no 
Journal of Agricultural Research 
Vot IX, No. 4 
Table II .—Equations of balanced discharge curves used in development of general formula 
Size of orifice. 
Equation. 
Depth. 
Length. 
Feet. 
Feet. 
0* 5 
I. 0 
Q= 2 . 424 k°- t0S *. 
•5 
*•5 
0=3.624A ososs . 
•5 
2. 0 
g=4.822A 0 - 4 « a! . 1 
I. 0 
2.0 
I. 0 
3*o 
e=i4.842A°« 110 . 
I. 0 
4.0 
Q= ig.yygk 0 * 622 . 
1-5 
3-o 
£>=22.75iA°- 486# . 
4.0 
D=3°-374*°- 47 “ 
i-5 
4*5 
0=3 4.293A 0 - 4680 . 
2 . 0 
4.0 
0=44-668A°-‘ mo . 
2 . 0 ■ 
4*5 
0—48.6ooA°- 46t0 . 
The coefficients of the revised equations given in Table II were plotted 
logarithmically against the areas of the orifices, and they also were in 
separate groups for each depth of orifice, but are not shown here because 
the reduction in the size of the plot would obscure the grouping. 
Straight lines, drawn to meet at a common point, fairly represent the 
several sets of plotted points, and give a simple law of their variation. 
The equations of these lines follow: 
When d=0.5 foot, c =4.85a 1 - 00 . 
d=1.0 foot, c = 4.90a 101 . 
d= 1.5 feet, c=4.95a 10 *. 
d=2.0 feet, c = 5.00a 1 - 08 . 
The coefficient and exponent values of the area of the orifice, a, 
were plotted and found to be represented by (4.8+0. id) and 
(0.02^+0.99), respectively, which unite as the coefficient of the head 
c= (4.8+0. id)a< 0 - 0M+0 - M >. 
Consolidating the expressions for the exponent and coefficient values 
of the head, h, gives the general formula for the discharge through 
submerged rectangular orifices placed according to the conditions which 
have been taken as the standard: 
£?= ((4.8+o. 1 d) o( 0 - 02d+0 - 89 )) fe( 0 -«5d+o.°fxi _ 
in which “Q” equals the discharge in second-feet; “d” equals depth of 
orifice in feet; “a” equals area of orifice in square feet; equals 
area of cross section of water in channel of approach in square feet; 
and “h” equals the difference in feet between the water levels upstream 
and downstream from the orifice. 
