FROUDE

Overview

The FROUDE function calculates the Froude number (Fr), a dimensionless number used in fluid mechanics to characterize the influence of gravity on fluid motion. The Froude number is defined as the ratio of a characteristic velocity to the square root of the product of gravitational acceleration and a characteristic length:

where:

• $V$ is the characteristic velocity (m/s)
• $L$ is the characteristic length (m)
• $g$ is the acceleration due to gravity (m/s², default 9.80665)

The Froude number is important in the study of open channel flows, ship hydrodynamics, and other applications where gravity plays a significant role in fluid behavior. Optionally, the squared form of the Froude number can be returned.

For more information, see the fluids.core documentation  and the fluids GitHub repository .

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

Usage

To use the function in Excel:

=FROUDE(V, L, [g], [squared])

• V (float, required): Characteristic velocity in m/s.
• L (float, required): Characteristic length in meters.
• g (float, optional, default=9.80665): Acceleration due to gravity in m/s².
• squared (bool, optional, default=FALSE): If TRUE, returns the squared Froude number.

The function returns a single value (float): the Froude number (dimensionless), or its squared value if squared is TRUE. If the input is invalid, an error message (string) is returned.

Examples

Example 1: Standard Froude Number

In Excel:

=FROUDE(1.83, 2)

Expected output:

Example 2: Froude Number with Custom Gravity

In Excel:

=FROUDE(1.83, 2, 1.63)

Expected output:

Example 3: Squared Froude Number

In Excel:

=FROUDE(1.83, 2, 9.80665, TRUE)

Expected output:

Example 4: Squared Froude Number with Custom Gravity

In Excel:

=FROUDE(1.83, 2, 1.63, TRUE)

Expected output:

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.
 
    Args:
        V: Characteristic velocity in m/s.
        L: Characteristic length in meters.
        g: Acceleration due to gravity in m/s² (default: 9.80665).
        squared: If True, returns the squared Froude number (default: False).
 
    Returns:
        The Froude number (float, dimensionless), or its squared value if squared is True. Returns an error message (str) if input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        V = float(V)
        L = float(L)
        g = float(g)
        squared = bool(squared)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if L <= 0 or g <= 0:
        return "Invalid input: 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

Example Workbook

Link to Workbook