FT_CRANE

Overview

The FT_CRANE function calculates the Crane fully turbulent Darcy friction factor for flow in commercial pipe. This specialized friction factor is used with the Crane Technical Paper No. 410 (commonly known as Crane TP 410) methodology for calculating pressure loss coefficients (K-factors) in pipe fittings, valves, and other flow elements. The Crane TP 410 manual, titled Flow of Fluids Through Valves, Fittings, and Pipe, is an industry-standard reference for hydraulic calculations in piping systems.

Unlike general friction factor correlations that require both Reynolds number and relative roughness, this function requires only the pipe inner diameter. This is because the Crane friction factor is specifically intended for determining loss coefficients for fittings rather than calculating friction losses along straight pipe runs. The friction factor values are tabulated in Crane TP 410 for standard pipe sizes and are intended to represent fully turbulent flow conditions in commercial steel pipe.

This implementation uses the fluids library, which reconstructs the tabulated Crane friction factors by applying the Colebrook equation with diameter-dependent roughness values from the Farshad correlation for bare carbon steel pipe. The effective Reynolds number term (\rho V / \mu) is set to 7.5 \times 10^6 to match the published table values. The underlying Colebrook equation is:

\frac{1}{\sqrt{f}} = -2 \log_{10} \left( \frac{\varepsilon / D}{3.7} + \frac{2.51}{\text{Re} \sqrt{f}} \right)

where f is the Darcy friction factor, \varepsilon is the pipe roughness, D is the pipe diameter, and \text{Re} is the Reynolds number. For the Crane method, this equation is evaluated at fully turbulent conditions. For further details, see the fluids friction documentation.

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

Excel Usage

=FT_CRANE(D)

• D (float, required): Pipe inner diameter (m)

Returns (float): Darcy friction factor for fully turbulent flow, or error message (str).

Examples

Example 1: Typical commercial pipe 100mm diameter

Inputs:

D
0.1

Excel formula:

=FT_CRANE(0.1)

Expected output:

0.0163

Example 2: Small pipe diameter 25mm

Inputs:

D
0.025

Excel formula:

=FT_CRANE(0.025)

Expected output:

0.0226

Example 3: Large pipe diameter 500mm

Inputs:

D
0.5

Excel formula:

=FT_CRANE(0.5)

Expected output:

0.0118

Example 4: Medium pipe diameter 200mm

Inputs:

D
0.2

Excel formula:

=FT_CRANE(0.2)

Expected output:

0.0152

Python Code

import micropip
await micropip.install(["fluids"])
from fluids.friction import ft_Crane as fluids_ft_Crane

def ft_crane(D):
    """
    Calculate the Crane fully turbulent Darcy friction factor for flow in commercial pipe.

    See: https://fluids.readthedocs.io/fluids.friction.html#fluids.friction.ft_Crane

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

    Args:
        D (float): Pipe inner diameter (m)

    Returns:
        float: Darcy friction factor for fully turbulent flow, or error message (str).
    """
    try:
        D = float(D)
    except (ValueError, TypeError):
        return "Error: D must be a number."

    if D <= 0:
        return "Error: D must be positive."

    try:
        result = fluids_ft_Crane(D)
        return float(result)
    except Exception as e:
        return f"Error computing ft_crane: {str(e)}"

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