CONFINEMENT

Calculates the Confinement number for two-phase flow, relating capillary and buoyancy effects relative to channel size.

Excel Usage

=CONFINEMENT(D, rhol, rhog, sigma, g)

D (float, required): Channel diameter (m)
rhol (float, required): Density of liquid (kg/m³)
rhog (float, required): Density of gas (kg/m³)
sigma (float, required): Surface tension (N/m)
g (float, optional, default: 9.80665): Acceleration due to gravity (m/s²)

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

Example 1: Microchannel case with strong confinement

Inputs:

D	rhol	rhog	sigma	g
0.001	1077	76.5	0.00427	9.80665

Excel formula:

=CONFINEMENT(0.001, 1077, 76.5, 0.00427, 9.80665)

Expected output:

0.659698

Example 2: Medium channel with moderate density contrast

Inputs:

D	rhol	rhog	sigma	g
0.002	900	1.2	0.03	9.80665

Excel formula:

=CONFINEMENT(0.002, 900, 1.2, 0.03, 9.80665)

Expected output:

0.922441

Example 3: Very small channel with strong capillary confinement

Inputs:

D	rhol	rhog	sigma	g
0.0005	1000	0.6	0.072	9.80665

Excel formula:

=CONFINEMENT(0.0005, 1000, 0.6, 0.072, 9.80665)

Expected output:

5.42084

Example 4: Large channel with weak confinement effects

Inputs:

D	rhol	rhog	sigma	g
0.01	800	1	0.002	9.80665

Excel formula:

=CONFINEMENT(0.01, 800, 1, 0.002, 9.80665)

Expected output:

0.0505221

Python Code

Show Code

from fluids.core import Confinement as fluids_confinement

def confinement(D, rhol, rhog, sigma, g=9.80665):
    """
    Calculate the Confinement number (Co) for two-phase flow in a channel.

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

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

    Args:
        D (float): Channel diameter (m)
        rhol (float): Density of liquid (kg/m³)
        rhog (float): Density of gas (kg/m³)
        sigma (float): Surface tension (N/m)
        g (float, optional): Acceleration due to gravity (m/s²) Default is 9.80665.

    Returns:
        float: Confinement number (float), or error message string.
    """
    try:
        D = float(D)
    except (ValueError, TypeError):
        return "Error: D must be a numeric value."
    try:
        rhol = float(rhol)
    except (ValueError, TypeError):
        return "Error: rhol must be a numeric value."
    try:
        rhog = float(rhog)
    except (ValueError, TypeError):
        return "Error: rhog must be a numeric value."
    try:
        sigma = float(sigma)
    except (ValueError, TypeError):
        return "Error: sigma must be a numeric value."
    try:
        g = float(g)
    except (ValueError, TypeError):
        return "Error: g must be a numeric value."

    if D <= 0:
        return "Error: D must be positive."
    if rhol <= 0:
        return "Error: rhol must be positive."
    if rhog < 0:
        return "Error: rhog must be non-negative."
    if sigma <= 0:
        return "Error: sigma must be positive."
    if g <= 0:
        return "Error: g must be positive."
    if rhol <= rhog:
        return "Error: rhol must be greater than rhog."

    try:
        result = fluids_confinement(D, rhol, rhog, sigma, g)
    except Exception as e:
        return f"Error: Failed to calculate Confinement number: {str(e)}"
    return result

Online Calculator

D *

Channel diameter (m)

rhol *

Density of liquid (kg/m³)

rhog *

Density of gas (kg/m³)

sigma *

Surface tension (N/m)

Acceleration due to gravity (m/s²)