Orifice Flow Calculator (Bernoulli, Q=Cd·A·√(2ΔP/ρ))

Orifice Flow Calculator (Bernoulli, Q=Cd·A·√(2ΔP/ρ)) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: number, select
Output type: json
Sample coverage: 4
API ready: Yes

Overview

Calculate incompressible fluid flow through a thin-plate orifice using the Bernoulli equation and discharge coefficient C_d. Enter the orifice diameter, pressure difference, fluid density, and compatible units to get volumetric flow, mass flow, orifice velocity, area, and optionally the pipe diameter ratio β.

When to use

Estimate flow through an orifice plate from a measured differential pressure.
Convert orifice diameter, pressure, and density values between supported engineering units.
Check volumetric flow, mass flow, throat velocity, and β=d/D for an orifice installation.

How it works

1Enter the orifice diameter, pressure difference, fluid density, and discharge coefficient C_d.
2Select units for diameter, pressure, and density; the calculator converts the inputs for the calculation.
3Optionally enter the upstream pipe diameter to calculate the diameter ratio β=d/D.
4The result returns orifice area, volumetric flow in m³/s, L/s, L/min, and m³/h, plus mass flow and orifice velocity.

Use cases

Sizing and checking differential-pressure orifice flow measurements in water systems.
Estimating air flow through a known orifice when density and pressure difference are available.
Comparing orifice and pipe diameters through the calculated β ratio.

Examples

1. Water orifice plate flow estimate

Process engineer

Background

A process engineer needs to estimate water flow through a sharp-edged orifice plate from a measured pressure difference.

Problem

Calculate volumetric flow, mass flow, orifice velocity, and the diameter ratio for a 50 mm orifice in a 100 mm pipe.

How to use

Enter d=0.05 m, D=0.1 m, ΔP=10000 Pa, ρ=1000 kg/m³, and C_d=0.61.

Orifice diameter unit: m; pipe diameter unit: m; pressure unit: Pa; density unit: kg/m³; decimal places: 4.

Outcome

The calculator returns β=0.5, area≈0.002 m², Q≈0.0054 m³/s, 5.3564 L/s, 321.3853 L/min, and 19.2831 m³/h. Mass flow is approximately 5.3564 kg/s and orifice velocity is approximately 2.728 m/s.

2. Air flow through a 50 mm orifice

HVAC engineer

Background

An HVAC engineer wants to estimate air flow through an orifice using a pressure difference measured in kilopascals.

Problem

Calculate flow without entering an upstream pipe diameter.

How to use

Enter d=50 mm, ΔP=5 kPa, ρ=1.2 kg/m³, and C_d=0.62. Leave the pipe diameter blank.

FAQ

What equation does the calculator use?

It uses Q=C_d·A·√(2·ΔP/ρ), with A=π·d²/4. It also calculates mass flow and orifice velocity from the corresponding formulas.

What value should I use for C_d?

The default is 0.61, a typical value for a sharp-edged thin-plate orifice. Use a more suitable value when one is available for your installation.

Which units are supported?

Diameter supports m, cm, and mm; pressure supports Pa, kPa, bar, atm, and psi; density supports kg/m³ and g/cm³.

Is the pipe diameter required?

No. Pipe diameter is optional and is used only to calculate the diameter ratio β=d/D.

What input limits apply?

Pressure difference must be nonnegative, density must be greater than zero, and C_d must be between 0 and 1.

Orifice diameter unit: mm; pressure unit: kPa; density unit: kg/m³; decimal places: 4.

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Water orifice plate flow estimate

2. Air flow through a 50 mm orifice

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