def Smith(x, rhol, rhog):
    """Calculates void fraction in two-phase flow according to the model of 
    [1]_, also given in [2]_ and [3]_.

    .. math::
        \\alpha = \\left\\{1 + \\left(\\frac{1-x}{x}\\right)
        \\left(\\frac{\\rho_g}{\\rho_l}\\right)\\left[K+(1-K)
        \\sqrt{\\frac{\\frac{\\rho_l}{\\rho_g} + K\\left(\\frac{1-x}{x}\\right)}
        {1 + K\\left(\\frac{1-x}{x}\\right)}}\\right] \\right\\}^{-1}

    Parameters
    ----------
    x : float
        Quality at the specific tube interval []
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]

    Returns
    -------
    alpha : float
        Void fraction (area of gas / total area of channel), [-]

    Notes
    -----
    [1]_ is an easy to read paper and has been reviewed.
    The form of the expression here is rearranged somewhat differently
    than in [1]_ but has been verified to be numerically equivalent. The form
    of this in [3]_ is missing a square root on a bracketed term; this appears
    in multiple papers by the authors.

    Examples
    --------
    >>> Smith(.4, 800, 2.5)
    0.959981235534199

    References
    ----------
    .. [1] Smith, S. L. "Void Fractions in Two-Phase Flow: A Correlation Based 
       upon an Equal Velocity Head Model." Proceedings of the Institution of 
       Mechanical Engineers 184, no. 1 (June 1, 1969): 647-64. 
       doi:10.1243/PIME_PROC_1969_184_051_02.  
    .. [2] Xu, Yu, and Xiande Fang. "Correlations of Void Fraction for Two-
       Phase Refrigerant Flow in Pipes." Applied Thermal Engineering 64, no. 
       1-2 (March 2014): 242–51. doi:10.1016/j.applthermaleng.2013.12.032. 
    .. [3] Dalkilic, A. S., S. Laohalertdecha, and S. Wongwises. "Effect of 
       Void Fraction Models on the Two-Phase Friction Factor of R134a during 
       Condensation in Vertical Downward Flow in a Smooth Tube." International 
       Communications in Heat and Mass Transfer 35, no. 8 (October 2008): 
       921-27. doi:10.1016/j.icheatmasstransfer.2008.04.001.
    """
    K = 0.4
    x_ratio = (1 - x) / x
    root = ((rhol / rhog + K * x_ratio) / (1 + K * x_ratio)) ** 0.5
    alpha = (1 + x_ratio * (rhog / rhol) * (K + (1 - K) * root)) ** -1
    return alpha
