Mar. 6, 1916 
Flow through Weir Notches 
1097 
This indicates that a mean velocity of one-third foot per second is allow¬ 
able where an error of i per cent in discharge is permissible. 
By superimposing upon the similar curves for Cipolletti notches the 
curves showing the effect of different end and bottom contractions upon 
the discharges through rectangular notches, it was found that the end- 
contraction distances for Cipolletti notches should be taken from about 
the middle point of the side of the notch instead of from the end of the 
crest, in order to make the results of the two types of notches comparable. 
Since the minimum bottom and end contractions possible without 
increasing the discharges beyond an allowable limit increase with the 
increase of the head run, weir boxes should be designed so as to give 
discharges within the allowable limit when the highest head intended 
to be run over the notch is being run. Francis stated (5, p. 72 and 134): 
In order that the end contraction may be complete, the sill and sides of the weir 
must be so far removed from the bottom and lateral sides of the reservoir (weir box) 
that they may produce no more effect upon the discharge than if they were removed 
a distance infinitely great. 
He concludes from his experiments than an end contraction of 1 H 
and a bottom contraction of 2H are the least permissible in order that his 
formula may apply. 
Smith (10, p. 120) gave the necessary end contractions as 3 H. He 
also suggested (p. 122) that the effect of contraction should not be con¬ 
fused with the effect of velocity of approach, which is so commonly done 
in taking the term “complete con traction” to include both the effect 
of contraction and the velocity of approach. Cipolletti (3, p. 23-24) 
accepted the results of the Francis experiments for end and bottom 
contractions. He also quotes a rule deduced by Lesbros from results of 
his (Lesbros's) experiments, that both contractions should be at least 2.7 
times the depth of the nappe. Cipolletti (3), from the experiments of 
Francis (5), deduced the following: (1) When the end contractions 
equal 2 H and the bottom contraction 3 H, the bottom and side walls no 
longer have any appreciable effect upon the discharges through the notch. 
This condition, he states, may cause an increase of about 0.15 per cent 
in the discharge. (2) With end contractions of 1.5 H and a bottom 
contraction of 2.5 H the increase in discharge would be about 0.5 per cent. 
(3) With end contractions of iH and a bottom contraction of 2 H the 
discharges will be increased about 1 per cent. He also takes account of 
the fact that the velocity of approach must not exceed a certain limit. 
The ratio of the cross-sectional area of the weir box to the cross- 
sectional area of the notch necessary for complete contraction has been 
given by Carpenter (2, p. 29) as 7. The coefficient using this expression 
of ratio was proposed by J. Weisbach in 1845 and has been elaborated 
upon by a number of writers and experimenters (6, p. 312). Figure 16 
indicates that there is no fixed value of the ratio A to a which will insure 
