FROUDE

Overview

The FROUDE function calculates the Froude number (Fr), a dimensionless quantity used in fluid mechanics to characterize flow regimes where gravitational and inertial forces are dominant. Named after English engineer William Froude, this number is essential for analyzing open channel flows, ship hydrodynamics, and free-surface phenomena.

The Froude number represents the ratio of inertial forces to gravitational forces acting on a fluid element:

Fr = \frac{V}{\sqrt{gL}}

where V is the characteristic velocity (m/s), g is the gravitational acceleration (m/s²), and L is the characteristic length (m). The function can also return the squared form of the Froude number (Fr^2 = V^2 / gL) when the squared parameter is set to True.

Flow regimes are classified based on the Froude number value: - Subcritical flow (Fr < 1): Gravitational forces dominate; disturbances propagate upstream - Critical flow (Fr = 1): Inertial and gravitational forces are balanced - Supercritical flow (Fr > 1): Inertial forces dominate; disturbances cannot propagate upstream

This implementation uses the fluids library, an open-source Python package for fluid dynamics calculations. For more details on the function parameters and additional examples, see the fluids.core.Froude documentation. The Froude number concept is also discussed in standard fluid mechanics references including Perry’s Chemical Engineers’ Handbook and Cengel & Cimbala’s Fluid Mechanics.

This example function is provided as-is without any representation of accuracy.

Excel Usage

=FROUDE(V, L, g, squared)

• V (float, required): Characteristic velocity (m/s)
• L (float, required): Characteristic length (m)
• g (float, optional, default: 9.80665): Gravitational acceleration (m/s²)
• squared (bool, optional, default: false): If true, returns squared Froude number

Returns (float): Froude number (float), or error message string.

Examples

Example 1: Demo case 1

Inputs:

V	L	g	squared
1.83	2	9.80665	false

Excel formula:

=FROUDE(1.83, 2, 9.80665, FALSE)

Expected output:

0.4116

Example 2: Demo case 2

Inputs:

V	L	g	squared
1.83	2	1.63	false

Excel formula:

=FROUDE(1.83, 2, 1.63, FALSE)

Expected output:

1.0135

Example 3: Demo case 3

Inputs:

V	L	g	squared
1.83	2	9.80665	true

Excel formula:

=FROUDE(1.83, 2, 9.80665, TRUE)

Expected output:

0.1694

Example 4: Demo case 4

Inputs:

V	L	g	squared
1.83	2	1.63	true

Excel formula:

=FROUDE(1.83, 2, 1.63, TRUE)

Expected output:

1.0272

Python Code

import micropip
await micropip.install(["fluids"])
from fluids.core import Froude as fluids_froude

def froude(V, L, g=9.80665, squared=False):
    """
    Calculate the Froude number (Fr) for a given velocity, length, and gravity.

    See: https://fluids.readthedocs.io/fluids.core.html#fluids.core.Froude

    This example function is provided as-is without any representation of accuracy.

    Args:
        V (float): Characteristic velocity (m/s)
        L (float): Characteristic length (m)
        g (float, optional): Gravitational acceleration (m/s²) Default is 9.80665.
        squared (bool, optional): If true, returns squared Froude number Default is False.

    Returns:
        float: Froude number (float), or error message string.
    """
    try:
        V = float(V)
        L = float(L)
        g = float(g)
        squared = bool(squared)
    except Exception:
        return "Error: V, L, and g must be numeric values."
    if L <= 0 or g <= 0:
        return "Error: L and g must be positive."
    try:
        result = fluids_froude(V, L=L, g=g, squared=squared)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

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