Orifice Flow
Flow through a sharp-edged orifice from a pressure differential — Q = C_d·A·√(2ΔP/ρ).
Your recent runs (stored only in your browser)
No calculations yet — results land here so you can compare runs.
The engineering
The square root is Torricelli's: pressure difference becomes jet kinetic energy, so flow goes with √ΔP — a meter that reads 4× the differential is passing only 2× the flow. C_d bundles the real-world haircuts, mainly the vena contracta where the jet necks down past the sharp edge; 0.61 is the classic sharp-edge value.
This card is the incompressible, plain-orifice form. For custody-transfer accuracy the standards (ISO 5167) compute C_d from tap geometry and β-ratio, and gases above ~20% ΔP/P need an expansibility factor — but for sizing a drain, a restrictor, or a rupture-flow estimate, this is the equation everyone actually uses.
Where this math comes from
Evangelista Torricelli, Galileo's last assistant, showed in 1644 that efflux speed is √(2gh) — a falling-body law smuggled into fluids. Jean-Charles de Borda explained in 1766 why real jets pass less than the geometric area predicts: the stream contracts to about 61% of the hole, the vena contracta that lives on in C_d.
The orifice plate then became process industry's workhorse meter — cheap, no moving parts, ruthlessly standardized. Twentieth-century committee work (ASME, then ISO 5167) measured C_d across thousands of geometries so that a plate machined in Huntsville and one in Hamburg read the same barrel of oil alike.
- 1644Evangelista TorricelliEfflux law — the √ in the formula.
- 1766Jean-Charles de BordaVena contracta explains C_d ≈ 0.61.
- 1738Daniel BernoulliPressure-to-velocity budget underpinning the meter.
- 1980ISOISO 5167 standardizes orifice metering worldwide (first edition).
See the full timeline of the math behind every calculator →
Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.