 



which is the same as (4) of Art. 85. 



COB. 4. If the upper side coincides with the surface of 

 the liquid, h l = 0, and (10) becomes 



Q = 



which agrees with (2) of Art. 85. 



(2) When the orifice is a triangle whose vertex is 

 downwards and the base horizontal. 



Let a : I be the ratio of the altitude to the base ; then 

 _ J 

 o, 



which in (9), and integrating between the limits x = and 

 x = h 7i t , gives 



