Free-Flow Equations for V-Notch Weirs of Any Angle

There are six standard angles for V-notch weirs:

22-1/2º
30º
45º
60º
90º
120º

From time to time this range of sizes is not enough...

Sometimes there is a need to correct for a weir plate cut at an incorrect angle. While other times the flows of a particular site don’t match up well with the flow characteristics of the standard sizes of V-notch weirs.

Regardless of the reason, there is a need to be able to calculate discharge equations for intermediate V-notches.

For V-notches between 25 and 100 degrees, the Kindsvater-Shen relationship can be applied to calculate the free-flow discharge equation (Kulin and Compton).

Discharge Equation for Intermediate V-Notches

The equation is as follows:

Equation — Free-flow Discharge (Kulin & Compton)

Q = discharge (cfs)
Ce = effective discharge coefficient
h1 = head on the weir (feet)
h1e = h1 + kh (feet)
kh = head correction factor (feet)
θ = angle of V — notch

The effective discharge coefficient, Ce, and the head correction factor, kh, can be obtained from the charts below (BSI):

effective discharge coefficient for V-notch weirs from 25 to 100 degrees

head correction factor for V-notch weirs from 25 to 100 degrees

Note that the equation and correction factors apply to fully contracted V-notches. Partially contracted (90º)V-notches rely on different Ce values.

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Image: The Devon Karst Research Society

Sources: Kuhlin, G. and Compton, P., A Guide to Methods and Standards for the Measurement of Water Flow, Special Publication 421, National Bureau of Standards, 1975, British Standards Institution, Standard No. 2680-4A, Methods of Measurement of Liquid Flow in Open Channels: Part 4A, Thin Plate Weirs and Venturi Flumes, 1965