34 The; Colorado Experiment Station. 
is decreased by 5 % and only by 10% when the submergence 
amounts to 40% of the head. 
The various formulae for submerged weirs are not satisfac¬ 
tory, partly because they call for accurate measurement cf the 
submergence, which is difficult and untrustworthy. The table 
here given of the corrections to be applied to the ordinary 
weir tables does not call for any close measurement and thus 
it enables the submerged weir to be used in many cases with fair 
satisfaction where it has been considered inapplicable. The amount 
of backing up can usually be told within moderate limits. Whether, 
for instance, this submergence is 25% or 30% of the total head 
makes little difference; the correction to the tabular value is 5% 
in one case and 6% in the other. With greater amounts of sub¬ 
mergence the error in estimating would bring in greater variations 
in the estimate of the discharge, but we are then approaching con¬ 
ditions which it is generally possible to avoid. 
SUBMERGED WEIRS. 
Corrections to apply to the ordinary weir. 
h 
Correction 
h 
Correction 
H 
per cent. 
H 
per cent. 
.01 
1 + 0 . 6 % 
.45 
— 13 . 
% 
.05 
! + 1 . 0 % 
.50 
— 16 . 
% 
.10 
1 + 0 . 7 % 
.55 
— 19 . 
% 
.13 
+ 0 . 0 % 
.60 
— 22 . 
% 
.15 
— 0 . 6 % 
.65 
— 26 . 
% 
.20 
— 2 . 0 % 
.70 
— 30 . 
% 
.25 
— 5 . 0 % 
.75 
— 35 . 
% 
.30 
— 6 . 0 % 
.80 
— 41 . 
% 
.35 
— 9 . 0 % 
.85 
— 48 . 
% 
.40 
— 10 . % 
.90 
— 56 . 
% 
.95 
— 68 . 
% 
H is total head over weir, 
h is amount of back water 
h —7 — H is proportion of depth or head, 
expressed decimally, which is back 
water. 
+ or — indicates whether the correction is to be added or subtracted 
from the tabular values of Tables III to VI. 
Example of the use of the table: The water on a weir is 12 inches 
deep, but the weir is drowned to the depth of 3 inches. What is the 
discharge, the other conditions being good and the weir 3 feet long. 
An ordinary weir for this case would have a discharge per table 
IV., of 9.99 second feet. Here “h” is 25% of H and the correction is 
5%, to be subtracted, thus giving a result of 9.49 cubic feet per second. 
By using this table it is possible to make use of the weir in 
many laterals where there are not good conditions for the ordinary 
weir. 
WEIRS NOT LEVEL. 
From settling or other causes it sometimes happens that weirs 
are not level, and it may be necessary to get the best results possible 
for the time being. The tables may be used for that purpose with a 
small amount of calculation by the following formula: Hi and 
H 2 are the depths at the ends of the sill, H x being the greater; Q x 
is the quantity for the depth Hj with a weir of corresponding 
length, obtained by the use of the tables, and 0 2 is the quantity 
if the depth had been H 2 . Hence in such case, find the discharge 
