Orifice Sizing Calculator – Accurate Flow Rate Calculation

orifice size and flow calculations

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Flow Rate Calculation for Fluids Through an Orifice or Nozzle

The flow rate of a fluid passing through an orifice or nozzle can be determined using the following equation:

Fluid Flow Through an Orifice or Nozzle

q = Cd A 1 - β 4 2 g n h L

Where:

  • q = Flow rate
  • Cd = Coefficient of discharge
  • A = Cross-sectional area
  • β = Diameter ratio (d₁/d₂)
  • gₙ = Acceleration due to gravity
  • hL = Head loss

Instead of using the coefficient of discharge (Cd), a more practical approach is to apply the flow coefficient (C), which is defined as:

Flow Coefficient Formula

C = C d 1 - β 4

q = C A 2 g n h L

Where:

  • C = Flow coefficient
  • Cd = Coefficient of discharge
  • β = Diameter ratio (d₁/d₂)

By utilizing the flow coefficient, engineers and fluid mechanics professionals can achieve more accurate calculations for fluid dynamics, hydraulic systems, and nozzle flow efficiency.

Coefficient of Discharge for Orifice Flow (ISO 5167)

The coefficient of discharge (Cd) for orifice flow can be determined using the Reader-Harris/Gallagher (1998) equation as specified in ISO 5167:

Coefficient of Discharge Formula

Coefficient of discharge for orifice

Where:

  • β = Diameter ratio (d₁/d₂)
  • ReD = Reynolds number based on the larger diameter
  • d₁ = Smaller internal diameter
  • d₂ = Larger internal diameter

Tap Configurations and Coefficient Adjustments

The values of L₁ and L₂ depend on the type of pressure tap used:

  • Corner taps: L₁ = L₂ = 0
  • D and D/2 taps: L₁ = 1, L₂ = 0.47
  • 1-inch taps: L₁ = L₂ = 0.0254/d₁ (for d₁ in meters)

By applying these fluid flow equations, engineers can enhance flow measurement accuracy in hydraulic systems, pipelines, and industrial fluid applications.

Select orifice type:
Select values to input:
Pressures
Flow rates and velocities
Orifice dimensions and coefficients
Fluid properties

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Description

p1 - pressure on the inlet
Absolute pressure in front of the orifice
p2 - pressure on the outlet
Absolute pressure after the orifice
Δp - pressure drop
Pressure difference between pipe start and pipe end
Δω - pressure loss
That can't be recovered after the orifice
D1 - diameter of tube
Internal pipe diameter
D2 - orifice size
Diameter of orifice
e - expansion factor
Coefficient used for compressible flow calculation
C - coefficient of discharge
Coefficient used for orifice plate based on ISO 5167
ReD - upstream Reynolds number
Reynolds number calculated in front of the orifice
K - resistance coefficient
That you can use in pipeline calculation, as orifice is creating local pressure losses in the pipeline
q1 - volumetric flow rate
Fluid flow rate in terms of units of volume per unit of time on the inlet conditions
q - standard flow
Flow rate at standard conditions. Used only if the selected fluid is gas.
ṁ - mass flow rate
Fluid flow rate in terms of units of mass per unit of time
V1 - upstream velocity
Flow velocity in front of the orifice where flow diameter is D1
T1 - upstream temperature
Fluid temperature for gas density calculation based on the ideal gas state equation
ρ1 - upstream density
Fluid density in the front of orifice in terms of mass per unit of volume
R - gas constant
Gas constant in terms of energy per unit of mass and temperature, for gas density calculation using ideal gas state equation
κ - isentropic coefficient
Specific heat ratio
ν - kinematic viscosity
Result of fluid particles colliding to each other and moving at different velocities in terms of area per square unit of time
μ - dynamic viscosity
Result of fluid particles colliding to each other and moving at different velocities in terms of mass per square unit of distance and time

Sizing calculation setup

Select orifice type based on the measuring taps placement
Corner taps
When measuring taps are placed in the orifice corners
Flange taps
When measuring taps are placed in the orifice flanges
D - D/2
When measuring taps are placed in front and after the orifice on given distance
Select value to input. You should enter selected one. The other one will be calculated
p2
pressure downstream from the orifice
Δp
measured pressure difference in front and after the orifice
Select value to input. You should enter selected one. The other one will be calculated
ν
kinematic viscosity
μ
dynamic viscosity
Select value to input. Available only if gas is selected. You should enter selected one. The other one will be calculated
T1
upstream temperature.
ρ1
upstream density.
Select fluid type
Gas
for compressible flow where ideal gas state equation is applicable
Liquid
for incompressible flow of liquids
Application of ISO 5167 constraints
ISO constraints
Deselect if you don't want to check if the orifice and the flow conditions are within the limits of the ISO standard.

Why Use This Orifice Sizing Calculator?

Our orifice sizing calculator quickly determines the actual flow rate through an orifice plate flow meter using just a few inputs. By measuring the pressure drop caused by the orifice plate in the pipeline, this tool provides precise flow calculations for engineers and technicians.

When Should You Use This Calculator?

  • Liquids and perfect gases
  • Subsonic, single-phase fluid flow
  • Circular pipelines

Not suitable for: Pulsating flows, rectangular ducts, or non-ideal gases.

When Is This Calculator Not Applicable?

This tool does not support:

  • Multiphase flows (e.g., liquid with solid particles or undissolved gases)
  • Non-ideal gas flows (gases that don’t follow the ideal gas law)

What Inputs Are Required for Orifice Flow Calculation?

To perform a precise orifice plate flow rate calculation, enter the following:

  • Throat diameter of the orifice plate
  • Pipe interior diameter
  • Fluid properties – Density and viscosity (for liquids)
  • Gas properties – Gas constant, pressure, and temperature (for gases)

For gas flow calculations, density is automatically computed using the perfect gas equation based on real conditions.

How Does This Orifice Plate Calculator Work?

The calculation follows ISO 5167-2 standards to ensure accuracy. Reliable results are only achieved if the orifice plate design meets these criteria.

ISO 5167-2 Orifice Plate Flow Conditions

For Corner, D, and D/2 Pressure Tappings:

  • Orifice diameter (d) > 12.5 mm
  • Pipe diameter (D) between 50 mm and 1000 mm
  • Beta ratio (β) between 0.1 and 0.75
  • Reynolds number (ReD) > 5000 (if β < 0.56)
  • Reynolds number (ReD) > 16000 × β² (if β > 0.56)

For Flange Pressure Tappings:

  • d > 12.5 mm
  • D between 50 mm and 1000 mm
  • β between 0.1 and 0.75
  • ReD > 5000 and ReD > 170 × β² × D

What Happens If These Conditions Aren’t Met?

If the orifice plate or flow conditions do not comply with ISO 5167-2, the calculator will display a warning message. However, you can choose to bypass ISO constraints and proceed with the calculation at your own discretion.

Try the Orifice Sizing Calculator Now!

Get fast, accurate orifice flow rate calculations using our easy-to-use tool. Perfect for engineers, fluid mechanics specialists, and industrial applications!

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Features in desktop app

  • Save/Open multiple results
  • Export to Word and Excel
  • Print results
  • Create list of custom fluid properties
  • Resistance factor K for valves/fittings
  • Pipe surface roughness selection
  • Pipe material selection
  • Gauge vs absolute pressure toggle
  • Compressible isothermal flow
  • Dry air isothermal flow
  • Gas offtake flow
  • Natural gas flow
  • No admin rights required to install
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