Flow Tables for Circular Weirs

Measuring open channel (non-full pipe) flows in round pipes can be difficult when measurement costs need to be low or where power is not available at the site. There are proprietary weir inserts available, but they can be inconveniently sizes or insensitive or unrated for the flow rates anticipated.

General Circular Weir Flow Equation

The source equation is drawing from Addison’s Hydraulic Measurements – A Manual for Engineers.

Equation — General Circular Weir Flow

Q = discharge (liters / sec)
d = diameter of circular orifice (decimeters)
h = height over the weir (decimeters)
Cd = coefficient of discharge as given by:

Example: Calculating Discharge Over a Circular Weir

In this example, Kevin, a new engineer, is verifying the discharge values estimated by a computer program and his final test of the computer program's accuracy is for a circular weir. He chooses a 14-inch (0.3556m) inside diameter circular weir placed in an 18-inch (0.4572m) pipe and a 2-inch (0.0508m) water depth over the weir. He then verifies the results of the computer program by calculating the discharge using the following equation:

Example Equation — Calculating Discharge Over a Circular Weir

Pre-Generated Circular Weir Flow Tables

To aid users, Openchannelflow has developed flow (discharge) tables for three medium sized Circular Weirs. The weirs are 2-inches H and flow is calculated from 0.2-feet of head (the recommended minimum for thin-plate weirs) to the top of the circular weir.

While three flow tables have been developed, additional tables can be readily generated for different weir height / pipe diameter combinations.

Finally, remember that in using these flow tables, the approaching flow must be subcritical. Supercritical flows cannot be accurately measured by thin-plate weirs (circular or otherwise).

Source: Flow in Circular Conduits