Orifice Flow Rate Calculator
From the opening size, the head, and a discharge coefficient, get the volume of fluid leaving an orifice each second — plus the ideal exit speed behind it.
Four inputs, real flow
Enter the discharge coefficient, the orifice area, the head, and gravity and the calculator returns the flow rate (Cd·A·√(2gh)) and the ideal exit velocity at once.
Cd does real work
The discharge coefficient (~0.62 for a sharp hole) is not a fudge factor — it captures the vena contracta, the jet narrowing just past the opening that cuts the flow below the ideal A × v.
What is an orifice flow rate calculator?
Head and hole size in, discharge out
An orifice flow rate calculator works out how fast a liquid drains through an opening in the side or bottom of a tank, given the height of fluid above the hole (the head), the area of the hole, and a discharge coefficient. It pairs Torricelli's law — that an ideal jet leaves at the same speed as a free fall from the head height — with a correction for how real jets behave. The result is the volumetric flow rate Q, in cubic metres per second, the number you need to size a drain, time a tank emptying, or estimate spill rates. The calculator also reports the ideal exit velocity so you can see both pieces of the formula.
Enter the discharge coefficient, orifice area, head, and gravity to get the flow rate and exit velocity instantly.
The flow rate is the ideal Torricelli speed multiplied by the opening area and the discharge coefficient.
Q = Cd × A × √(2 × g × h)First the ideal exit velocity is √(2 × g × h) — the same speed an object would reach falling from height h. Multiply by the orifice area A to get the ideal flow, then by the discharge coefficient Cd (between 0 and 1) to get the real flow, because the jet contracts to less than the hole's area just downstream.
Suppose a tank holds 2 m of water above a 0.01 m² sharp-edged orifice, with Cd = 0.62 and g = 9.81 m/s².
Exit velocity
√(2 × 9.81 × 2) = √39.24 ≈ 6.264184 m/s — the ideal Torricelli speed.
Ideal flow
A × v = 0.01 × 6.264184 ≈ 0.062642 m³/s — if the jet filled the whole hole.
Real flow rate
Cd × ideal = 0.62 × 0.062642 ≈ 0.038838 m³/s — the actual discharge.
The flow rate Q is how much fluid leaves the orifice every second — about 0.038838 m³/s, or 38.8 litres per second, in the example. Two things drive it. The head sets the exit speed through the square root, so flow grows with the square root of depth: a tank four times deeper discharges only twice as fast, and as it empties the flow tapers off rather than stopping abruptly. The orifice area scales the flow directly — double the hole and you double the discharge. The discharge coefficient is the reality check: for a sharp-edged hole the jet necks down to roughly 62 % of the opening area (the vena contracta) and loses a little to friction, so Cd ≈ 0.62 is typical; a smoothly rounded nozzle wastes far less and can reach 0.97 or more. The exit velocity shown alongside is the ideal Torricelli value, independent of the fluid's density — water and oil leave the same height at the same ideal speed. To turn the flow rate into an emptying time you would integrate as the head falls, since Q itself drops as the tank drains.
The model is a good engineering estimate, but a couple of assumptions are worth keeping in mind.
Steady head, sub-merged-jet assumptions, and SI units
This is the steady, free-discharge orifice equation: it assumes a constant head, an orifice small compared with the tank, atmospheric pressure on the jet, and a thin, sharp-edged or characterised opening. A draining tank has a falling head, so Q decreases over time; a submerged outlet, a pressurised vessel, a long pipe, or a very viscous fluid needs a different treatment. The inputs are SI — area in m², head in metres, gravity in m/s² — so the flow rate comes back in m³/s; convert from other units before entering them.