Orifice Flow Calculator

The orifice flow equation is Q = Cd × A × √(2·ΔP/ρ), where Q is the volumetric flow rate, Cd is the discharge coefficient, A = πd²/4 is the orifice bore area, ΔP is the pressure drop across the orifice plate, and ρ is the fluid density. It comes from Bernoulli's equation applied between the upstream pipe and the vena contracta, corrected by the empirical discharge coefficient. Enter d, ΔP, ρ and Cd in the calculator above to evaluate it instantly.

The discharge coefficient Cd is the dimensionless ratio of the actual flow rate through an orifice to the ideal (frictionless, no-contraction) flow rate. It lumps together the jet contraction at the vena contracta and viscous losses, so it is always less than 1. Cd depends on the orifice edge geometry, the beta ratio β = d/D, the pressure-tap arrangement, and the Reynolds number. The "Discharge coeff. (Cd)" tab of this calculator can back-calculate Cd from a measured flow rate.

For a thin, sharp-edged concentric orifice plate in turbulent pipe flow, Cd is typically 0.60–0.65, and 0.61 is the standard default used across engineering references — which is why this calculator defaults Cd to 0.61. Rounded or chamfered entrances suppress the vena contracta and reach 0.95–0.99, while very small beta ratios with corner taps can read slightly below 0.60. Always confirm against your plate manufacturer's data sheet or the ISO 5167 table for your exact orifice type.

The beta ratio β = d/D (orifice bore diameter divided by upstream pipe inside diameter) shifts Cd slightly: typical values rise from about 0.595 at β = 0.10 to about 0.632 at β = 0.75 for sharp-edged plates with flange or corner taps at high Reynolds numbers. The reference table on this page lists Cd vs beta ratio in steps of 0.05, and the "Use" button copies any row's Cd straight into the calculator. Larger beta ratios also raise the velocity-of-approach effect, which ISO 5167 handles with the 1/√(1−β⁴) factor.

Measure or choose four inputs: the orifice bore diameter d, the differential pressure ΔP across the plate, the fluid density ρ, and the discharge coefficient Cd (default 0.61 for sharp-edged). Compute the bore area A = πd²/4, the ideal velocity √(2ΔP/ρ), then Q = Cd·A·√(2ΔP/ρ). The Flow rate tab above does this in one click and reports Q in m³/s, L/s, L/min, m³/h, GPM and CFM, plus mass flow and the velocity through the orifice.

Rearrange the orifice flow equation to solve for the bore diameter: d = √(4Q / (Cd·π·√(2ΔP/ρ))). Pick your available pressure drop and fluid density, enter the target flow rate Q and Cd, and the "Orifice size (d)" tab returns the required bore diameter — the restriction-orifice sizing workflow used for flow limiting and pressure reduction. Round up to the nearest manufacturable bore and re-check the resulting flow with the Flow rate tab.

Invert the equation once more: ΔP = (ρ/2)·(Q/(Cd·A))². Enter the known flow rate, bore diameter, density and Cd in the "Pressure drop (ΔP)" tab and it returns the differential pressure the plate will develop. This is the standard check when an orifice plate is used as a flow-measurement primary element: the measured ΔP maps back to flow through this same relation.

For a gas, first obtain the density at operating conditions with the ideal-gas relation ρ = P·M/(R·T) — the gas-density mini tool on this page does that from absolute pressure, temperature and a gas preset (air, nitrogen, natural gas, CO₂, and more). Then use the same Q = Cd·A·√(2ΔP/ρ) formula. This incompressible treatment is accurate while the pressure drop is small relative to the absolute line pressure (rule of thumb: ΔP/P below about 5–10%); for large pressure ratios a full compressible-flow treatment with the expansion factor ε per ISO 5167 is required.

When liquid discharges from a tank through an orifice under a liquid head H, the driving term becomes Torricelli's velocity √(2gH) instead of √(2ΔP/ρ): Q = Cd·A·√(2gH). The "Free jet / tank head" tab implements exactly this — enter the orifice diameter, the head of liquid above the orifice centre, and Cd to get the tank-drain or free-jet flow rate. Example: a 50 mm sharp-edged orifice (Cd = 0.61) under 2 m of water head discharges about 0.0075 m³/s (7.5 L/s).

The vena contracta is the narrowest point of the jet just downstream of the orifice, where the streamlines finish converging — its area is smaller than the bore itself. The jet contraction (described by the contraction coefficient) plus wall friction means the real flow is only about 61% of the ideal Bernoulli prediction for a sharp edge, hence Cd ≈ 0.61. Rounding the inlet edge weakens the contraction, which is why rounded nozzles reach Cd ≈ 0.95–0.99.

The mean velocity in the orifice bore is simply v = Q/A, where A = πd²/4. Every result on this page includes it: it equals Cd·√(2ΔP/ρ) in pressure-drop mode, or Cd·√(2gH) in free-jet mode. Keep it below erosion and noise limits for your service — a sanity check competitors that only report flow rate leave out.

All three are differential-pressure flow elements, but the orifice plate is a thin plate with a sharp-edged hole (cheapest, highest permanent pressure loss, Cd ≈ 0.61), a flow nozzle has a rounded inlet (Cd ≈ 0.95–0.99, moderate loss), and a venturi has a converging–throat–diverging profile that recovers most of the pressure (lowest loss, most expensive). This calculator covers the sharp-edged orifice plate; set Cd ≈ 0.98 to approximate a rounded nozzle bore.

No. This tool computes flow through a single localized restriction (an orifice or orifice plate) from the pressure drop across it. Friction losses distributed along a length of pipe — the Darcy–Weisbach f·(L/D)·v²/2g calculation with Colebrook friction factors — belong to our Darcy–Weisbach calculator, and gravity-driven flow in open channels belongs to the open-channel-flow calculator. Use this page when the question is "how much fluid passes this hole at this ΔP"; use those when the question is about the pipe run itself.

Results are shown in m³/s, L/s, L/min, m³/h, US gallons per minute (GPM) and cubic feet per minute (CFM), plus mass flow in kg/s when the density is known. Inputs accept mm, cm, m and inches for diameter; Pa, kPa, mbar, bar and psi for pressure drop; and kg/m³, g/L or lb/ft³ for density, so both metric and imperial orifice-flow problems work without manual conversion.