How this calculation works
A large reservoir converts the liquid head into an ideal efflux speed. The discharge coefficient adjusts the ideal area-times-speed flow; it does not directly specify the actual jet speed.
Q = Cd·A√(2gH)A worked example
A 10 mm opening at 1 m constant head, Cd = 0.6 and g = 10 m/s² gives about 12.6447 L/min. Doubling head multiplies flow by √2.
Good to know
Free outlet and matching surface/outlet pressure. The coefficient is an entered assumption. No changing reservoir level, submerged outlet, pipe network, compressible fluid or calibrated device rating is modeled.
Reference: OpenStax: Bernoulli’s equation (opens in a new tab) ↗
Head becomes an ideal velocity scale
For a large reservoir with matching surface and outlet pressures, ideal head H gives a speed scale √(2gH). Multiply by the opening area to obtain ideal volume discharge. The entered coefficient scales that ideal flow.
At the default 1 m head and g = 10 m/s², the ideal speed is √20 m/s. A 10 mm opening and Cd = 0.6 then give about 12.6447 L/min. This numerical example uses supplied assumptions rather than a calibrated opening.
The tank fill and drain calculator assumes constant rates; a shrinking liquid head can invalidate that assumption for a gravity outlet.
Area and head affect discharge differently
Doubling a circular opening diameter multiplies its area and modeled flow by four when Cd and head stay fixed. Doubling head multiplies flow only by √2. The comparison table changes head alone so those two effects are not mixed.
A tank fill and drain calculator can use a constant entered flow, but real drainage from a finite tank often has a falling head. A single-head discharge result is not the total drain time for that changing-level problem.
A discharge coefficient is not a jet-speed reading
Cd can reflect contraction and other flow effects. Multiplying the ideal speed by Cd does not automatically give the actual local jet speed, because the jet cross-section may differ from the hole area. The page therefore labels √(2gH) as an ideal speed value.
The model assumes a freely discharging outlet and no separate downstream pipe resistance or submerged backpressure. Use vertical head to the opening centre. A different pressure boundary requires a different energy balance.
A few questions, answered
Does Cd = 1 describe every smooth opening?
No. It is the ideal comparison; real discharge coefficients depend on the actual device and flow conditions.
What if the head is zero?
The modeled gravity-driven discharge is zero.
Is the entered diameter the tank diameter?
No. It is the circular outlet-opening diameter.