TURB_CHURCHILL

This function computes turbulent internal-flow Nusselt number using the Churchill–Zajic correlation. It combines Reynolds number, Prandtl number, and Darcy friction factor in a broadly applicable model for fully developed turbulent pipe convection.

Excel Usage

=TURB_CHURCHILL(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: Churchill-Zajic example

Inputs:

Re	Pr	fd
100000	1.2	0.0185

Excel formula:

=TURB_CHURCHILL(100000, 1.2, 0.0185)

Expected output:

260.556

Example 2: Higher Reynolds number

Inputs:

Re	Pr	fd
200000	0.8	0.02

Excel formula:

=TURB_CHURCHILL(200000, 0.8, 0.02)

Expected output:

440.755

Example 3: Mid Reynolds number

Inputs:

Re	Pr	fd
50000	2	0.022

Excel formula:

=TURB_CHURCHILL(50000, 2, 0.022)

Expected output:

196.368

Example 4: Lower Reynolds number

Inputs:

Re	Pr	fd
150000	1	0.017

Excel formula:

=TURB_CHURCHILL(150000, 1, 0.017)

Expected output:

326.138

Python Code

Show Code

from ht.conv_internal import turbulent_Churchill_Zajic as ht_turbulent_Churchill_Zajic

def turb_churchill(Re, Pr, fd):
    """
    Calculate turbulent Nusselt number using Churchill-Zajic.

    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_Churchill_Zajic(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 (-).