r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [2]_ as in [1]_.

    .. math::
        Nu = \frac{(f/8)RePr}{12.48Pr^{2/3} - 7.853Pr^{1/3} + 3.613\ln Pr + 5.8 + C}\\
        C = 2.78\ln((f/8)^{0.5} Re/45)

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    fd : float
        Darcy friction factor [-]

    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    Range according to [1]_ is 0.5< Pr ≤ 2000  and 10^4 ≤ Re ≤ 5*10^6.

    Examples
    --------
    >>> turbulent_Sandall(Re=1E5, Pr=1.2, fd=0.0185)
    229.0514352970239

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Sandall, O. C., O. T. Hanna, and P. R. Mazet. “A New Theoretical
       Formula for Turbulent Heat and Mass Transfer with Gases or Liquids in
       Tube Flow.” The Canadian Journal of Chemical Engineering 58, no. 4
       (August 1, 1980): 443–47. doi:10.1002/cjce.5450580404.

def turbulent_Sandall(Re, Pr, fd):
    r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [2]_ as in [1]_.

    .. math::
        Nu = \frac{(f/8)RePr}{12.48Pr^{2/3} - 7.853Pr^{1/3} + 3.613\ln Pr + 5.8 + C}\\
        C = 2.78\ln((f/8)^{0.5} Re/45)

    Parameters
    ----------
    Re : float
        Reynolds number, [-]
    Pr : float
        Prandtl number, [-]
    fd : float
        Darcy friction factor [-]

    Returns
    -------
    Nu : float
        Nusselt number, [-]

    Notes
    -----
    Range according to [1]_ is 0.5< Pr ≤ 2000  and 10^4 ≤ Re ≤ 5*10^6.

    Examples
    --------
    >>> turbulent_Sandall(Re=1E5, Pr=1.2, fd=0.0185)
    229.0514352970239

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Sandall, O. C., O. T. Hanna, and P. R. Mazet. “A New Theoretical
       Formula for Turbulent Heat and Mass Transfer with Gases or Liquids in
       Tube Flow.” The Canadian Journal of Chemical Engineering 58, no. 4
       (August 1, 1980): 443–47. doi:10.1002/cjce.5450580404.
    '''
    C = 2.78*log((fd/8.)**0.5*Re/45.)
    return (fd/8.)**0.5*Re*Pr/(12.48*Pr**(2/3.) - 7.853*Pr**(1/3.) 
                               + 3.613*log(Pr) + 5.8 + C)