ECKERT

Overview

The ECKERT function calculates the Eckert number ($Ec$), a dimensionless number used in fluid dynamics and heat transfer to characterize the relationship between a flow’s kinetic energy and the enthalpy difference due to temperature. It is defined as:

where $V$ is the velocity (m/s), $C_p$ is the specific heat capacity (J/kg/K), and $\Delta T$ is the temperature difference (K).

The Eckert number is important in analyzing high-speed flows and situations where viscous dissipation is significant. For more details, see the fluids.core Eckert documentation  and the fluids GitHub repository .

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

Usage

To use the function in Excel:

=ECKERT(V, Cp, dT)

• V (float, required): Velocity in meters per second (m/s).
• Cp (float, required): Specific heat capacity in joules per kilogram per kelvin (J/kg/K).
• dT (float, required): Temperature difference in kelvin (K).

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

Examples

Example 1: Moderate velocity and temperature difference

In Excel:

=ECKERT(10, 2000, 25)

Expected output:

Example 2: Higher velocity

In Excel:

=ECKERT(20, 2000, 25)

Expected output:

Example 3: Higher heat capacity

In Excel:

=ECKERT(10, 4000, 25)

Expected output:

Example 4: Larger temperature difference

In Excel:

=ECKERT(10, 2000, 50)

Expected output:

This means, for example, that for a velocity of 10 m/s, heat capacity of 2000 J/kg/K, and temperature difference of 25 K, the Eckert number is 0.002.

Python Code

import math
 
def eckert(V, Cp, dT):
    """
    Calculate the Eckert number (Ec) for a given velocity, heat capacity, and temperature difference.
 
    Args:
        V: Velocity in meters per second (m/s).
        Cp: Specific heat capacity in joules per kilogram per kelvin (J/kg/K).
        dT: Temperature difference in kelvin (K).
 
    Returns:
        The Eckert number (float), 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:
        V = float(V)
        Cp = float(Cp)
        dT = float(dT)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if Cp == 0 or dT == 0:
        return "Invalid input: Cp and dT must be nonzero."
    Ec = V ** 2 / (Cp * dT)
    return round(Ec, 6)

Live Demo

Example Workbook

Link to Workbook