TURB_FRIEND

This function computes turbulent Nusselt number in internal pipe flow using the Friend–Metzner correlation. It requires Reynolds number, Prandtl number, and Darcy friction factor and is primarily used for high-Prandtl-number applications.

Excel Usage

=TURB_FRIEND(Re, Pr, fd)

Re (float, required): Reynolds number (-).
Pr (float, required): Prandtl number (-).
fd (float, required): Darcy friction factor (-).

Returns (float): Turbulent Nusselt number for pipe flow (-).

Example 1: Friend-Metzner example

Inputs:

Re	Pr	fd
100000	100	0.0185

Excel formula:

=TURB_FRIEND(100000, 100, 0.0185)

Expected output:

1738.34

Example 2: Higher Prandtl number

Inputs:

Re	Pr	fd
200000	200	0.02

Excel formula:

=TURB_FRIEND(200000, 200, 0.02)

Expected output:

4699.95

Example 3: Mid Prandtl number

Inputs:

Re	Pr	fd
50000	50	0.022

Excel formula:

=TURB_FRIEND(50000, 50, 0.022)

Expected output:

729.025

Example 4: Lower Reynolds number

Inputs:

Re	Pr	fd
150000	80	0.017

Excel formula:

=TURB_FRIEND(150000, 80, 0.017)

Expected output:

2282.29

Python Code

Show Code

from ht.conv_internal import turbulent_Friend_Metzner as ht_turbulent_Friend_Metzner

def turb_friend(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using Friend-Metzner.

    See: https://ht.readthedocs.io/en/latest/ht.conv_internal.html

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

    Args:
        Re (float): Reynolds number (-).
        Pr (float): Prandtl number (-).
        fd (float): Darcy friction factor (-).

    Returns:
        float: Turbulent Nusselt number for pipe flow (-).
    """
    try:
        return ht_turbulent_Friend_Metzner(Re=Re, Pr=Pr, fd=fd)
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

Re *

Reynolds number (-).

Pr *

Prandtl number (-).

fd *

Darcy friction factor (-).