DEAN

Overview

The DEAN function calculates the Dean number (De), a dimensionless number used in fluid mechanics to characterize flow in curved pipes or channels. The Dean number is defined as:

where $D_i$ is the inner diameter of the pipe, $D$ is the diameter of curvature or spiral, and $Re$ is the Reynolds number. The Dean number is important for predicting secondary flow patterns and pressure drops in curved pipes.

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:

=DEAN(reynolds, inner_diameter, curvature_diameter)

• reynolds (float, required): Reynolds number (dimensionless).
• inner_diameter (float, required): Inner diameter of the pipe (m).
• curvature_diameter (float, required): Diameter of curvature or spiral (m).

The function returns a single value (float): the Dean number (dimensionless), or an error message (string) if the input is invalid.

Examples

Example 1: Standard Calculation

In Excel:

=DEAN(10000, 0.1, 0.4)

Expected output:

Example 2: Larger Reynolds Number

In Excel:

=DEAN(20000, 0.2, 0.5)

Expected output:

Example 3: Small Diameters

In Excel:

=DEAN(5000, 0.05, 0.2)

Expected output:

Example 4: Equal Diameters

In Excel:

=DEAN(15000, 0.3, 0.3)

Expected output:

Python Code

import micropip
await micropip.install('fluids')
from fluids.core import Dean as fluids_dean
 
def dean(reynolds, inner_diameter, curvature_diameter):
    """
    Calculate the Dean number (De) for flow in a curved pipe or channel.
 
    Args:
        reynolds: Reynolds number (dimensionless).
        inner_diameter: Inner diameter of the pipe (m).
        curvature_diameter: Diameter of curvature or spiral (m).
 
    Returns:
        The Dean number (float), or an error message (str) if the input is invalid.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        Re = float(reynolds)
        Di = float(inner_diameter)
        D = float(curvature_diameter)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if D == 0:
        return "Invalid input: curvature_diameter cannot be zero."
    try:
        result = fluids_dean(Re, Di, D)
    except Exception as e:
        return f"Error: {str(e)}"
    return float(result)

Live Notebook

Edit this function in a live notebook .

Live Demo