r'''Calculates drag coefficient of a smooth sphere using the method in
    [1]_ as described in [2]_.

    .. math::
        C_D = \left[\frac{1}{(\phi_1 + \phi_2)^{-1} + (\phi_3)^{-1}} + \phi_4\right]^{0.1}

        \phi_1 = (24Re^{-1})^{10} + (21Re^{-0.67})^{10} + (4Re^{-0.33})^{10} + 0.4^{10}

        \phi_2 = \left[(0.148Re^{0.11})^{-10} + (0.5)^{-10}\right]^{-1}

        \phi_3 = (1.57\times10^8Re^{-1.625})^{10}

        \phi_4 = \left[(6\times10^{-17}Re^{2.63})^{-10} + (0.2)^{-10}\right]^{-1}

    Parameters
    ----------
    Re : float
        Reynolds number of the sphere, [-]

    Returns
    -------
    Cd : float
        Drag coefficient [-]

    Notes
    -----
    Range is Re <= 1E6.
    Original work has been reviewed.

    Examples
    --------
    >>> Almedeij(200.)
    0.7114768646813396

    References
    ----------
    .. [1] Almedeij, Jaber. "Drag Coefficient of Flow around a Sphere: Matching
       Asymptotically the Wide Trend." Powder Technology 186, no. 3
       (September 10, 2008): 218-23. doi:10.1016/j.powtec.2007.12.006.
    .. [2] Barati, Reza, Seyed Ali Akbar Salehi Neyshabouri, and Goodarz
       Ahmadi. "Development of Empirical Models with High Accuracy for
       Estimation of Drag Coefficient of Flow around a Smooth Sphere: An
       Evolutionary Approach." Powder Technology 257 (May 2014): 11-19.
       doi:10.1016/j.powtec.2014.02.045.

def Almedeij(Re):
    r'''Calculates drag coefficient of a smooth sphere using the method in
    [1]_ as described in [2]_.

    .. math::
        C_D = \left[\frac{1}{(\phi_1 + \phi_2)^{-1} + (\phi_3)^{-1}} + \phi_4\right]^{0.1}

        \phi_1 = (24Re^{-1})^{10} + (21Re^{-0.67})^{10} + (4Re^{-0.33})^{10} + 0.4^{10}

        \phi_2 = \left[(0.148Re^{0.11})^{-10} + (0.5)^{-10}\right]^{-1}

        \phi_3 = (1.57\times10^8Re^{-1.625})^{10}

        \phi_4 = \left[(6\times10^{-17}Re^{2.63})^{-10} + (0.2)^{-10}\right]^{-1}

    Parameters
    ----------
    Re : float
        Reynolds number of the sphere, [-]

    Returns
    -------
    Cd : float
        Drag coefficient [-]

    Notes
    -----
    Range is Re <= 1E6.
    Original work has been reviewed.

    Examples
    --------
    >>> Almedeij(200.)
    0.7114768646813396

    References
    ----------
    .. [1] Almedeij, Jaber. "Drag Coefficient of Flow around a Sphere: Matching
       Asymptotically the Wide Trend." Powder Technology 186, no. 3
       (September 10, 2008): 218-23. doi:10.1016/j.powtec.2007.12.006.
    .. [2] Barati, Reza, Seyed Ali Akbar Salehi Neyshabouri, and Goodarz
       Ahmadi. "Development of Empirical Models with High Accuracy for
       Estimation of Drag Coefficient of Flow around a Smooth Sphere: An
       Evolutionary Approach." Powder Technology 257 (May 2014): 11-19.
       doi:10.1016/j.powtec.2014.02.045.
    '''
    phi4 = ((6E-17*Re**2.63)**-10 + 0.2**-10)**-1
    phi3 = (1.57E8*Re**-1.625)**10
    phi2 = ((0.148*Re**0.11)**-10 + 0.5**-10)**-1
    phi1 = (24*Re**-1)**10 + (21*Re**-0.67)**10 + (4*Re**-0.33)**10 + 0.4**10
    Cd = (1/((phi1 + phi2)**-1 + phi3**-1) + phi4)**0.1
    return Cd