BOND

Calculates the Bond number, which compares gravitational effects to surface tension effects for a fluid interface.

Excel Usage

=BOND(rhol, rhog, sigma, L)

rhol (float, required): Density of liquid (kg/m³)
rhog (float, required): Density of gas (kg/m³)
sigma (float, required): Surface tension (N/m)
L (float, required): Characteristic length (m)

Returns (float): Bond number [-]

Example 1: Water bubble in air

Inputs:

rhol	rhog	sigma	L
1000	1.2	0.0728	0.01

Excel formula:

=BOND(1000, 1.2, 0.0728, 0.01)

Expected output:

13.4545

Example 2: Mercury drop in water

Inputs:

rhol	rhog	sigma	L
13546	1000	0.485	0.005

Excel formula:

=BOND(13546, 1000, 0.485, 0.005)

Expected output:

6.34197

Example 3: Small length scale (capillary dominated)

Inputs:

rhol	rhog	sigma	L
800	1	0.025	0.0001

Excel formula:

=BOND(800, 1, 0.025, 0.0001)

Expected output:

0.00313421

Example 4: Handbook example

Inputs:

rhol	rhog	sigma	L
1000	1.2	0.0589	2

Excel formula:

=BOND(1000, 1.2, 0.0589, 2)

Expected output:

665187

Python Code

Show Code

from fluids.core import Bond as fluids_Bond

def bond(rhol, rhog, sigma, L):
    """
    Calculate the Bond number (Bo), also known as the Eötvös number (Eo).

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

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

    Args:
        rhol (float): Density of liquid (kg/m³)
        rhog (float): Density of gas (kg/m³)
        sigma (float): Surface tension (N/m)
        L (float): Characteristic length (m)

    Returns:
        float: Bond number [-]
    """
    try:
        return float(fluids_Bond(rhol=float(rhol), rhog=float(rhog), sigma=float(sigma), L=float(L)))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

rhol *

Density of liquid (kg/m³)

rhog *

Density of gas (kg/m³)

sigma *

Surface tension (N/m)

L *

Characteristic length (m)