Orifice flow
An orifice is a calibrated restriction: the flow is the theoretical velocity through the throat reduced by a discharge coefficient that absorbs the vena contracta. For a gas there is a second limit — once the downstream pressure falls far enough the throat chokes, and further reduction changes nothing.
| Quantity | Value | Note |
|---|---|---|
| Orifice diameter | 10.00 mm | 78.5 mm² |
| Pressure drop | 100.0 kPa | across the orifice |
| Density | 1000 kg/m³ | at the flowing temperature |
| Discharge coefficient | 0.61 | 0.61 sharp-edged, 0.98 rounded entry |
| Theoretical velocity | 14.14 m/s | √(2ΔP/ρ) |
| Actual flow | 2.44 m³/h | Cd × A × v |
| Flow in litres per second | 0.678 L/s | |
| Mass flow | 2439 kg/h | |
| Reynolds at the throat | 1.414e+5 | water viscosity assumed at 1 mPa·s |
| Jet power | 68 W | kinetic energy, not pumping power |
The discharge coefficient is the whole uncertainty. A sharp-edged orifice is 0.61, a short tube 0.82 and a rounded entry 0.98 — a 60% spread in flow for the same hole, decided entirely by the inlet geometry.
v = √(2ΔP/ρ) · Bernoulli, assuming no losses outside the coefficient.
Q = Cd·A·v · The coefficient absorbs the vena contracta.
(2/(k+1))^(k/(k−1)) · 0.528 for air.
ṁ = Cd·A·P₁√(k/RT)·(2/(k+1))^((k+1)/2(k−1)) · Independent of downstream pressure.
A clear path from inputs to results.
An orifice is a calibrated restriction: the flow is the theoretical velocity through the throat reduced by a discharge coefficient that absorbs the vena contracta and the inlet losses. For a gas there is a second limit — once the downstream pressure falls far enough the throat chokes, and further reduction changes nothing.
How to use
- Choose liquid or gas service.
- Enter the orifice diameter and the pressure conditions in absolute terms.
- For a liquid, add the density and the discharge coefficient.
- For a gas, add the specific-heat ratio and the gas constant.
- Read the flow, the jet velocity and the flow regime.
The formula
Reference: ISO 5167 for orifice plates; the compressible-flow expression is the isentropic choked-nozzle result from Shapiro, The Dynamics and Thermodynamics of Compressible Fluid Flow.
Worked example
A 10 mm orifice under 100 kPa of water pressure
- Orifice diameter 10 mm, discharge coefficient 0.61.
- Pressure drop 100 kPa across the orifice.
- Water at 1000 kg/m³.
- 1
The throat area is π × 0.005² = 78.5 mm².
- 2
Bernoulli velocity is √(2 × 100,000 / 1000) = 14.14 m/s.
- 3
The flow is 0.61 × 78.5×10⁻⁶ × 14.14 = 6.78×10⁻⁴ m³/s.
- 4
That is 2.44 m³/h, or 0.68 litres a second.
- 5
The mass flow is 2,439 kg/h at that density.
- 6
The jet carries 0.5 × 1000 × 78.5×10⁻⁶ × 14.14³ × 0.61 = 68 W of kinetic power.
2.44 m³/h · 14.14 m/s · 2,439 kg/h · 68 W of jet power.
Interpreting the result
The discharge coefficient is the whole uncertainty. A sharp-edged orifice is 0.61, a short tube 0.82 and a rounded entry 0.98 — a 60% spread in flow for the same hole, decided entirely by the inlet geometry. For gas, the other thing to watch is the critical ratio: below 0.528 for air, the throat is sonic and the flow stops responding to downstream pressure.
Assumptions & limitations
- The liquid is incompressible and single-phase, with a Reynolds number high enough for the stated discharge coefficient.
- The gas is ideal with a constant specific-heat ratio; the model is poor near the critical point.
- Pressures are absolute. A gauge reading will be wrong by the atmospheric pressure, which matters at these ratios.
- The orifice is sharp-edged and the approach velocity is neglected.
- No cavitation, flashing or two-phase flow is modelled.
- Viscosity is taken as 1 mPa·s for the Reynolds check, which is water at 20 °C.
Frequently asked questions
What discharge coefficient should I use?
0.61 for a sharp-edged orifice, 0.62 for a square-edged plate in a large pipe, 0.82 for a short tube or nozzle, and 0.98 for a well-rounded entry. The value depends on the inlet geometry, not on the fluid or the pressure.
Why does doubling the pressure drop not double the flow?
Because the velocity goes with the square root of the pressure drop. Four times the drop doubles the flow; two times the drop gives 1.41 times. It is the same square-root relationship as a valve or a pipe.
What is the jet power for?
It is the kinetic energy leaving the orifice, which is what does the work in a jet, a spray or a mixing eductor. It is not the pumping power — that is the flow times the pressure drop, and is considerably larger.
What does choked flow mean for a gas?
The gas reaches sonic velocity at the throat, and the mass flow is fixed by the upstream pressure and temperature alone. Lowering the downstream pressure further produces no additional flow — which is why a vacuum pump downstream of a choked orifice is wasted effort.
Can I use this for a nozzle?
Yes, with the right coefficient — 0.98 for a well-rounded converging nozzle. A converging-diverging nozzle is a different calculation because the expansion continues past the throat, and the isentropic area-Mach relation is needed.
Methodology last reviewed 2026-10-21. Results are informational and not financial or engineering advice — see our disclaimer.