ABSTRACT OF FRANCIS* EXPERIMENTS ON WEIRS. 
(Depth h as in all cases been corrected for velocity. Supply canal 14 feet wide.) 
Serial No. 
Depth of 
Water on 
Weir in feet. 
Coefficient 
for the 
Experiments ! 
Length | 
of Weir, feet j 
No. 
Contractions 
COMMENTS 
1-4 
1.56 
3.318 
10 
2 
---- 
* 
5-10 
1.25 
3.334 
10 
2 
11-33 
1.00 
3.322 
10 
2 
SERIES A. 
56-61 
0.80 
3.325 
10 
2 
Lrest of weir is 5 feet above bottom of channel of approach 
72-78 
0.62 
3.328 
10 
2 
-r 
36-43 
1.06 
3.353 
10 
2 
SERIES B. 
62-66 
0.83 
> 
3.340 
10 
2 
Same as A, except that crest is only 2 feet above bottom 
79-84 
0.65 
3.326 
10 
2 
of channel. 
44-50 
0.98 
3.341 
10 
0 
SERIES c. 
67-71 
0.80 
3.339 
10 
0 
\ . 
k 
( anal made same width as the weir, suppressing contrac¬ 
tion, otherwise as in A. 
51-55 
1.00 
3.327 
10 
0 
SERIES D. 
Water cannot expand after passing weir. 
34-5 
1.02 
3.360 
8 
4 
SERIES E. 
Water 5 feet deep. 
85-8 
0.68 
3.337 
8 
4 
Water 2 feet deep. 
In both sets two bays, separated by partition 2 feet wide 
giving 4 contractions. 
width correspond to cases of weirs erected in^flumesTnd of same 
lutn as tlume, C to weir at low T er end, D to weir at middle. 
Attention has already been called to the contraction of a 
stream as it passes through the weir or other opening. This 
will be especially noticed in cases where the opening is 
smaller than the channel leading to it. The formula giving 
the discharge really consists of several factors, one of which 
is the velocity of the water passing the weir, and another the 
sectional area of the stream where it has this velocity. Now 
the effect of the contraction is to lessen the area, not of the 
weir, but of the stream passing through it in which the water 
has the velocity given by ihe other factor. In consequence, 
the effective length of the weir is shortened. Hence in this 
formula for L is used, not the actual length of the sill, but 
the effective length, which is found by applying a correction 
tor the contraction to the measured length. 
^1 he amount of this contraction depends upon the dis- 
\m5 e i at * i sides are from the parallel sides of the weir. 
W hen close, the contraction is small, but when the distance 
