303 
1908-9.] Discharge of Water from Circular Weirs. 
charge. Thus the conditions of actual discharge are not exactly the same 
as those assumed in calculating the theoretical flow. 
The coefficients of discharge for the drowned orifice are given also in 
Table II. ; the average value of the coefficient for heads above the top of the 
orifice is 0‘ 631. The dotted line in fffi. 5 shows the theoretical discharge 
as calculated from the approximate formula given above. The difference 
between the results obtained from the accurate expression and those from 
the approximate one is not great ; it amounts to about 6 per cent, when 
the water is just level with the top of the hole, and diminishes to 2J per 
cent, at the highest head taken. The results obtained graphically from 
the accurate expression may be in error to the extent of about 1 per cent., 
due partly to drawing and partly to the planimeter. 
It is of interest to note the position of the layer of maximum discharge 
for any height of the water surface. This is marked upon each of the 
curves of figs. 2 and 4, and dotted lines are drawn through the points. The 
heights of the points were measured, and are given in the last column of 
Table I., in terms of D. The height of the plane of maximum discharge 
gradually rises and approaches D/2 as the head is increased, a result which 
was to be expected. 
Summary. 
The discharge of water through a vertical circular orifice is represented 
by an expression which does not admit of a direct mathematical solution, but 
from which results have been obtained by graphical means. The shape 
of the curve of actual discharge is similar to that found for the theoretical 
discharge ; both curves are sensibly straight lines for positions of the water 
surface between the centre and the top of the orifice. The value of the 
coefficient of discharge probably lies between 0625 and Q’630 for low heads. 
{Issued separately May 11, 1909.) 
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