LARGE ORIFICES 



127 



shows the error of the second assumption. Fig. 69 indicates how 

 the velocity perpendicular to the orifice varies, and how it differs from the 

 theoretical velocity *J 2 g h, as given by the horizontal ordinates of the 

 parabola in n q. Here the actual velocity is represented in elevation and 

 plan by the corresponding ordi- 

 nates of the curves a c I, and a' 

 c' a". 



The solid represented in plan 

 and elevation by the shaded areas 

 will then represent to scale the 

 volume discharged per second ; 

 while the solid bounded by the 

 plane of the orifice ; the per- 

 pendiculars an, bq, a' p', a" p" \ 

 and the curved surface of the 

 parabola, represented by n p q, 

 will represent to the same scale 

 the theoretical discharge. The 

 ratio of these volumes thus gives 

 the coefficient of discharge. 



In spite of the recognised 

 fallacies embodied in the method 

 of treatment outlined above, the 

 difficulties encountered in a 

 rigorous treatment are so many 

 and the results obtained so 

 cumbrous, that we are still com- 

 pelled to fall back on the more 

 simple, though inaccurate, formu- 

 lae, together with these experi- 

 mentally deduced coefficients. 



The assumptions, however, become more rational if the state of affairs 

 at the vena contracta be considered instead of at the orifice. Here we 

 may assume with some reason that the flow is everywhere perpendicular 

 to the cross section of the stream, and that the pressure throughout is 

 sensibly uniform and equal to that of the atmosphere, BO that, except for 

 the retarding effect of the atmosphere at the boundaries, the velocity at 

 any point in this section, at a depth h, below the free surface in the 

 vessel, is sensibly equal to */ 2 g h. The more important cases of flow 

 will now be considered on this assumption. 





FIG. 69. 



