Orifice Flow Calculator
Calculate orifice flow with transparent engineering inputs and the displayed formula.
Run deterministic checks for missing or mixed units, physical bounds, detectable out-of-range values and formula applicability. This is not an engineering approval or a complete code/compliance check.
Export the current calculation inputs and outputs with formula, assumptions, confirmed source credits, automated verification status, tool version and timestamp.
PROFENG Pro unlocks calculation-record exports. The calculation itself remains free.
PROFENG provides this tool for engineering screening and educational use. Check the calculation basis, units, physical assumptions, applicable standards, safety factors, equipment data and project-specific requirements before design, procurement or operation.
Turn this result into a calculation record
Carry the tool context into the PROFENG calculation-check and record workspace without implying certification or engineering approval.
Why use this orifice flow calculator?
Calculate orifice flow with transparent engineering inputs and the displayed formula. The displayed relationship is Q = Cd A √(2ΔP/ρ).
What this calculation does
This calculator determines flow from discharge coefficient, orifice diameter, differential pressure, density. Use it for preliminary hydraulic screening, sanity checks and transparent comparison of operating cases before detailed equipment or piping design.
Formula and engineering variables
Q = Cd A √(2ΔP/ρ)
| Variable | Definition | Unit | Working guidance |
|---|---|---|---|
cd | Discharge coefficient | dimensionless | Illustrative screening band: 0 to about 6.2. This is not a design limit. |
diameter | Orifice diameter | m | Illustrative screening band: 0 to about 1 m. This is not a design limit. |
dp | Differential pressure | Pa | Illustrative screening band: 0 to about 200,000 Pa. This is not a design limit. |
rho | Density | kg/m³ | Illustrative screening band: 0 to about 9,980 kg/m³. This is not a design limit. |
Ranges above are screening guidance or physical bounds where stated. They are not code limits or manufacturer ratings.
Calculated outputs
- Flow (m³/s): cd*(Math.PI*diameter*diameter/4)*Math.sqrt(2*dp/rho)
Worked example
- Discharge coefficient (cd) = 0.62
- Orifice diameter (diameter) = 0.03 m
- Differential pressure (dp) = 20,000 Pa
- Density (rho) = 998 kg/m³
(0.62)*(Math.PI*(0.03)*(0.03)/4)*Math.sqrt(2*(20000)/(998)) = 0.002775 m³/sFlow: 0.002775 m³/sAssumptions
- Inputs describe one consistent operating case and use the displayed units.
- Fluid properties are represented by the entered values and are treated as uniform for the calculation.
- Steady-state behavior is assumed unless the formula explicitly includes time dependence.
Limitations
- Transient effects, fittings, compressibility, cavitation margin and manufacturer performance data may require separate treatment.
- Final piping and rotating-equipment design must use the governing project criteria and applicable codes or standards.
- Flow is treated as steady and incompressible.
- Cd is supplied for the applicable geometry and flow regime.
- The equation omits beta-ratio, expansibility, tapping and installation corrections required by complete differential-pressure meter standards.
- The displayed default values are a worked example only; replace them with traceable project or measurement data.
Formula source and acknowledgement
Relationship used: Q = Cd A √(2ΔP/ρ) as a simplified incompressible orifice-discharge relationship.
The underlying engineering basis follows Frank M. White, Henry Xue, Fluid Mechanics 9th edition (2021), McGraw Hill.
Implementation note: White supports the underlying orifice-discharge relationship; ISO 5167 provides differential-pressure measurement context. This is not a complete ISO 5167 meter calculation.
Credit for the underlying method belongs to the cited author(s). PROFENG presents its own implementation and wording and is not affiliated with or endorsed by the authors or publishers.
Limits of use for this relationship
- Flow is treated as steady and incompressible.
- Cd is supplied for the applicable geometry and flow regime.
- The equation omits beta-ratio, expansibility, tapping and installation corrections required by complete differential-pressure meter standards.
Read the PROFENG methodology for formula sourcing and automated checks →
How to use it
Start with the inputs shown above, review the assumptions or options, then generate the result. Where the tool creates a file, keep the original until you have opened and checked the downloaded output.
Frequently asked questions
What does Orifice Flow Calculator calculate?
This calculator determines flow from discharge coefficient, orifice diameter, differential pressure, density. Use it for preliminary hydraulic screening, sanity checks and transparent comparison of operating cases before detailed equipment or piping design.
What formula does Orifice Flow Calculator use?
The calculator uses Q = Cd A √(2ΔP/ρ). Every input used by the implementation is listed in the variable table on this page.
How is the worked example for Orifice Flow Calculator checked?
PROFENG substitutes the displayed default values into the implemented relationship and compares the result against automated verification cases where an independent verifier is available.
What assumptions matter most for Orifice Flow Calculator?
Inputs describe one consistent operating case and use the displayed units. Fluid properties are represented by the entered values and are treated as uniform for the calculation. Steady-state behavior is assumed unless the formula explicitly includes time dependence.
Can I use this result for final design or procurement?
Use it as an engineering screening calculation. Final design, procurement, operation or compliance decisions require project-specific data and the applicable engineering method, standard or manufacturer information.
QA, changelog and corrections
Last QA update: 30 September 2026.
Automated verification passed – 30 September 2026 – six numerical cases checked, with dimensional checks, independent cross-checks for calculators, and unit round-trip checks for converters where applicable.
Changelog
30 September 2026 – source/indexation status, metadata and correction pathway reviewed. Engineering tools display the automated verification label only when they are inside the passing Part 3 verification scope.