def Zigrang_Sylvester_1(Re, eD):
    r'''Calculates Darcy friction factor using the method in
     Zigrang and Sylvester (1982) [2]_ as shown in [1]_.

    .. math::
        \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7D}
        - \frac{5.02}{Re}\log A_5\right]

        A_5 = \frac{\epsilon}{3.7D} + \frac{13}{Re}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    eD : float
        Relative roughness, [-]

    Returns
    -------
    fd : float
        Darcy friction factor [-]

    Notes
    -----
    Range is 4E3 <= Re <= 1E8;  4E-5 <= eD <= 5E-2.

    Examples
    --------
    >>> Zigrang_Sylvester_1(1E5, 1E-4)
    0.018646892425980794

    References
    ----------
    .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and
       Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence
       and Combustion 90, no. 1 (January 1, 2013): 1-27.
       doi:10.1007/s10494-012-9419-7
    .. [2] 	Zigrang, D. J., and N. D. Sylvester."Explicit Approximations to the
       Solution of Colebrook's Friction Factor Equation." AIChE Journal 28,
       no. 3 (May 1, 1982): 514-15. doi:10.1002/aic.690280323.
    '''
    A5 = eD/3.7 + 13/Re
    ff = (-4*log10(eD/3.7 - 5.02/Re*log10(A5)))**-2
    return 4*ff
r'''Calculates Darcy friction factor using the method in
     Zigrang and Sylvester (1982) [2]_ as shown in [1]_.

    .. math::
        \frac{1}{\sqrt{f_f}} = -4\log\left[\frac{\epsilon}{3.7D}
        - \frac{5.02}{Re}\log A_5\right]

        A_5 = \frac{\epsilon}{3.7D} + \frac{13}{Re}

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    eD : float
        Relative roughness, [-]

    Returns
    -------
    fd : float
        Darcy friction factor [-]

    Notes
    -----
    Range is 4E3 <= Re <= 1E8;  4E-5 <= eD <= 5E-2.

    Examples
    --------
    >>> Zigrang_Sylvester_1(1E5, 1E-4)
    0.018646892425980794

    References
    ----------
    .. [1] Winning, H. and T. Coole. "Explicit Friction Factor Accuracy and
       Computational Efficiency for Turbulent Flow in Pipes." Flow, Turbulence
       and Combustion 90, no. 1 (January 1, 2013): 1-27.
       doi:10.1007/s10494-012-9419-7
    .. [2] 	Zigrang, D. J., and N. D. Sylvester."Explicit Approximations to the
       Solution of Colebrook's Friction Factor Equation." AIChE Journal 28,
       no. 3 (May 1, 1982): 514-15. doi:10.1002/aic.690280323.