6 BULLETIN 831, U. S. DEPARTMENT OF AGRICULTURE. 



The Bazin formula is more complicated and may be expressed as, 

 ^ /„ „, ir , 0.0984XA ^ rr H 2 \ , 



The constant C is dependent not only upon the width of the 

 crest, but also upon its shape. The data resulting from the experi- 

 ments to determine this factor are not consistent even for the same 

 form of weir crest, but vary according to the head. They do, however, 

 form a basis for the approximation of discharge over any form of weir 

 under conditions ordinarily encountered. ■ 



As has been stated, the experimental data from which discharges 

 are to be computed include heads of only from 4 to 6 feet, whereas 

 flow over spillways varies from to 14 feet deep. The effect of 

 form of crest and friction decreases as the head increases, and it 

 is also probably true that the coefficient for many ordinary forms of 

 weir sections would tend toward a common constant value if the 

 heads were indefinitely increased. This would be due to the more 

 definite form of the "nappe" resulting. It is assumed also that 

 flow over the spillway may be affected by the form of the nappe, 

 which in turn varies when it discharges freely, merely touching the 

 upstream crest edge, adheres to the downstream face of the crest, 

 adheres to the top of the crest, adheres to both top and downstream 

 face, remains detached but becomes wetted underneath, adheres to 

 top, but remains detached from face and becomes wetted underneath ; 

 or it may be replaced by a depressed nappe having air imprisoned 

 underneath at less than atmospheric pressure. A method of eliminat- 

 ing the effects of the last condition is shown in figure 2, Plate IV. 

 Experiments have been conducted to determine the influence of the 

 various conditions, and its extent, under heads of from to 5 feet 

 and over different forms of model dams, with crests ranging from a 

 sharp edge to a width of 16 feet. Tables have been published giving 

 the results of these experiments and coefficients for almost any form 

 of weir crest to be applied for discharge computations of spillways 

 under the various conditions. 1 



So much depends upon the judgment of the person making the 

 assumptions, which in turn become fixed factors in the computations, 

 that there very often appears the greatest difference in the resulting 

 dimensions. The writer has had a case called to his attention where 

 three engineers computing the dimensions of a dam as a suitable 

 design for a certain location, and starting with the same assumed 

 discharge, varied as much as 14 per cent in the discharge for a given 

 crest length and head in a maximum discharge of approximately 

 100,000 second feet, 



1 The information concerning these tables and the discussion relative to weir discharge 

 are hased on the writer's personal, opinion, resulting from a review of U. S. Geol. Survey 

 Bui. 200. " Weir Experiments, Coefficients, and Formulas," by Robert E. Horton. 



