118 



HYDRAULICS AND ITS APPLICATIONS 



or indeed at the outlet from any pipe fed by the mouthpiece, the 

 pressure at the vena contracta will, so long as this is greater than the 

 absolute zero, be reduced, and the discharge thereby increased if this 

 outlet runs full. 



This follows since the pressure difference at the vena contracta and at 

 the outlet increases with the ratio of the velocities and hence of the areas. 

 If however the final area of the tube be so large that the pressure at the 

 vena contracta is reduced to absolute zero ( 34 feet of water), continuity 

 of motion becomes impossible and the diverging tube ceases to run full. 

 Even with a moderate ratio of areas the angle of divergence of the sides 

 (Fig. 64 b) should not exceed 16 (Venturi), while the maximum effect 

 is obtained with an angle of about 6, the diameter increasing from 1 to 

 1*8 in a length = 9 diameters. 



The same increased discharge may be obtained, within limits, by the 

 substitution of a parallel discharge pipe of greater area than the discharge 

 orifice. 



Roman law recognised the latter fact, and prohibited the attachment of 

 pipes of greater diameter than the aperture provided at the reservoir, for 

 a distance of 50 feet. The possibility of a partial evasion of the law by 

 the application of a conical frustrum at the open end of the pipe was, 

 however, not apparently perceived. 



Sharp-edged Orifice with Converging Mouthpiece. If a conical con- 

 verging pipe be fitted external to the orifice, with its larger diameter 

 equal to that of the orifice, the coefficients of velocity and of discharge at 

 exit depend on the angle of convergence. 



The following values are taken from experiments by Castel, and 

 indicate that a maximum discharge is to be obtained when the angle 

 of convergence is about 13'20'. 



Diameter of mouthpiece = '61 inches. 



Diameter = '787 inches. 



