EULER

Calculates the Euler number as the ratio of pressure-drop effects to inertial effects in a flow.

Excel Usage

=EULER(dP, rho, V)

dP (float, required): Pressure drop (Pa)
rho (float, required): Fluid density (kg/m³)
V (float, required): Characteristic velocity (m/s)

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

Example 1: High pressure-drop liquid flow

Inputs:

dP	rho	V
100000	1000	4

Excel formula:

=EULER(100000, 1000, 4)

Expected output:

6.25

Example 2: Low pressure-drop gas flow

Inputs:

dP	rho	V
500	1.2	10

Excel formula:

=EULER(500, 1.2, 10)

Expected output:

4.16667

Example 3: Oil-like density with moderate pressure drop

Inputs:

dP	rho	V
2000	850	2

Excel formula:

=EULER(2000, 850, 2)

Expected output:

0.588235

Example 4: Higher density fluid with large pressure drop

Inputs:

dP	rho	V
200000	2000	5

Excel formula:

=EULER(200000, 2000, 5)

Expected output:

4

Python Code

Show Code

from fluids.core import Euler as fluids_euler

def euler(dP, rho, V):
    """
    Calculate the Euler number (Eu) for a fluid flow.

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

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

    Args:
        dP (float): Pressure drop (Pa)
        rho (float): Fluid density (kg/m³)
        V (float): Characteristic velocity (m/s)

    Returns:
        float: Euler number (float), or error message string.
    """
    try:
        dP_val = float(dP)
        rho_val = float(rho)
        V_val = float(V)
    except Exception:
        return "Error: All parameters must be numeric values."
    if rho_val == 0 or V_val == 0:
        return "Error: rho and V must be nonzero."
    try:
        result = fluids_euler(dP_val, rho_val, V_val)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

Online Calculator

dP *

Pressure drop (Pa)

rho *

Fluid density (kg/m³)

V *

Characteristic velocity (m/s)