Apr. 33,1917 
The Venturi Flume 
125 
Substituting these values in equation (5) or (6) gives 
O'—o. 14H„+0.02 )* —o. 6 (x— 0.02 H a —0.93) 
but since y=H d and x=c, 
( Ha — o.i4H 0 + o.o 2 ) j =o.6(c— o.02H a — 0.93) 
whence 
^ (H d — o.i4// a + o.o2) a +o t oi# a +o.56 
= 0.6 
After the combination of the value of the coefficient C with the theo¬ 
retical formula, equation (4) becomes 
Q- 
P (H d — o.i4// 0 +o.o2) 2 +o.oi// a +o.56lH 6 : 
L 0.6 J 2 
2 gJU 
Hi ‘ 
( 7 ) 
(2| + ff 0 )W.» 
in which the bracketed portion represents the coefficient for contraction 
H 2 
and friction, represents the wetted cross section of the throat of the 
flume, and the radical expression represents the velocity of flow. 
Simplifying the above equation gives 
Q = 6 . 68 H h 2 [(H d — o. 1 ^H a +0.02 ) 2 + 
o.oxi? 0 -(-o. 56 ]-y^ i 
( 8 ) 
(2 i + HJHJ 
which is the discharge formula for the V-notch Venturi flume. Table II 
has been computed for this equation. The experimental discharge 
values are shown in curve form in figure 5. 
Discharge values computed from equation (8), for any given H a , 
increase as H d is increased up to a certain point; but with further 
increase of H d the discharge values decrease. At first thought this 
seems to be impossible; but it must be true, because in the limiting 
case where H d = H a , H b becomes zero, and from the formula, Q must 
equal zero. Discharge values computed from equation (8) must plot 
into smoothly continuous curves of a reversed character, and these 
values must therefore ultimately decrease. From equation (7) it is 
evident that the wetted cross-sectional area of the throat varies as 
the square of the head, H b , while the velocity varies nearly as the 
square root of the difference in head, H dt and therefore for any given H a , 
as the H d increases the area decreases more rapidly than the velocity 
increases. 
The calibration experiments with the V-notch Venturi flume did not 
show any decrease in discharge, such as mentioned above. For each H a 
there is a definite limit to the value of the H d which may be obtained 
