382 



along the surface y = 0, v = U, p = TT, the pressure of 

 the atmosphere ; 



.-. 7T = +C. 



At the vena contract^ the fluid moves with the same ve 

 locity throughout the section, and along its surface we 

 have 



V 2 



h being its depth below the surface of the fluid; hence 

 we have 



V 2 = U 2 + 2ah. 1 

 But BV = AU. J 



These are not sufficient to determine all the unknown 

 quantities. Sufficient equations would have been found 

 if we could have integrated all the equations of motion. 

 The quantity h differs but little from the depth of the 

 orifice below the vena contracta. The quantity B also 

 depends chiefly on the nature of the orifice, and can be 

 measured. The quantity U is unknown, and must be 

 such that the motion is steady ; eliminating we get 



V= 



~ 



If the orifice be very small, we may reject f-r j , and we 



get 



V = V&amp;gt;2gh. 



When the velocity of the surface is not such as to 

 render the motion steady, the equations cannot be inte 

 grated, except on the supposition that the orifice is exces 

 sively small. It that case we may assume with sufficient 

 accuracy, that the particles of fluid once in a horizontal 



