ARCHIMEDES

Overview

The ARCHIMEDES function calculates the Archimedes number (Ar), a dimensionless quantity used to characterize the motion of particles or bubbles in a fluid. It represents the ratio of gravitational forces to viscous forces acting on a particle immersed in a fluid and is essential in fluid-particle interaction calculations, including sedimentation, fluidization, and bubble dynamics.

The Archimedes number is defined as:

Ar = \frac{L^3 \rho_f (\rho_p - \rho_f) g}{\mu^2}

where L is the characteristic length (typically particle diameter), \rho_f is the fluid density, \rho_p is the particle density, g is gravitational acceleration, and \mu is the dynamic viscosity of the fluid. The number captures the balance between buoyancy-driven motion and viscous resistance.

In physical terms, this dimensionless group can be interpreted as:

Ar = \frac{\text{Gravitational force}}{\text{Viscous force}}

Higher Archimedes numbers indicate that gravitational (buoyancy) effects dominate over viscous effects, which typically leads to faster settling or rising of particles. This number appears frequently in correlations for drag coefficients, terminal velocities, and fluidization behavior.

This implementation uses the fluids Python library, specifically the Archimedes function from the fluids.core module. For more details, see the fluids documentation. The underlying methodology follows standard 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

=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.

Examples

Example 1: Demo case 1

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:

470.41

Example 2: Demo case 2

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:

459843.75

Example 3: Demo case 3

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: Demo case 4

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

import micropip
await micropip.install(["fluids"])
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

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