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

Compute the flow rate through a thin-plate orifice for an incompressible fluid (ISO 5167 Bernoulli form with discharge coefficient C_d). Orifice area A=π·d²/4; volumetric flow Q=C_d·A·√(2·ΔP/ρ); mass flow ṁ=C_d·A·√(2·ρ·ΔP); throat velocity v_orifice=C_d·√(2·ΔP/ρ). If the upstream pipe diameter D is supplied the diameter ratio β=d/D is also returned. ΔP≥0, ρ>0, C_d in 0..1 (default 0.61 for a sharp-edged plate). Diameter in m/cm/mm, pressure in Pa/kPa/bar/atm/psi, density in kg/m³/g/cm³; volumetric flow reported in m³/s, L/s, L/min and m³/h.

> Canonical page: https://elysiatools.com/en/tools/orifice-flow-calculator

- **Category:** Math & Numbers

- **Keywords:** orifice flow, orifice plate, Bernoulli, discharge coefficient, ISO 5167, differential pressure flow meter, beta ratio, volumetric flow, mass flow, throat velocity, flow meter, fluid mechanics, Cd, ΔP

## 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.

## Inputs

- **Discharge Coefficient C_d** (number): Discharge coefficient C_d of the orifice (0 to 1). Typical sharp-edged thin-plate value ≈ 0.61.
- **Orifice Diameter d** (number): Orifice (throat) diameter d. Enter in the selected Orifice Diameter Unit.
- **Orifice Diameter Unit** (select)
- **Pipe Diameter D (optional, for β ratio)** (number): Upstream pipe inner diameter D. Optional — used only to compute the diameter ratio β=d/D. Enter in the selected Pipe Diameter Unit.
- **Pipe Diameter Unit** (select)
- **Pressure Difference ΔP** (number): Measured pressure differential ΔP across the orifice plate. Enter in the selected Pressure Unit.
- **Pressure Unit** (select)
- **Density ρ** (number): Fluid density ρ. Enter in the selected Density Unit.
- **Density Unit** (select)
- **Decimal Places** (number)

## 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

- Enter the orifice diameter, pressure difference, fluid density, and discharge coefficient C_d.
- Select units for diameter, pressure, and density; the calculator converts the inputs for the calculation.
- Optionally enter the upstream pipe diameter to calculate the diameter ratio β=d/D.
- The 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.

## Frequently asked questions

### 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.

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