def discharge_coefficient_to_K(D, Do, C):
    """Converts a discharge coefficient to a standard loss coefficient,
    for use in computation of the actual pressure drop of an orifice or other
    device.

    .. math::
        K = \\left[\\frac{\\sqrt{1-\\beta^4(1-C^2)}}{C\\beta^2} - 1\\right]^2
        
    Parameters
    ----------
    D : float
        Upstream internal pipe diameter, [m]
    Do : float
        Diameter of orifice at flow conditions, [m]
    C : float
        Coefficient of discharge of the orifice, [-]

    Returns
    -------
    K : float
        Loss coefficient with respect to the velocity and density of the fluid
        just upstream of the orifice, [-]

    Notes
    -----
    If expansibility is used in the orifice calculation, the result will not
    match with the specified pressure drop formula in [1]_; it can almost
    be matched by dividing the calculated mass flow by the expansibility factor
    and using that mass flow with the loss coefficient. 
    
    Examples
    --------
    >>> discharge_coefficient_to_K(D=0.07366, Do=0.05, C=0.61512)
    5.2314291729754
    
    References
    ----------
    .. [1] American Society of Mechanical Engineers. Mfc-3M-2004 Measurement 
       Of Fluid Flow In Pipes Using Orifice, Nozzle, And Venturi. ASME, 2001.
    .. [2] ISO 5167-2:2003 - Measurement of Fluid Flow by Means of Pressure 
       Differential Devices Inserted in Circular Cross-Section Conduits Running
       Full -- Part 2: Orifice Plates.
    """
    beta = Do / D
    beta2 = beta * beta
    beta4 = beta2 * beta2
    root_K = (1.0 - beta4 * (1.0 - C * C)) ** 0.5 / (C * beta2) - 1.0
    return root_K * root_K
