Mar. 6,1916 
Flow through Weir Notches 
1073 
1-foot notch, an equal number of lines would have been required to cover 
the points. If a single straight line is taken to represent the discharge 
curve, and it is placed to represent best the discharges with the lower 
heads, as was done above, the part of the true discharge curve for the 
higher heads diverges rapidly from the straight line. The curve formula 
takes account of the law of variation of the discharge curves better than 
does the straight-line formula, and, consequently, it appears that it will 
give closer values for the higher heads and for longer notches than those 
experimented with. 
The straight-line equation for the 0.5-foot notch was found to be 
J2-I.566H 1 * 504 . 
This equation was found to give discharge values within approximately 
1 per cent of the values indicated on the curve plotted from the experi¬ 
mental data. 
CIPOEEETTI NOTCHES 
With notches having side slopes of one horizontal to four vertical, 219 
tests were made. The actual crest lengths used were 0.50062 foot, 1.0050 
feet, 1.5028 feet, 2.0002 feet, 3.0011 feet, and 4.0058 feet, respectively, 
and these lengths were used throughout the following calculations. 
Derivation oe the Formula 
The difference between the areas of a Cipolletti and a rectangular notch 
with equal crest length is the area of a 28° 4' (approximately) triangular 
notch—that is, one having one to four side slopes. It was found, however, 
that the discharges through such a notch (see Table X) with a given 
head did not exactly equal the difference between the discharges through 
a rectangular and a Cipolletti notch with equal crest lengths and the 
same head. While the differences between the discharges through the 
Cipolletti and rectangular notches increase with the head for all crest 
lengths, there was no regular increase or decrease in the differences in 
the discharges with increases in the crest lengths so long as the heads 
were less than approximately 0.8 foot, but for higher heads the differences 
in discharges decreased as the crest lengths increased. The comparison 
of the differences is very unreliable for heads as low as 0.2 or 0.3 foot. 
The discharges through the 28° 4' notch are greater than the differences 
between the discharges of the Cipolletti and rectangular notches for 
all heads up to approximately 2.5 feet, the percentages of excess de¬ 
creasing with the increases in head and equaling zero with a head of 
approximately 2.5. 
The differences between the discharges through the rectangular and 
Cipolletti notches for each of the crest lengths were determined from the 
curves plotted from the experimental data and an average made for each 
0.1 foot of head. These averages were then plotted logarithmically 
against the head, and the equation of the curve representing the differ- 
