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

    .. math::
        Nu = \frac{Re Pr (f/8)^{0.5}} {4.5 + [0.155(Re(f/8)^{0.5})^{0.54}
        + (8/f)^{0.5}]Pr^{0.5}}

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

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

    Notes
    -----
    0.7 ≤ Pr ≤ 14.3 and 10^4 ≤ Re ≤ 5E4 and 0.0021 ≤ eD ≤ 0.095

    Examples
    --------
    >>> turbulent_Gowen_Smith(Re=1E5, Pr=1.2, fd=0.0185)
    131.72530453824106

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Gowen, R. A., and J. W. Smith. “Turbulent Heat Transfer from Smooth
       and Rough Surfaces.” International Journal of Heat and Mass Transfer 11,
       no. 11 (November 1968): 1657–74. doi:10.1016/0017-9310(68)90046-X.

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

    .. math::
        Nu = \frac{Re Pr (f/8)^{0.5}} {4.5 + [0.155(Re(f/8)^{0.5})^{0.54}
        + (8/f)^{0.5}]Pr^{0.5}}

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

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

    Notes
    -----
    0.7 ≤ Pr ≤ 14.3 and 10^4 ≤ Re ≤ 5E4 and 0.0021 ≤ eD ≤ 0.095

    Examples
    --------
    >>> turbulent_Gowen_Smith(Re=1E5, Pr=1.2, fd=0.0185)
    131.72530453824106

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Gowen, R. A., and J. W. Smith. “Turbulent Heat Transfer from Smooth
       and Rough Surfaces.” International Journal of Heat and Mass Transfer 11,
       no. 11 (November 1968): 1657–74. doi:10.1016/0017-9310(68)90046-X.
    '''
    return Re*Pr*(fd/8.)**0.5/(4.5 + (0.155*(Re*(fd/8.)**0.5)**0.54 + (8./fd)**0.5)*Pr**0.5)