Inputs
Liquid-water properties reference ↗ · Pure water, 0–99°C at 100 kPa absolute.
Results
Equation
β = d/D
The equation includes the velocity-of-approach correction for an orifice in a larger pipe. It assumes an incompressible liquid and a supplied discharge coefficient. Do not use this simple form for gas/steam flow or as a substitute for a required metering standard.
What this orifice calculation does
This tool uses the incompressible differential-pressure relation for a sharp restriction in a full pipe, including the velocity-of-approach correction through the beta ratio β = d/D. The discharge coefficient Cd accounts for the difference between ideal flow and the actual contraction and loss behavior of the device.
Because Cd is entered by the user, this is a flexible engineering calculator rather than a standards-compliance implementation. A traceable metering calculation requires the correct primary-element geometry, pressure-tap configuration, Reynolds-number range, installation requirements, and discharge-coefficient correlation from the applicable standard or calibration.
When to use it
- Quick liquid-flow estimates when pipe diameter, orifice diameter, Cd, density, and differential pressure are known.
- Estimating differential pressure for a proposed liquid flow through a known restriction.
- Sensitivity checks for beta ratio or discharge coefficient.
- Educational and preliminary design calculations where a user-supplied Cd is appropriate.
Assumptions and limits
- The pipe is full and the liquid is single phase and approximately incompressible.
- The flow is steady enough for the differential-pressure relation to be meaningful.
- The discharge coefficient entered is appropriate for the actual device geometry, Reynolds number, beta ratio, pressure taps, and installation.
- The model does not calculate expansibility, compressibility, cavitation, or flashing.
- The differential pressure across the meter is not the same thing as permanent unrecovered system pressure loss.
Common mistakes
- Assuming Cd is always 0.61. That can be a rough starting point for some sharp-edged orifices, but a metering-quality Cd depends on geometry and operating conditions.
- Using orifice diameter in place of pipe diameter. Both are needed because the approach-velocity correction depends on β = d/D.
- Using gauge differential pressure as though it were an absolute pressure. Differential pressure itself is a pressure difference, so gauge versus absolute reference cancels. The important issue is that both taps describe the same pressure difference and units.
- Using this liquid equation for gas or steam. Compressible flow requires an expansion factor and additional thermodynamic treatment.
- Ignoring upstream disturbances. Elbows, valves, reducers, swirl, and insufficient straight run can change a meter's effective coefficient.
For standards-based metering
ISO 5167 defines requirements for differential-pressure flow measurement devices in full circular conduits and includes limits on geometry, Reynolds number, installation, and uncertainty. ISO 5167-2 specifically addresses orifice plates. Use the standard, vendor data, or a calibrated coefficient when the result is used for custody transfer, performance testing, regulated measurement, or any other high-consequence measurement.
For ordinary line friction outside the meter, use the Pipe Friction Loss Calculator.
References: ISO 5167-1 overview and ISO 5167-2 orifice-plate overview.
Equation values and input guide
Choose the unknown, then enter the meter dimensions, operating liquid density and a discharge coefficient justified for the meter and pressure taps. The calculated differential is the tap pressure difference, not permanent system loss.
- Q
- Liquid volume flow, converted to m³/s in the equation.
- D, d
- Upstream pipe inside diameter and orifice opening diameter, respectively, in m after conversion. The restriction diameter must be smaller than the pipe bore.
- β
- Diameter ratio d/D, dimensionless. β⁴ is its fourth power.
- Aₒ or At
- Area of the orifice opening, πd²/4, in m².
- Cd
- Discharge coefficient, dimensionless. Obtain it from calibration, applicable correlation or vendor information for the operating range.
- ρ
- Operating liquid density in kg/m³.
- ΔP
- Positive pressure difference between the specified taps in Pa after conversion. Supply that differential, not a single pressure reading.
Use the unit selectors beside the inputs. Units shown in the equations must be consistent when checking the math by hand.