About the Orifice Flow Calculator
This orifice flow calculator estimates how much liquid passes through a sharp-edged orifice, a nozzle or a simple hole in a tank or pipe. Enter the orifice diameter, the pressure difference across it (or the liquid head above it), the fluid density and a discharge coefficient, and it returns the flow in m³/h, litres per minute and US gallons per minute, plus mass flow and velocity.
It suits engineers sizing restriction orifices and spray nozzles, technicians estimating a leak from a known hole and pressure, and students practising the orifice equation. If the orifice sits in a pipe, enter the pipe bore and the calculator applies the velocity-of-approach factor using the beta ratio; for a hole in the side of a large tank, leave the pipe diameter at zero.
The equation is for incompressible liquids. For gases it is only a rough guide when the pressure drop is small compared with the upstream absolute pressure. The discharge coefficient matters most: about 0.61 for a sharp-edged orifice, around 0.8 for a short square-edged tube and 0.95–0.99 for a well-rounded nozzle. For custody-transfer or precise metering, use the coefficient and expansion corrections in ISO 5167 or ASME MFC-3M.
With the default inputs, the volumetric flow rate is 15.26 m³/h. Change any value above to recalculate instantly.
How to use the orifice flow calculator
- 1Enter the orifice or nozzle diameter.
- 2Enter the pipe bore, or leave 0 for a hole in a tank.
- 3Set the discharge coefficient for the orifice shape.
- 4Choose pressure difference or head and enter the value.
- 5Enter the liquid density and read the flow rate.
Formula and method
The orifice equation comes from Bernoulli’s equation between the upstream flow and the jet, combined with continuity. The ideal jet velocity is √(2ΔP/ρ); the discharge coefficient Cd lumps together the contraction of the jet (vena contracta) and friction losses, so the real flow is Cd times the ideal flow through the orifice area. A sharp-edged orifice has Cd ≈ 0.6 mostly because the jet necks down to about 62% of the hole area.
When the orifice is in a pipe, the liquid already moves toward it, so the velocity-of-approach factor 1/√(1 − β⁴) is applied. With no pipe diameter entered, β = 0 and the factor is 1, which models a hole in a large tank (Torricelli’s law when expressed with head, v = √(2gh)). Pressure in kPa is converted to pascals; g = 9.80665 m/s². Results assume an incompressible liquid and a fully turbulent, steady flow.
- Q
- Volumetric flow rate (m³/s)
- Cd
- Discharge coefficient
- A
- Orifice area (m²)
- ΔP
- Pressure difference across the orifice (Pa)
- ρ
- Liquid density (kg/m³)
- β
- Ratio of orifice diameter to pipe diameter
- h
- Liquid head above the orifice centre (m)
Worked examples
25 mm sharp-edged orifice, water, 100 kPa (1 bar)
The orifice area is π × 0.025² ÷ 4 ≈ 4.909×10⁻⁴ m² and the ideal jet speed is √(2 × 100,000 ÷ 998) ≈ 14.16 m/s. Multiplying by Cd = 0.61 gives about 0.00424 m³/s — roughly 15.3 m³/h or 254 L/min.
50 mm orifice plate in a 100 mm pipe, 40 kPa
β = 50 ÷ 100 = 0.5, so the approach factor is 1/√(1 − 0.0625) ≈ 1.033. Q = 0.61 × 0.001963 × √(2 × 40,000 ÷ (998 × 0.9375)) ≈ 0.01108 m³/s, about 39.9 m³/h or 176 US gpm.
10 mm hole, 3 m below the water surface of a tank
Three metres of water is 998 × 9.80665 × 3 ≈ 29.36 kPa. The jet speed is √(2 × 9.80665 × 3) ≈ 7.67 m/s, and with Cd = 0.61 through a 78.5 mm² hole the leak is about 22 L/min.
Frequently asked questions
What is the orifice flow equation?+
Q = Cd × A × √(2ΔP/ρ), where Cd is the discharge coefficient, A the orifice area, ΔP the pressure drop and ρ the liquid density. In a pipe, divide by √(1 − β⁴) to account for the approach velocity.
What discharge coefficient should I use?+
About 0.60–0.62 for a sharp-edged orifice or a hole drilled in thin plate, roughly 0.8 for a short square-edged tube, and 0.95–0.99 for a smooth, well-rounded nozzle. Orifice plate standards give Cd as a function of beta ratio and Reynolds number.
How does flow change with pressure through an orifice?+
Flow is proportional to the square root of the pressure difference. Doubling the pressure raises flow by only about 41%, and you need four times the pressure to double the flow.
Can I use this for air or gas?+
Only as a rough estimate when the pressure drop is less than a few percent of the upstream absolute pressure. Larger drops need an expansibility factor, and once the downstream absolute pressure falls below roughly half the upstream absolute pressure (about 0.53 for air) the flow becomes choked and no longer rises as downstream pressure drops.
How do I calculate flow from a hole in a tank?+
Use the liquid height above the centre of the hole as head. The jet velocity is √(2gh) (Torricelli’s law), and the flow is Cd × hole area × that velocity — enter the head and leave the pipe diameter at zero.