6 BULLETIN 831, IT. S. DEPARTMENT OF AGRICULTURE. 
The Bazin formula is more complicated and may be expressed as, 
Q=(0.405 + °^ 84 ) (l + 0.55(p|yLHV2lH. 
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 beconies 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. 
The 
1C information concerning those tables and the discussion relative to weir discharge 
are based on the writer's personal opinion, resulting from a review of TJ. S. Geol. Survey 
Bui. 200, " Weir Experiments, Coefficients, and Formulas," by Robert E. Ilorton. 
