DEAN

Calculates the Dean number for curved-flow systems, combining Reynolds effects with curvature geometry.

Excel Usage

=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)

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

Example 1: Curved pipe with moderate curvature ratio

Inputs:

reynolds	inner_diameter	curvature_diameter
10000	0.1	0.4

Excel formula:

=DEAN(10000, 0.1, 0.4)

Expected output:

5000

Example 2: Higher Reynolds number with larger pipe geometry

Inputs:

reynolds	inner_diameter	curvature_diameter
20000	0.2	0.5

Excel formula:

=DEAN(20000, 0.2, 0.5)

Expected output:

12649.1

Example 3: Smaller pipe and curvature dimensions

Inputs:

reynolds	inner_diameter	curvature_diameter
5000	0.05	0.2

Excel formula:

=DEAN(5000, 0.05, 0.2)

Expected output:

2500

Example 4: Equal inner and curvature diameters

Inputs:

reynolds	inner_diameter	curvature_diameter
15000	0.3	0.3

Excel formula:

=DEAN(15000, 0.3, 0.3)

Expected output:

15000

Python Code

Show Code

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.

    See: https://fluids.readthedocs.io/en/latest/fluids.core.html#fluids.core.Dean

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

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

    Returns:
        float: Dean number (float), or error message string.
    """
    try:
        Re = float(reynolds)
        Di = float(inner_diameter)
        D = float(curvature_diameter)
    except (TypeError, ValueError):
        return "Error: All parameters must be numeric values."

    if D == 0:
        return "Error: curvature_diameter cannot be zero."

    try:
        result = fluids_dean(Re, Di, D)
    except Exception as e:
        return f"Error: {str(e)}"

    return float(result)

Online Calculator

reynolds *

Reynolds number (dimensionless)

inner_diameter *

Inner diameter of the pipe (m)

curvature_diameter *

Diameter of curvature or spiral (m)