polykin.flow.friction

Cd_sphere

Cd_sphere(Rep: float) -> float

Calculate the drag coefficient of an isolated sphere.

For laminar as well as for turbulent flow, the drag coefficient is given by:

\[ C_{d} = \frac{24}{Re_p} \left(1 + 0.173 Re_p^{0.657}\right) + \frac{0.413}{1 + 16300 Re_p^{-1.09}} \]

where \(Re_p = \rho v D_p / \mu\) is the particle Reynolds number.

References

• Turton, R., and O. Levenspiel. "A short note on the drag correlation for spheres", Powder technology 47.1 (1986): 83-86.

PARAMETER	DESCRIPTION
Rep	Particle Reynolds number. TYPE: float

RETURNS	DESCRIPTION
float	Drag coefficient for an isolated sphere.

See also

• vt_sphere: related method to estimate the terminal velocity.

Examples:

Calculate the drag coefficient for a tennis ball traveling at 30 m/s.

>>> from polykin.flow import Cd_sphere
>>> Dp = 6.7e-2  # m
>>> mu = 1.6e-5  # Pa·s
>>> rho = 1.2    # kg/m³
>>> v = 30.      # m/s
>>> Rep = rho*v*Dp/mu
>>> Cd = Cd_sphere(Rep)
>>> print(f"Cd = {Cd:.2f}")
Cd = 0.47

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

def Cd_sphere(Rep: float) -> float:
    r"""Calculate the drag coefficient of an isolated sphere.

    For laminar as well as for turbulent flow, the drag coefficient is given
    by:

    $$ C_{d} = \frac{24}{Re_p} \left(1 + 0.173 Re_p^{0.657}\right) 
             + \frac{0.413}{1 + 16300 Re_p^{-1.09}} $$

    where $Re_p = \rho v D_p / \mu$ is the particle Reynolds number.

    **References**

    * Turton, R., and O. Levenspiel. "A short note on the drag correlation for
      spheres", Powder technology 47.1 (1986): 83-86.

    Parameters
    ----------
    Rep : float
        Particle Reynolds number.

    Returns
    -------
    float
        Drag coefficient for an isolated sphere. 

    See also
    --------
    * [`vt_sphere`](vt_sphere.md): related method to estimate the terminal
      velocity.

    Examples
    --------
    Calculate the drag coefficient for a tennis ball traveling at 30 m/s.
    >>> from polykin.flow import Cd_sphere
    >>> Dp = 6.7e-2  # m
    >>> mu = 1.6e-5  # Pa·s
    >>> rho = 1.2    # kg/m³
    >>> v = 30.      # m/s
    >>> Rep = rho*v*Dp/mu
    >>> Cd = Cd_sphere(Rep)
    >>> print(f"Cd = {Cd:.2f}")
    Cd = 0.47
    """
    return 24/Rep*(1 + 0.173*Rep**0.657) + 0.413/(1 + 16300*Rep**(-1.09))

Graphical Illustration