EULER

Overview

The EULER function calculates the Euler number (Eu), a dimensionless number used in fluid dynamics to characterize the relationship between the pressure forces and inertial forces within a fluid flow. The Euler number is defined as:

where $\Delta P$ is the pressure drop (Pa), $\rho$ is the fluid density (kg/m³), and $V$ is the characteristic velocity (m/s).

The Euler number is commonly used in the analysis of fluid flow, especially in the context of pressure drop calculations and the design of piping systems. It is particularly useful for comparing different flow situations and for scaling experimental results.

For more information, see the fluids GitHub repository  and the official documentation .

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

Usage

To use the function in Excel:

=EULER(dP, rho, V)

• dP (float, required): Pressure drop in Pascals (Pa).
• rho (float, required): Fluid density in kilograms per cubic meter (kg/m³).
• V (float, required): Characteristic velocity in meters per second (m/s).

The function returns a single value (float): the Euler number (dimensionless), or an error message (string) if the input is invalid or out-of-range.

Examples

Example 1: Standard Water Flow

In Excel:

=EULER(1E5, 1000, 4)

Expected output:

Example 2: Air Flow in a Duct

In Excel:

=EULER(500, 1.2, 10)

Expected output:

Example 3: Oil Flow with Low Velocity

In Excel:

=EULER(2000, 850, 2)

Expected output:

Example 4: High Pressure Drop, High Density

In Excel:

=EULER(2E5, 2000, 5)

Expected output:

Python Code

import micropip
await micropip.install('fluids')
from fluids.core import Euler as fluids_euler
 
def euler(dP, rho, V):
    """
    Calculate the Euler number (Eu) for a fluid flow.
 
    Args:
        dP: Pressure drop in Pascals (Pa).
        rho: Fluid density in kilograms per cubic meter (kg/m³).
        V: Characteristic velocity in meters per second (m/s).
 
    Returns:
        The Euler number (float, dimensionless), or an error message (str) if the input is invalid or out-of-range.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        dP_val = float(dP)
        rho_val = float(rho)
        V_val = float(V)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if rho_val == 0 or V_val == 0:
        return "Invalid input: 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 round(result, 2)

Live Notebook

Edit this function in a live notebook .

Live Demo