def velocity_of_approach_factor(D, Do):
    """Calculates a factor for orifice plate design called the `velocity of
    approach`.
    
    .. math::
        \\text{Velocity of approach} = \\frac{1}{\\sqrt{1 - \\beta^4}}
        
    Parameters
    ----------
    D : float
        Upstream internal pipe diameter, [m]
    Do : float
        Diameter of orifice at flow conditions, [m]

    Returns
    -------
    velocity_of_approach : float
        Coefficient of discharge of the orifice, [-]

    Notes
    -----
    
    Examples
    --------
    >>> velocity_of_approach_factor(D=0.0739, Do=0.0222)
    1.0040970074165514
    
    References
    ----------
    .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
       Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
    """
    return (1.0 - (Do / D) ** 4) ** -0.5
