Froude Number Calculator Formula

Understand the math behind the froude number calculator. Each variable explained with a worked example.

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Formulas Used

Froude Number

froude = velocity / sqrt(9.80665 * depth)

Shallow-Water Wave Speed

wave_speed = sqrt(9.80665 * depth)

Variables

VariableDescriptionDefault
velocityFlow Velocity(m/s)3
depthHydraulic Depth(m)1

How It Works

Froude Number

The Froude number characterises the ratio of flow inertia to gravitational effects in open-channel flow.

Formula

Fr = v / sqrt(g d)

  • *v* = mean flow velocity
  • *g* = gravitational acceleration
  • *d* = hydraulic depth (cross-section area divided by top width)

    • Fr < 1: subcritical (tranquil). Fr = 1: critical. Fr > 1: supercritical (rapid).

    Worked Example

    River at 3 m/s with 1 m depth.

    velocity = 3depth = 1
    1. 01Fr = v / sqrt(g d)
    2. 02Fr = 3 / sqrt(9.807 * 1)
    3. 03Fr = 3 / 3.131
    4. 04Fr = 0.958 (subcritical, but nearly critical)

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