Orifice Flow Calculator

The flow rate of liquid through an orifice or nozzle — Q = C_dA√(2ΔP/ρ) — driven by a pressure difference or a head of fluid, with the discharge coefficient for the opening.

Units

Driven by

Orifice diameter d (mm)

Fluid

Fluid density ρ (kg/m³)

Pressure difference ΔP (kPa)

Opening type (discharge coeff.)

Discharge coefficient C_d

Flow rate—

Flow Through a Hole

Push a fluid through a small opening and its speed is set by the pressure or head driving it — the same principle that empties a tank through a drain or meters flow through an orifice plate. The ideal jet speed comes straight from energy: faster the bigger the pressure difference, slower the denser the fluid.

Q = C_d · A · √(2ΔP / ρ) · with a head: ΔP = ρ g h

A is the opening area, ΔP the pressure difference across it (or ρgh for a height of fluid), and ρ the density. The one piece that needs judgement is the discharge coefficient C_d.

Why the Discharge Coefficient Matters

Real flow does not fill the opening cleanly. Just downstream of a sharp-edged hole the jet necks down to a vena contracta narrower than the hole itself, and friction trims it further, so the actual flow is only about 61% of the ideal — hence C_d near 0.61. Round the entry into a smooth nozzle or venturi and the jet stays full, pushing C_d up to 0.97 to 0.98. Choosing the right coefficient is the difference between a good estimate and a wrong one.

Frequently Asked Questions

Head or pressure – which do I use?

They are interchangeable: a head h of liquid is just a pressure dP = rho g h. Use head for an open tank draining under gravity, pressure for a pumped or pressurised line.

Why is the flow less than ideal?

Because the jet contracts and rubs against the edge. The discharge coefficient captures both effects in one number; ignore it and you over-predict flow by up to 40% on a sharp orifice.

Does this work for air or gas?

Only at small pressure ratios. At larger ratios gases compress and can choke at the throat, which this incompressible formula does not model – use compressible-flow methods there.

Related calculators

Pipe Flow Calculator — velocity and flow in a full pipe.
Pressure Drop Calculator — friction loss along a line.
Reynolds Number Calculator — the flow regime behind the coefficient.
Flow Rate Converter — switch between GPM, L/s and m3/h.

For education and estimating. Real metering and sizing use standards (such as ISO 5167) with calibrated coefficients, Reynolds-number corrections and installation effects; verify critical flows by test or with a flow engineer.