Estimate free discharge through a fully wetted circular opening, infer its inside diameter, or calculate average velocity from flow and area. The opening model assumes Cd = 0.62 unless changed and excludes pipe losses and backwater; it is not a complete overflow-pipe design.

Opening model: fully wetted circular opening, free discharge, negligible approach velocity. Default Cd = 0.62. Excludes pipe friction, fittings and backwater; not a drainage design approval.

Upstream water surface must be above the top of the opening.

Discharge coefficient

0.62 is an assumed estimate; use a coefficient calibrated for the opening.

Related Calculators

Overflow Flow Rate Formula

v = Q / A; Q = Cd (ฯ€ Dยฒ / 4) โˆš(2 g H)

Variables:

  • OFR is the overflow flow rate per unit area (cross-sectional average velocity, m/s)
  • DR is the discharge rate (volumetric flow rate, mยณ/s)
  • A is the flow area (mยฒ)

To calculate overflow flow rate per unit area (average velocity), divide the discharge rate by the flow area.

How to Calculate Overflow Flow Rate?

For average velocity, use the flow-and-area mode below. For opening flow, select flow, enter inside diameter and head above the opening center, and select Calculate. To infer diameter, select diameter and enter positive flow and head. The upstream water surface must be above the opening top; the default coefficient is an estimate.

  1. First, determine the discharge rate (mยณ/s). 
  2. Next, determine the flow area (mยฒ). 
  3. Next, gather the formula from above: OFR = DR / A.
  4. Finally, calculate the Overflow Flow Rate (average velocity).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

discharge rate (m^3/s) = 78

area (m^2) = 20

Overflow Flow Rate (average velocity) = 78 / 20 = 3.9 m/s

FAQs

What is the significance of calculating the Overflow Flow Rate?

Calculating the Overflow Flow Rate (flow per unit area, i.e., average velocity) is useful in engineering and environmental studies to help assess loading/velocities through an opening or channel and to support drainage and overflow design checks.

Can the Overflow Flow Rate formula be used for any type of fluid?

Yes. Since OFR = DR/A is simply volumetric flow rate divided by area, it gives the cross-sectional average velocity for any fluid as long as the discharge rate and area are defined consistently (for gases, interpret the volumetric flow rate at the stated conditions).

How does the area of a channel affect the Overflow Flow Rate?

For a fixed discharge rate (DR), the overflow flow rate per unit area (OFR = DR/A) decreases as area increases. Conversely, for a fixed allowable OFR (velocity limit), a larger area can pass a higher discharge rate.

Are there any limitations to using the Overflow Flow Rate formula?

The formula gives a cross-sectional average velocity and does not capture non-uniform velocity profiles, turbulence, or changes in area along the flow path. It is most appropriate as a simple, steady-state average-value calculation.