Orifice Flow Rate Calculator

Calculator

Example data table

Formula used

For incompressible flow through an orifice, a common engineering estimate is:

• Q is volumetric flow rate (m³/s).
• C_d is discharge coefficient (dimensionless).
• A is orifice area, A = πd²/4.
• ΔP is pressure drop across the orifice (Pa).
• ρ is fluid density (kg/m³).

If you provide a pipe diameter, the calculator applies a plate-style correction:

This is a simplified correction and should not replace detailed standard-based sizing.

How to use this calculator

1. Select Pressure drop or Head mode.
2. Enter the orifice diameter and choose its unit.
3. Set C_d; use 0.61 if unsure for sharp edges.
4. Enter density. Add viscosity if you want Reynolds number.
5. Provide ΔP (pressure mode) or h and g (head mode).
6. Optionally enter pipe diameter to apply β-correction.
7. Press Calculate. Results appear above the form.
8. Use the buttons to export CSV or PDF.

Professional article

Orifice discharge overview

Orifice meters estimate liquid discharge using a pressure difference across a restriction. For a sharp‑edged plate, a typical discharge coefficient ranges from 0.60 to 0.65. This calculator combines diameter, density, and pressure drop to report flow rate, velocity, and mass flow for rapid sizing. Use SI inputs reliably.

Diameter sensitivity and scaling

Flow scales with orifice area, so diameter has a squared effect. Doubling diameter increases area fourfold and, for the same pressure drop, raises flow about four times. Small measurement errors in diameter therefore matter. Use calipers, verify roundness, and confirm units during conversions. Record diameter to at least 0.01 mm.

Interpreting pressure drop inputs

Pressure‑drop mode accepts ΔP in Pa, kPa, bar, MPa, or psi. Because velocity depends on √ΔP, quadrupling ΔP doubles flow. In practice, ΔP is limited by pump capacity and allowable energy loss. Use stable upstream conditions and avoid transient readings on vibrating gauges. Consider filtering signals and averaging over time.

Head-to-pressure conversion

Head mode converts elevation head to pressure using ΔP = ρ g h. With water near 20°C, ρ ≈ 998 kg/m³ and g ≈ 9.80665 m/s², so 1 m of head is about 9.79 kPa. This helps for tanks, weirs, and gravity‑fed systems. Account for temperature if density shifts.

Pipe diameter and beta correction

When the orifice is installed in a pipe, contraction and profile effects influence discharge. The optional pipe diameter applies a simplified correction 1/√(1−β⁴), where β = d/D. As β approaches 1, correction grows quickly. Keep β moderate and ensure straight runs for repeatability. Measure D at the same location.

Reynolds number as a regime check

Reynolds number indicates whether viscous effects may alter performance. Enter dynamic viscosity to estimate Re. For water at 20°C, μ is roughly 1.0 mPa·s, while light oils can be 50–200 mPa·s. Low Re may reduce Cd, so calibration improves confidence. Enter viscosity in cP or mPa·s.

Uncertainty budgeting for reports

Uncertainty is dominated by Cd selection, pressure measurement, and geometry. If Cd is uncertain by 5%, predicted flow changes by 5%. If ΔP has 2% error, flow varies about 1% due to the square root. Combine tolerances conservatively for documentation and peer review. Repeat tests to validate repeatability carefully.

Operational use and exports

Use results for preliminary design, troubleshooting, and sensitivity checks. Compare m³/s with practical units like L/s, m³/h, or gpm, then export CSV for logs and PDF for reports. For compressible gases, flashing, cavitation risk, or two‑phase flow, apply specialized standards. Document assumptions beside every exported file.

FAQs

1. What value should I use for Cd?

Sharp‑edged orifices often use Cd ≈ 0.61. If you have manufacturer data or calibration, use that value. Cd varies with geometry, Reynolds number, and installation conditions.

2. Does the calculator work for gases?

It is intended for incompressible liquids. Gas flow can require expansibility factors and choking checks. Use a gas-specific method or standard when pressure ratios are significant.

3. Why does my flow change a lot with diameter?

Flow is proportional to area, and area scales with d². A small diameter change produces a larger area change, so measure diameter carefully and verify units.

4. What is the pipe diameter correction?

If you enter pipe diameter D, the tool applies a simplified 1/√(1−β⁴) factor with β=d/D. It approximates plate effects but is not a substitute for full standard-based calculations.

5. What does Reynolds number tell me here?

Re helps indicate whether viscous effects may influence Cd. Very low Re can reduce discharge performance. Use it as a screening metric, not a guarantee of accuracy.

6. Can I use head instead of pressure drop?

Yes. Head mode converts h to ΔP using ΔP=ρgh. It is helpful for tank levels and gravity lines. Ensure density matches fluid temperature and composition.

7. How should I report results in a document?

State inputs, units, assumptions, and the Cd source. Include ΔP or head, fluid properties, and whether pipe correction was used. Export the PDF for a consistent calculation record.