Reynolds Number (Advanced) Calculator Formula

Understand the math behind the reynolds number (advanced) calculator. Each variable explained with a worked example.

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Formulas Used

Reynolds Number

re = density * velocity * length / viscosity

Kinematic Viscosity

kinematic_visc = viscosity / density

Variables

VariableDescriptionDefault
densityFluid Density(kg/m3)1000
velocityFlow Velocity(m/s)2
lengthCharacteristic Length(m)0.05
viscosityDynamic Viscosity(Pa s)0.001

How It Works

Reynolds Number

The Reynolds number predicts whether flow will be laminar (smooth) or turbulent (chaotic).

Formula

Re = rho v L / mu

  • *rho* = fluid density
  • *v* = flow velocity
  • *L* = characteristic length (pipe diameter, plate length)
  • *mu* = dynamic viscosity

    • For pipe flow: Re < 2300 is laminar, 2300-4000 is transitional, > 4000 is turbulent.

    Worked Example

    Water (rho = 1000, mu = 0.001) at 2 m/s through a 5 cm pipe.

    density = 1000velocity = 2length = 0.05viscosity = 0.001
    1. 01Re = rho v L / mu
    2. 02Re = 1000 * 2 * 0.05 / 0.001
    3. 03Re = 100 / 0.001 = 100 000
    4. 04This is well into the turbulent regime.

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