122 
Journal of Agricultural Research 
Vol. IX, No. 4 
The effect upon the discharge caused by different arrangements of the 
channels of approach and recession is shown by the following experi¬ 
mental results. The discharges for each condition have been com¬ 
pared with those for the standard arrangement. 
Extending the converging section to a length of approximately 6 feet instead 
of 3 feet, as in the standard plan (fig. 7), but with the same angle of convergence, 
caused a decrease in discharge of not to exceed 0.5 per cent for any depth of 
water. 
A channel of approach with parallel sides, having a side slope of yi to 1 and 
a bottom width of 2 feet, joined to the upstream end of the Venturi flume caused a 
decrease in discharge of less than 1 per cent for any depth of water. This change 
was comparable to eliminating the 90 0 wings at the upstream end and joining 
the device directly to the lined section of a ditch. 
With the standard construction for the upstream portion of the flume, a channel 
of recession similar to the previously described channel of approach was pro¬ 
vided. This change had no appreciable effect upon the discharge for any depth 
of water. 
A piece of 2- by 4-inch timber was placed on edge at the upstream end of the 
flume and nailed to the floor. Its position was normal to the axis of the flume, 
and it extended across the full width of the section. The increase in discharge 
due to this change did not exceed 1 per cent for any depth of water. 
DERIVATION OP FORMULA FOR DISCHARGE THROUGH THE V-NOTCH VENTURI 
FhUME 
From Bernoulli's theorem: 
VJ 
2 g 
+ p+H b 
(0 
n which V a and H a represent the velocity and head at the gage in the 
upstream section and V b and H b represent the velocity and head in the 
throat section. 
from (1) VV= V a t +2gH i 
where H d =H a —H b 
Q=A a V a =A b V b 
H b *V. b 
A b V b 2 
substituting (3) in (2) 
V b * 
(2 y 3 +H a )?f 
H b *V b ' 
(2 y 3 +H a )*H a * 
2 gH d 
V„- 
2 gH d 
C 2 X+H a )'H a > 
and 
HJ I WEI 
Q=ViA b -?±. 1 / HI 
V (2 y 3 +H a yH< 
(2) 
(3) 
(4) 
