Circular Weirs for Measuring Flows in Partially Full Pipes Calculator

January 23, 2026

This calculator estimates discharge over a circular weir installed at the outlet of a partially full pipe. It uses the published “General Circular Weir Flow” relationship attributed to Addison (1941) and reproduced in Optimizing Stormwater Treatment Practices: A Handbook of Assessment and Maintenance. Inputs can be entered in centimeters or inches and are converted internally to decimeters as required by the original equation. A practical installation check is included: the pipe inside diameter should exceed the weir opening diameter by at least 2 in.

Circular Weirs for Measuring Flows in Partially Full Pipes Calculator

Input (Metric + Imperial linked)

d — weir (orifice) diameter (cm)

d — weir (orifice) diameter (in)

h — head over the weir (cm)

h — head over the weir (in)

Results

h/d

0.4115

0.59

Q (Metric) — L/s

43.974

Q (Imperial) — cfs

1.553

Equations

Discharge coefficient

C^d = 0.555 + 1110 · (h/d) + 0.041 · (h/d)

where h/d is dimensionless.

Flow equation

Q = C^d · [ 10.12 · (h/d)^1.975 − 2.66 · (h/d)^3.78 ] · d^5/2

Q in L/s, and d, h in dm (this tool converts from cm/in to dm internally).