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)

    Frequently Asked Questions

    What is the physical meaning of the Froude number?

    It compares the speed of the flow to the speed of surface gravity waves. When Fr > 1, flow moves faster than waves can propagate upstream, so upstream conditions cannot influence downstream.

    How does the Froude number relate to ship design?

    For ships, the Froude number (based on hull length) determines wave-making resistance. Ships are most efficient below the hull speed, roughly Fr = 0.4.

    What happens at Fr = 1?

    Critical flow, with minimum specific energy for a given discharge. This condition is used in weir design to measure flow rates.

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