polykin.transport.flow

fD_Haaland

fD_Haaland(Re: float, er: float) -> float

Calculate the Darcy friction factor using Haaland's equation.

For turbulent flow, i.e., \(Re \gtrsim 2300\), the friction factor is given by the following explicit expression:

\[ \frac{1}{\sqrt{f}}= -1.8 \log \left[\left(\frac{\epsilon/D}{3.7}\right)^{1.11} + \frac{6.9}{Re} \right] \]

This equation is as accurate as Colebrook's but has the advantage of being explicit.

References

• Haaland, S. E. "Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow", ASME. J. Fluids Eng. March 1983; 105(1): 89-90.

PARAMETER	DESCRIPTION
Re	Reynolds number. TYPE: float
er	Relative pipe roughness, \(\epsilon/D\). TYPE: float

RETURNS	DESCRIPTION
float	Darcy friction factor.

See also

• fD_Colebrook: alternative method.

Examples:

Calculate the friction factor for water flowing at 2 m/s through a PVC pipe with an internal diameter of 25 mm.

>>> from polykin.transport import fD_Haaland
>>> rho = 1e3 # kg/m³
>>> mu = 1e-3 # Pa·s
>>> D = 25e-3 # m
>>> v = 2.    # m/s
>>> Re = rho*v*D/mu
>>> er = 0.0015/25 # from pipe table
>>> fD = fD_Haaland(Re, er)
>>> print(f"fD = {fD:.3f}")
fD = 0.021

Source code in src/polykin/transport/flow.py

def fD_Haaland(Re: float, er: float) -> float:
    r"""Calculate the Darcy friction factor using Haaland's equation.

    For turbulent flow, i.e., $Re \gtrsim 2300$, the friction factor
    is given by the following explicit expression:

    $$ \frac{1}{\sqrt{f}}= -1.8 \log \left[\left(\frac{\epsilon/D}{3.7}\right)^{1.11} 
       + \frac{6.9}{Re} \right] $$

    This equation is as accurate as Colebrook's but has the advantage of
    being explicit.

    **References**

    * Haaland, S. E. "Simple and Explicit Formulas for the Friction Factor in
      Turbulent Pipe Flow", ASME. J. Fluids Eng. March 1983; 105(1): 89-90.

    Parameters
    ----------
    Re : float
        Reynolds number.
    er : float
        Relative pipe roughness, $\epsilon/D$.

    Returns
    -------
    float
        Darcy friction factor.

    See also
    --------
    * [`fD_Colebrook`](fD_Colebrook.md): alternative method.

    Examples
    --------
    Calculate the friction factor for water flowing at 2 m/s through a PVC pipe
    with an internal diameter of 25 mm.
    >>> from polykin.transport import fD_Haaland
    >>> rho = 1e3 # kg/m³
    >>> mu = 1e-3 # Pa·s
    >>> D = 25e-3 # m
    >>> v = 2.    # m/s
    >>> Re = rho*v*D/mu
    >>> er = 0.0015/25 # from pipe table
    >>> fD = fD_Haaland(Re, er)
    >>> print(f"fD = {fD:.3f}")
    fD = 0.021
    """
    check_range_warn(Re, 2.3e3, inf, 'Re')

    return (1/(1.8*log10((er/3.7)**1.11 + 6.9/Re)))**2

Graphical Illustration