def entrance_beveled_orifice(Di, do, l, angle):
    """Returns loss coefficient for a beveled or chamfered orifice entrance to 
    a pipe flush with the wall of a reservoir, as shown in [1]_.

    .. math::
        K = 0.0696\\left(1 - C_b\\frac{l}{d_o}\\right)\\lambda^2 + \\left(\\lambda
        -\\left(\\frac{d_o}{D_i}\\right)^2\\right)^2
        
    .. math::
        \\lambda = 1 + 0.622\\left[1-C_b\\left(\\frac{l}{d_o}\\right)^{\\frac{1-
        (l/d_o)^{0.25}}{2}}\\right]
    
    .. math::
        C_b = \\left(1 - \\frac{\\Psi}{90}\\right)\\left(\\frac{\\Psi}{90}
        \\right)^{\\frac{1}{1+l/d_o}}
        
    .. figure:: fittings/flush_mounted_beveled_orifice_entrance.png
       :scale: 30 %
       :alt: Beveled orifice entrace mounted straight; after [1]_

    Parameters
    ----------
    Di : float
        Inside diameter of pipe, [m]
    do : float
        Inside diameter of orifice, [m]
    l : float
        Length of bevel measured parallel to the pipe length, [m]
    angle : float
        Angle of bevel with respect to the pipe length, [degrees]

    Returns
    -------
    K : float
        Loss coefficient [-]

    Examples
    --------
    >>> entrance_beveled_orifice(Di=0.1, do=.07, l=0.003, angle=45)
    1.2987552913818574

    References
    ----------
    .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical
       and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.
    """
    Cb = (1 - angle / 90.0) * (angle / 90.0) ** (1.0 / (1 + l / do))
    lbd = 1 + 0.622 * (1 - Cb * (l / do) ** ((1 - (l / do) ** 0.25) / 2.0))
    return 0.0696 * (1 - Cb * l / do) * lbd ** 2 + (lbd - (do / Di) ** 2) ** 2
