when there is no velocity to take into account. The V represents the velocity in feet per second.
Triangular or V notches are usually formed so that the angle between the two sides is 90°, when the breadth at any point will always be twice the vertical height measured at the centre. The discharge in this case varies as the square root of the fifth power of the height instead of the third power as with the rectangular notch. The reason for the alteration of the power is that approximately the discharge over a notch with any given head varies as the cross-sectional area of the body of water passing over it. The area of the 90° notch is half that of a circumscribing rectangular notch, so that the discharge of a V notch is approximately equal to that of a rectangular notch having a width equal to half the width of the V notch at water level, and as the total width is equal to double the depth of water passing over the notch the half width is equal to the full depth and the discharge is equal to that of a rectangular notch having a width equal to the depth of water flowing over the V notch from time to time, both being measured in the same unit, therefore ____ ____ ____ C \/ H^3 becomes C x H x \/ H^3 which equals C \/ H^5.
The constant C will, however, vary from that for the rectangular notch to give an accurate result.
TABLE No. 6.
TRIANGULAR OR V NOTCHES.
____
Discharge = C x \/ H^5.
Values of C.
———————+———————————-+———————————— H Measured in | Feet. | Inches. ———————+—————+——————+—————-+—————— Discharge in | Gallons | C. ft per | Gallons | C. ft per | per hour | min | per hour. | min ———————+—————+——————+—————-+—————— Alexander | 59,856 | 160 | 120.0 | 0.321 Cotterill | 57,013 | 152.4 | 114.3 | 0.306 Molesworth | 59,201 | 158.2 | 118.7 | 0.317 Thomson | 57,166 | 152.8 | 114.6 | 0.306 ———————+—————+——————+—————-+——————
Cotterill's formula for the discharge in cubic feet per minute
is
_______
16 x C x B \/ 2g H^3
when B = breadth of notch in feet and H = height of water in feet and can be applied to any proportion of notch. When B = 2H, that is, a 90° notch, C = .595 and the formula becomes ____ 152.4 \/ H^5,
and when B = 4H, that is, a notch containing an angle of 126°
51' 36", C = .62 and the formula is then written
____
318 \/ H^5.