def C_long_radius_nozzle(D, Do, rho, mu, m):
    r'''Calculates the coefficient of discharge of a long radius nozzle used
    for measuring flow rate of fluid, based on the geometry of the nozzle, 
    mass flow rate through the nozzle, and the density and viscosity of the
    fluid.
    
    .. math::
        C = 0.9965 - 0.00653\beta^{0.5} \left(\frac{10^6}{Re_D}\right)^{0.5}
        
    Parameters
    ----------
    D : float
        Upstream internal pipe diameter, [m]
    Do : float
        Diameter of long radius nozzle orifice at flow conditions, [m]
    rho : float
        Density of fluid at `P1`, [kg/m^3]
    mu : float
        Viscosity of fluid at `P1`, [Pa*s]
    m : float
        Mass flow rate of fluid through the nozzle, [kg/s]
        
    Returns
    -------
    C : float
        Coefficient of discharge of the long radius nozzle orifice, [-]

    Notes
    -----
    
    Examples
    --------
    >>> C_long_radius_nozzle(D=0.07391, Do=0.0422, rho=1.2, mu=1.8E-5, m=0.1)
    0.9805503704679863
    
    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 5167-3:2003 - Measurement of Fluid Flow by Means of Pressure 
       Differential Devices Inserted in Circular Cross-Section Conduits Running
       Full -- Part 3: Nozzles and Venturi Nozzles.
    '''
    A_pipe = pi/4.*D*D
    v = m/(A_pipe*rho)
    Re_D = rho*v*D/mu
    beta = Do/D
    return 0.9965 - 0.00653*beta**0.5*(1E6/Re_D)**0.5