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.

    Frequently Asked Questions

    What is the physical meaning of the Reynolds number?

    It represents the ratio of inertial forces to viscous forces. High Re means inertia dominates (turbulent); low Re means viscosity dominates (laminar).

    Why does the transition occur around Re = 2300?

    This is an empirical observation for smooth pipe flow. Small disturbances are damped by viscosity at low Re but amplified at high Re.

    Does the Reynolds number apply to gases?

    Yes. Gases have lower density but also lower viscosity, so Re can still be high for fast flows.

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