Reynolds Number Calculator

Reynolds Number is evaluated from Fluid Velocity, Hydraulic Diameter and Fluid. The calculation reports Reynolds Number, Flow Regime and Darcy Friction Factor.

Results

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About the Reynolds Number Calculator

Reynolds Number is treated here as a quantitative relation between Fluid Velocity, Hydraulic Diameter, Fluid and Custom Density and Reynolds Number, Flow Regime, Darcy Friction Factor and Velocity.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Re = ρvD / mu (slug/ft^3, ft/s, ft, lb·s/ft^2)
Re = vD / ν (kinematic viscosity, ft^2/s)
Re < 2,300: Laminar → f = 64/Re
Re 2,300 - 4,000: Transitional
Re > 4,000: Turbulent → f approximately 0.316/Re^0.25

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Re = ρvD / mu (slug/ft^3, ft/s, ft, lb·s/ft^2)
Re = vD / ν (kinematic viscosity, ft^2/s)
Re < 2,300: Laminar → f = 64/Re
Re 2,300 - 4,000: Transitional
Re > 4,000: Turbulent → f approximately 0.316/Re^0.25

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Residential Water Pipe — Laminar or Turbulent?

Inputs

velocity_fps: 5 diameter_in: 0.75 fluid_type: Water (60°F): ρ=1.938, μ=2.35e-5
Reynolds Number: 25,771. Flow Regime: Turbulent. Darcy Friction Factor: 0.02494. Velocity: 1.524 m/s

With Fluid Velocity = 5, Hydraulic Diameter = 0.75 and Fluid = Water (60 degF): ρ=1.938, mu=2.35e-5 as the stated inputs, the result is Reynolds Number = 25,771, Flow Regime = Turbulent and Darcy Friction Factor = 0.02494. Each value corresponds to the declared output fields.

Example 2: HVAC Ductwork Air Flow

Inputs

velocity_fps: 12 diameter_in: 12 fluid_type: Air (68°F): ρ=0.002378, μ=3.73e-7
Reynolds Number: 989,617. Flow Regime: Turbulent. Darcy Friction Factor: 0.01002. Velocity: 3.658 m/s

With Fluid Velocity = 12, Hydraulic Diameter = 12 and Fluid = Air (68 degF): ρ=0.002378, mu=3.73e-7 as the stated inputs, the result is Reynolds Number = 989,617, Flow Regime = Turbulent and Darcy Friction Factor = 0.01002. Each value corresponds to the declared output fields.

Example 3: Laminar Flow — Slow Viscous Oil in Pipe

Inputs

velocity_fps: 0.5 diameter_in: 2 fluid_type: Custom density: 1.72 viscosity: 0.001
Reynolds Number: 143. Flow Regime: Turbulent. Darcy Friction Factor: 0.03471. Velocity: 0.152 m/s

With Fluid Velocity = 0.5, Hydraulic Diameter = 2, Fluid = Custom and Custom Density = 1.72 as the stated inputs, the result is Reynolds Number = 143, Flow Regime = Turbulent and Darcy Friction Factor = 0.03471. Each value corresponds to the declared output fields.

Example 4: Boeing 737 Wing — Boundary Layer Transition

Inputs

velocity_fps: 440 fluid_type: Air (68°F): ρ=0.002378, μ=3.73e-7
Velocity: 134.112 m/s

With Fluid Velocity = 440 and Fluid = Air (68 degF): ρ=0.002378, mu=3.73e-7 as the stated inputs, the result is Velocity = 134.112 m/s. Each value corresponds to the declared output fields.

Common Use Cases

  • Determine if flow in a pipe is laminar or turbulent
  • Calculate Reynolds number for water flowing through a duct
  • Check transition from laminar to turbulent for air over a wing