104 



HYDRAULICS AND ITS APPLICATIONS 



if the particles had fallen freely through a height h feet under the action 

 of gravity. 



The truth of the above theorem was demonstrated by Torricelli, 1 

 who showed that a vertical jet of fluid would rise very approxiuiotely to 

 the free level in the vessel from which it was supplied. 



Due, however, to the viscosity of the liquid, to surface tension, and to the 

 resistance of the air, the velocity is always slightly less than this theoretical 

 value, and is given by C v V 2 g h, where C v is called the Coefficient of 

 Velocity. The value of C v can only be determined experimentally, but with 

 a sharp-lipped orifice increases with /* from about '96 to '994. Weisbach 

 gives the following values for an orifice of '033 feet diameter : 



At the vena contracta the stream lines for the first time become parallel 

 and perpendicular to the cross section of the stream, so that if a c be the 

 sectional area of the vena contracta in square feet, the volume discharged 

 per second = C v V 2 g h X a c cubic ft. If a is the area of the orifice, the 

 ratio -' is termed the Coefficient of Contraction, and is denoted by 



C c . The discharge is thus given by C e C v V 2 g h X a = C V 2 // ' h 

 X a cub. ft. sec. 



Here C is termed the coefficient of discharge, 



These coefficients vary with the head h ; with the area of the orifice ; 

 and with the shape of the orifice and its position. 



The following table, giving values of (7, abridged from Hamilton 



De rnotu gravium uaturaliter accelerate (1643). 



