polykin.reactors.rtd

E_laminar_flow

E_laminar_flow(t: float, tavg: float) -> float

Differential residence time distribution for a tubular reactor with laminar flow.

\[ E(t) = \begin{cases} 0 , & t < \bar{t}/2 \\ \frac{1}{2}\frac{\bar{t}^2}{t^3}, & \text{else} \end{cases} \]

References

• Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley & Sons, 1999, p. 343.

PARAMETER	DESCRIPTION
t	Residence time. TYPE: float
tavg	Average residence time, \(\bar{t}\). TYPE: float

RETURNS	DESCRIPTION
float	Differential residence time distribution.

See also

• F_laminar_flow: related method to determine the cumulative distribution.

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

def E_laminar_flow(t: float, tavg: float) -> float:
    r"""Differential residence time distribution for a tubular reactor with
    laminar flow.

    $$ E(t) =
    \begin{cases}
        0 ,                               & t < \bar{t}/2 \\
        \frac{1}{2}\frac{\bar{t}^2}{t^3}, & \text{else}
    \end{cases} $$

    **References**

    * Levenspiel, O. "Chemical reaction engineering", 3rd ed., John Wiley &
      Sons, 1999, p. 343.

    Parameters
    ----------
    t : float
        Residence time.
    tavg : float
        Average residence time, $\bar{t}$.

    Returns
    -------
    float
        Differential residence time distribution.

    See also
    --------
    * [`F_laminar_flow`](F_laminar_flow.md): related method to determine the
      cumulative distribution.
    """
    q = t/tavg
    if q < 1/2:
        return 0
    else:
        return 0.5 * tavg**2 / t**3