def Idelchik(dp, voidage, vs, rho, mu, L=1):
    """Calculates pressure drop across a packed bed of spheres as in [2]_,
    originally in [1]_.

    .. math::
        \\frac{\\Delta P}{L\\rho v_s^2} d_p  = \\frac{0.765}{\\epsilon^{4.2}}
        \\left(\\frac{30}{Re_l} + \\frac{3}{Re_l^{0.7}} + 0.3\\right)

    .. math::
        Re_l = (0.45/\\epsilon^{0.5})Re_{Erg}

    .. math::
        Re_{Erg} = \\frac{\\rho v_s  D_p}{\\mu(1-\\epsilon)}

    Parameters
    ----------
    dp : float
        Particle diameter of spheres [m]
    voidage : float
        Void fraction of bed packing [-]
    vs : float
        Superficial velocity of the fluid (volumetric flow rate/cross-sectional 
        area)[m/s]
    rho : float
        Density of the fluid [kg/m^3]
    mu : float
        Viscosity of the fluid, [Pa*s]
    L : float, optional
        Length the fluid flows in the packed bed [m]

    Returns
    -------
    dP : float
        Pressure drop across the bed [Pa]

    Notes
    -----
    :math:`0.001 < Re_{Erg} <1000`
    This equation is valid for void fractions between 0.3 and 0.8. Cited as
    by Bernshtein.

    Examples
    --------
    >>> Idelchik(dp=8E-4, voidage=0.4, vs=1E-3, rho=1E3, mu=1E-3)
    1571.909125999067

    References
    ----------
    .. [1] Idelchik, I. E. Flow Resistance: A Design Guide for Engineers.
       Hemisphere Publishing Corporation, New York, 1989.
    .. [2] Allen, K. G., T. W. von Backstrom, and D. G. Kroger. "Packed Bed
       Pressure Drop Dependence on Particle Shape, Size Distribution, Packing
       Arrangement and Roughness." Powder Technology 246 (September 2013):
       590-600. doi:10.1016/j.powtec.2013.06.022.
    """
    Re = rho * vs * dp / mu / (1 - voidage)
    Re = 0.45 / voidage ** 0.5 * Re
    right = 0.765 / voidage ** 4.2 * (30.0 / Re + 3.0 / Re ** 0.7 + 0.3)
    left = dp / L / rho / vs ** 2
    return right / left
