def diffuser_curved(Di1, Di2, l):
    """Returns loss coefficient for any curved wall pipe expansion
    as shown in [1]_.

    .. math::
        K_1 = \\phi(1.43-1.3\\beta^2)(1-\\beta^2)^2

    .. math::
        \\phi = 1.01 - 0.624\\frac{l}{d_1} + 0.30\\left(\\frac{l}{d_1}\\right)^2
        - 0.074\\left(\\frac{l}{d_1}\\right)^3 + 0.0070\\left(\\frac{l}{d_1}\\right)^4

    .. figure:: fittings/curved_wall_diffuser.png
       :scale: 25 %
       :alt: diffuser curved; after [1]_

    Parameters
    ----------
    Di1 : float
        Inside diameter of original pipe (smaller), [m]
    Di2 : float
        Inside diameter of following pipe (larger), [m]
    l : float
        Length of the curve along the pipe axis, [m]

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

    Notes
    -----
    Beta^2 should be between 0.1 and 0.9.
    A small mismatch between tabulated values of this function in table 11.3
    is observed with the equation presented.

    Examples
    --------
    >>> diffuser_curved(Di1=.25**0.5, Di2=1., l=2.)
    0.2299781250000002

    References
    ----------
    .. [1] Rennels, Donald C., and Hobart M. Hudson. Pipe Flow: A Practical
       and Comprehensive Guide. 1st edition. Hoboken, N.J: Wiley, 2012.
    """
    beta = Di1 / Di2
    phi = 1.01 - 0.624 * l / Di1 + 0.3 * (l / Di1) ** 2 - 0.074 * (l / Di1
        ) ** 3 + 0.007 * (l / Di1) ** 4
    return phi * (1.43 - 1.3 * beta ** 2) * (1 - beta ** 2) ** 2
