def diameter_ratio_cone_meter(D, Dc):
    """Calculates the diameter ratio `beta` used to characterize a cone 
    flow meter.
    
    .. math::
        \\beta = \\sqrt{1 - \\frac{d_c^2}{D^2}}
        
    Parameters
    ----------
    D : float
        Upstream internal pipe diameter, [m]
    Dc : float
        Diameter of the largest end of the cone meter, [m]
        
    Returns
    -------
    beta : float
        Cone meter diameter ratio, [-]

    Notes
    -----
    
    Examples
    --------
    >>> diameter_ratio_cone_meter(D=0.2575, Dc=0.184)
    0.6995709873957624
    
    References
    ----------
    .. [1] Hollingshead, Colter. "Discharge Coefficient Performance of Venturi,
       Standard Concentric Orifice Plate, V-Cone, and Wedge Flow Meters at 
       Small Reynolds Numbers." May 1, 2011. 
       https://digitalcommons.usu.edu/etd/869.
    """
    D_ratio = Dc / D
    return (1.0 - D_ratio * D_ratio) ** 0.5
