def flow_coefficient(D, Do, C):
    """Calculates a factor for differential pressure flow meter design called 
    the `flow coefficient`. This should not be confused with the flow 
    coefficient often used when discussing valves.
    
    .. math::
        \\text{Flow coefficient} = \\frac{C}{\\sqrt{1 - \\beta^4}}
        
    Parameters
    ----------
    D : float
        Upstream internal pipe diameter, [m]
    Do : float
        Diameter of flow meter characteristic dimension at flow conditions, [m]
    C : float
        Coefficient of discharge of the flow meter, [-]

    Returns
    -------
    flow_coefficient : float
        Differential pressure flow meter flow coefficient, [-]

    Notes
    -----
    This measure is used not just for orifices but for other differential 
    pressure flow meters [2]_.
    
    It is sometimes given the symbol K. It is also equal to the product of the
    diacharge coefficient and the velocity of approach factor [2]_.
    
    Examples
    --------
    >>> flow_coefficient(D=0.0739, Do=0.0222, C=0.6)
    0.6024582044499308
    
    References
    ----------
    .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
       Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
    .. [2] Miller, Richard W. Flow Measurement Engineering Handbook. 3rd
       edition. New York: McGraw-Hill Education, 1996.
    """
    return C * (1.0 - (Do / D) ** 4) ** -0.5
