Orifice & Nozzle Flow
Liquid flow through an orifice from the pressure drop, the drop a flow needs, or the orifice size for a flow — with your discharge coefficient and β.
Flow, pressure drop or orifice diameter, plus the bore area, β ratio, approach factor, jet velocity and Reynolds number when a viscosity is given — liquids only, Cd from your standard or meter data.
Example: A Ø20 orifice in a 50 mm bore at 50 kPa on water with Cd 0.61 passes 116.6 L/min (β 0.4, approach factor 1.013); 100 L/min at the same drop needs a Ø18.55 orifice.
Bernoulli,
with a coefficient.
Where the orifice equation comes from, what Cd and β do, and what the page does not attempt.
The equation
Across a sharp restriction the pressure energy lost equals the kinetic energy of the jet, so the ideal velocity is √(2Δp/ρ) and the flow Q = A·√(2Δp/ρ). A real orifice contracts the jet and loses some energy, which the discharge coefficient Cd captures: Q = Cd·A·√(2Δp/ρ). When the pipe bore is known the fluid already has velocity upstream, and the velocity-of-approach factor 1/√(1 − β⁴) (β = d/D) corrects for it.
Cd and β
Cd depends on the plate geometry, where the pressure taps sit and the Reynolds number — the standard (ISO 5167 for orifice plates) or the meter maker gives it. The page takes your value and does not guess one. Above β ≈ 0.75 standard coefficients are no longer defined, and at low Reynolds numbers Cd drifts, so both are flagged; enter a viscosity to see Re at the bore.
Liquids only
The equation is for incompressible flow. A gas expands through the restriction (expansibility factor) and can choke at high pressure ratios — neither is applied, so use it for water, oil and other liquids. Solving for the diameter iterates because the approach factor depends on the answer. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Incompressible orifice equation Q = Cd·A·√(2Δp/ρ) ÷ √(1 − β⁴) (Bernoulli with a discharge coefficient and the approach factor, as in ISO 5167); Cd is the user’s — no coefficient table is embedded
Last reviewed 21 September 2026. How results are checked: How we verify.