polykin.reactors.rtd

Pe_tube

Pe_tube(Re: float, Sc: float | None = None) -> float

Calculate the Péclet number for flow through a circular tube.

For laminar flow, the tube Péclet number \(Pe=(v d_t)/D\) is estimated by the following expression:

\[ Pe = \left( \frac{1}{Re Sc} + \frac{Re Sc}{192} \right)^{-1} \]

where \(Re\) is the Reynolds number and \(Sc\) is the Schmidt number.

For turbulent flow, the tube Péclet number is estimated by the following expression:

\[ Pe = \left( \frac{3\times10^{7}}{Re^{2.1}} + \frac{1.35}{Re^{0.125}} \right)^{-1} \]

Note

The equation gives the Péclet number based on tube diameter. To obtain the Péclet number based on tube length, the Péclet number must be multiplied by the length-to-diameter ratio.

References

• Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley & Sons, 1999, p. 310.

PARAMETER	DESCRIPTION
Re	Reynolds number based on tube diameter. TYPE: float
Sc	Schmidt number. Required only for laminar flow. TYPE: float | None DEFAULT: None

RETURNS	DESCRIPTION
float	Péclet number based on tube diameter.

Source code in src/polykin/reactors/rtd.py

def Pe_tube(Re: float, Sc: float | None = None) -> float:
    r"""Calculate the Péclet number for flow through a circular tube.

    For laminar flow, the tube Péclet number $Pe=(v d_t)/D$ is estimated by the
    following expression:

    $$ Pe = \left( \frac{1}{Re Sc} + \frac{Re Sc}{192} \right)^{-1} $$

    where $Re$ is the Reynolds number and $Sc$ is the Schmidt number.

    For turbulent flow, the tube Péclet number is estimated by the following
    expression:

    $$ Pe = \left( \frac{3\times10^{7}}{Re^{2.1}} + \frac{1.35}{Re^{0.125}} \right)^{-1} $$  

    !!! note

        The equation gives the Péclet number based on tube diameter. To obtain
        the Péclet number based on tube length, the Péclet number must be
        multiplied by the length-to-diameter ratio.

    **References**

    * Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley &
      Sons, 1999, p. 310.

    Parameters
    ----------
    Re : float
        Reynolds number based on tube diameter.
    Sc : float | None
        Schmidt number. Required only for laminar flow.

    Returns
    -------
    float
        Péclet number based on tube diameter.
    """
    if Re < 2300:
        if Sc is None:
            raise ValueError("`Sc` must be specified for laminar flow.")
        return 1/(1/(Re*Sc) + (Re*Sc)/192)
    else:
        # to be checked / improved
        return 1/(3e7/Re**2.1 + 1.35/Re**0.125)