CHAPTER VI. 



Large Oritices Rectangular Orifice Circular Orifice Submerged and partially submerged 

 Orifices Law of Comparison for Orifices Notches and Weirs Theoretical Formulae 

 Boussinesq's Theory Experimental Results and Formulae Francis Bazin Fteley and 

 Stearns Hamilton Smith Inclination of Weir Face Clinging Nappe Triangular Notch 

 Trapezoidal Weir Submerged Weirs Broad-crested Weirs Measurement by Weirs 

 Time of Discharge over Weirs. 



ART. 48. LARGE ORIFICES. 



WHERE an orifice is large, except where formed in the horizontal base 

 of a vessel the assumption that the mean velocity over its whole area is 

 sensibly equal to that at its centre of area is no longer true, and it 

 becomes necessary to take account of the variation of velocity at different 

 depths in its plane. As in the case of a small orifice a vena contracta is 

 formed of approximately the same sectional shape as the orifice, and 

 depending for its magnitude on the shape, dimensions, and head above 

 the latter, and on the circumstances governing the formation of stream 

 lines in the approaching vein. 



In the usual theoretical discussion of the flow from such an orifice the 

 two fundamental assumptions on which the theory is based are themselves 

 false and quite misleading, and while the results obtained are not without 

 value as forming the basis of useful empirical formulae, the treatment 

 cannot be looked upon as scientific. 



Briefly outlined, the method consists in assuming that at all points at 

 the same depth in the plane of an orifice the velocity of efflux is the same, 

 being that corresponding to the head of water above the point, and that 

 the direction of flow at each point is perpendicular to the plane of the 

 orifice. 



Calculating the discharge over a small element S a of the area, i.e., 

 x/ 2 g h . 8 a and summing such discharges over the elements which go to 

 make up the whole area, gives what is termed the theoretical discharge 



/ v 2 g h . 8 a, and this, when multiplied by an empirical constant 



termed the coefficient of discharge, gives the true discharge. 



Fig. 53, which indicates roughly how the velocity at the orifice 

 varies at different points in the cross section, sufficiently shows the error 

 involved in the first, while a consideration of the stream line formation 



