—35 
:han the crest of the weir. If air has free access under the 
'ailing sheet it may be as high as the crest, without affecting 
;he discharge; but if higher, the discharge is affected. The 
;orm is objectionable. In such cases the discharge may be 
:ound approximately. 
Let H ==the depth of water over the weir, up-stream side, 
in feet; h = the depth below the weir, above the crest, both 
measured in still water. The latter should be below the wave 
which is formed below the weir and measured in feet; d=^H — h. 
The discharge may be found approximately by consider¬ 
ing that the water flows over the weir for the depth, h , as 
though it came through an orifice of that height and under 
pressure H — h, and the upper portion of the stream for the 
remaining depth H --— h , or d, flows as over a weir. 
The discharge of the weir portion may be computed ac¬ 
cording to the tables given with this bulletin or by the formula. 
The discharge for the opening height, h, may be com¬ 
puted by determining the velocity due to the head, d , in feet 
per second, which according to the Torricellian theorem, is 
dWdy where £*= 64.4. The discharge through a foot length 
of the lower portion would then be 4.8 h d d , approximately. 
3 
That of the weir, 3.33 d 2 . Hence, the total discharge would 
be, for a portion of length L feet, 
Q = 3-33 L ^ 2 -|- 4.8 L h/d. 
This is not likely to vary by 5 per cent, if measurements are 
correctly made. All dimensions are measured in feet; the 
discharge is given in cubic feet per second. 
It is better to avoid the submerged weir, and instead use 
a flume placed in the ditch, of the same cross-section as the 
ditch, which should be rated at the different depths in the 
same manner as the measuring flumes near the heads of the 
canals in Colorado. The methods of the use of these will be 
described in a future bulletin. 
THE TRIANGULAR WEIR. 
The triangular notch or weir, proposed by James 1 horn- 
son, has been strongly recommended, as it has certain advan¬ 
tages due to the fact that the orifice preserves the same shape 
for all depths, and the ratio of the area to the weir peri¬ 
meter remains constant. The discharge depends only on the 
depth as well as the angle, instead of the width which is 
usually necessary also. The equation for the flowthrough such 
an opening may be found without difficulty to be 
8 — 
* Q = ism T dig Id 
where m is the coefficient of contraction, T the tangent of 
