r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [2]_ and [3]_ as in [1]_.

    .. math::
        Nu = \frac{(f/8)RePr}{C+12.7(f/8)^{1/2}(Pr^{2/3}-1)}\\
        C = 1.07 + 900/Re - [0.63/(1+10Pr)]

    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 ≤ 10^6  and 4000 ≤ Re ≤ 5*10^6

    Examples
    --------
    >>> turbulent_Petukhov_Kirillov_Popov(Re=1E5, Pr=1.2, fd=0.0185)
    250.11935088905105

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] B. S. Petukhov, and V. V. Kirillov, "The Problem of Heat Exchange
       in the Turbulent Flow of Liquids in Tubes," (Russian) Teploenergetika,
       (4): 63-68, 1958
    .. [3] B. S. Petukhov and V. N. Popov, "Theoretical Calculation of Heat
       Exchange in Turbulent Flow in Tubes of an Incompressible Fluidwith
       Variable Physical Properties," High Temp., (111): 69-83, 1963.

def turbulent_Petukhov_Kirillov_Popov(Re=None, Pr=None, fd=None):
    r'''Calculates internal convection Nusselt number for turbulent flows
    in pipe according to [2]_ and [3]_ as in [1]_.

    .. math::
        Nu = \frac{(f/8)RePr}{C+12.7(f/8)^{1/2}(Pr^{2/3}-1)}\\
        C = 1.07 + 900/Re - [0.63/(1+10Pr)]

    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 ≤ 10^6  and 4000 ≤ Re ≤ 5*10^6

    Examples
    --------
    >>> turbulent_Petukhov_Kirillov_Popov(Re=1E5, Pr=1.2, fd=0.0185)
    250.11935088905105

    References
    ----------
    .. [1] Rohsenow, Warren and James Hartnett and Young Cho. Handbook of Heat
       Transfer, 3E. New York: McGraw-Hill, 1998.
    .. [2] B. S. Petukhov, and V. V. Kirillov, "The Problem of Heat Exchange
       in the Turbulent Flow of Liquids in Tubes," (Russian) Teploenergetika,
       (4): 63-68, 1958
    .. [3] B. S. Petukhov and V. N. Popov, "Theoretical Calculation of Heat
       Exchange in Turbulent Flow in Tubes of an Incompressible Fluidwith
       Variable Physical Properties," High Temp., (111): 69-83, 1963.
    '''
    C = 1.07 + 900./Re - (0.63/(1. + 10.*Pr))
    return (fd/8.)*Re*Pr/(C + 12.7*(fd/8.)**0.5*(Pr**(2/3.) - 1.))