ARCHIMEDES

Calculates the Archimedes number, a dimensionless ratio comparing buoyancy-driven forces to viscous forces for a particle in a fluid.

Excel Usage

=ARCHIMEDES(L, rhof, rhop, mu, g)

L (float, required): Characteristic length (m)
rhof (float, required): Density of fluid (kg/m³)
rhop (float, required): Density of particle (kg/m³)
mu (float, required): Dynamic viscosity of fluid (Pa·s)
g (float, optional, default: 9.80665): Acceleration due to gravity (m/s²)

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

Example 1: Fine particle in a light gas

Inputs:

L	rhof	rhop	mu	g
0.002	2	3000	0.001	9.80665

Excel formula:

=ARCHIMEDES(0.002, 2, 3000, 0.001, 9.80665)

Expected output:

470.405

Example 2: Larger particle in a dense liquid

Inputs:

L	rhof	rhop	mu	g
0.005	1000	2500	0.002	9.81

Excel formula:

=ARCHIMEDES(0.005, 1000, 2500, 0.002, 9.81)

Expected output:

459844

Example 3: Moderate density contrast with higher viscosity

Inputs:

L	rhof	rhop	mu	g
0.01	800	1200	0.005	9.8

Excel formula:

=ARCHIMEDES(0.01, 800, 1200, 0.005, 9.8)

Expected output:

125440

Example 4: Alternate gravity constant for the reference case

Inputs:

L	rhof	rhop	mu	g
0.002	2	3000	0.001	10

Excel formula:

=ARCHIMEDES(0.002, 2, 3000, 0.001, 10)

Expected output:

479.68

Python Code

Show Code

from fluids.core import Archimedes as fluids_archimedes

def archimedes(L, rhof, rhop, mu, g=9.80665):
    """
    Calculate the Archimedes number (Ar) for a fluid and particle.

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

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

    Args:
        L (float): Characteristic length (m)
        rhof (float): Density of fluid (kg/m³)
        rhop (float): Density of particle (kg/m³)
        mu (float): Dynamic viscosity of fluid (Pa·s)
        g (float, optional): Acceleration due to gravity (m/s²) Default is 9.80665.

    Returns:
        float: Archimedes number (float), or error message string.
    """
    try:
        L_ = float(L)
        rhof_ = float(rhof)
        rhop_ = float(rhop)
        mu_ = float(mu)
        g_ = float(g)
    except (TypeError, ValueError):
        return "Error: All parameters must be numeric values."

    try:
        result = fluids_archimedes(L_, rhof_, rhop_, mu_, g_)
    except Exception as e:
        return f"Error: Failed to calculate Archimedes number: {str(e)}"

    return result

Online Calculator

L *

Characteristic length (m)

rhof *

Density of fluid (kg/m³)

rhop *

Density of particle (kg/m³)

mu *

Dynamic viscosity of fluid (Pa·s)

Acceleration due to gravity (m/s²)