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

    .. math::
        Nu = \frac{(f/8)RePr}{1.2 + 11.8(f/8)^{0.5}(Pr-1)Pr^{-1/3}}

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

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

    Notes
    -----
    Range according to [1]_ 50 < Pr ≤ 600  and 5*10^4 ≤ Re ≤ 5*10^6.
    The extreme limits on range should be considered!

    Examples
    --------
    >>> turbulent_Friend_Metzner(Re=1E5, Pr=100., fd=0.0185)
    1738.3356262055322

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Friend, W. L., and A. B. Metzner. “Turbulent Heat Transfer inside
       Tubes and the Analogy among Heat, Mass, and Momentum Transfer.” AIChE
       Journal 4, no. 4 (December 1, 1958): 393-402. doi:10.1002/aic.690040404.

def turbulent_Friend_Metzner(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}{1.2 + 11.8(f/8)^{0.5}(Pr-1)Pr^{-1/3}}

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

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

    Notes
    -----
    Range according to [1]_ 50 < Pr ≤ 600  and 5*10^4 ≤ Re ≤ 5*10^6.
    The extreme limits on range should be considered!

    Examples
    --------
    >>> turbulent_Friend_Metzner(Re=1E5, Pr=100., fd=0.0185)
    1738.3356262055322

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] Friend, W. L., and A. B. Metzner. “Turbulent Heat Transfer inside
       Tubes and the Analogy among Heat, Mass, and Momentum Transfer.” AIChE
       Journal 4, no. 4 (December 1, 1958): 393-402. doi:10.1002/aic.690040404.
    '''
    return (fd/8.)*Re*Pr/(1.2 + 11.8*(fd/8.)**0.5*(Pr - 1.)*Pr**(-1/3.))