Mar. 6,1916 
Flow through Weir Notches 
1083 
TRIANGULAR NOTCHES 
General theoretical formulas have been given for triangular notches 
(7, p. 46; 8, p. 168), and experiments with a 90° notch have been made 
by Thomson 1 (12, p. 181; 13, p. 154) and Barr. 3 * In the Fort Col¬ 
lins laboratory 98 tests were made with heads ranging from 0.2 foot to 
1.35 feet on weirs having triangular notches of 120°, 90°, 6o°, 30° and 
approximately 28° 4'. The side slopes for the last-named notch are 1 
horizontal to 4 vertical, and the tests were made with the idea that they 
might be of use in deriving a formula for discharges through Cipolletti 
notches. 
Derivation or Formulas 
The discharges through the different notches when plotted logarith¬ 
mically gave straight lines, as shown in figure 12. The equations for 
these lines were found to be as shown in Table IX. 
Table IX .—Equations for straight lines representing discharges through triangular 
notches 
Notch 
angle. 
Slope of 
sides, 
horizontal 
vertical. 
Equation of line. 
120° 
9 °: 
6o° 
3°° 
28V « 
73 2 
1. 000 
• 57 7 
.268 
. 250 
<2=4.400tf 2 - 4870 
j2=2. 4 87H 2 - 4805 
0 =i. 446 H 2 - 4705 
< 2 = 0 . 6848 H 2 - 4476 
g=o. 640 sH 2 - 4448 
“Approximate. 
The discharging streams had a free fall in all the tests except those for 
the 120 0 notch. The upper portion of the stream over the 120° notch 
adhered to the edge of the notch for a distance of approximately 0.1 
foot, the distance being quite uniform for all heads. The sides and crest 
of the notch used were of brass one-fourth inch thick, and were dressed 
at an angle of about 45 0 to a thickness of about one thirty-second inch 
at the edge. As the amount of adherence of nappe for the 120° notch 
depends upon the thickness of the edges of the notch, the use of such a 
notch is impracticable. 
The data for the 120° notch having been excluded, the general formula 
for the discharge through the triangular notches of 28° 4' to 90° was 
found to be 
Q— (0.025 + 2.462 S)H ( 2 ' s 
1 The formula derived by Thomson for the 90 ° notch was <2— 0 . 305// 3 / 2 in which Q is in cubic feet per 
minute and H is in inches. 
2 Barr found that with heads of 2 to 10 inches the coefficient C in Thomson’s formula ( Q—CH 5 / 2 ) varied 
from .3104 to . 2995 . Strickland found that Barr’s coefficient C for any head could be computed from the 
formula C= 0.2907+ h being in inches. 
27465°—16 - 3 
