r'''Calculates Nusselt number for natural convection around a vertical
    isothermal cylinder according to the results of [1]_ correlated by [2]_,
    presented in [3]_ and in more detail in [4]_.

    .. math::
        Nu_H = 0.48 Ra_H^{0.25},\; 10^{9} < Ra

        Nu_H = 51.5 + 0.0000726 Ra_H^{0.63},\; 10^{9} < Ra < 1.69 \times 10^{10}

        Nu_H = 0.148 Ra_H^{1/3} - 127.6 ,\; 1.69 \times 10^{10} < Ra

    Parameters
    ----------
    Pr : float
        Prandtl number [-]
    Gr : float
        Grashof number [-]
    turbulent : bool or None, optional
        Whether or not to force the correlation to return the turbulent
		 result; will return the laminar regime if False; leave as None for
        automatic selection

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

    Notes
    -----
    Author presents results as appropriate for both flat plates and cylinders.
    Height of 2.5 m with diameters of 2.4, 7.55, 15, 35, and 50 mm. Another
    experiment of diameter 58 mm and length of 6.5 m was considered.
    Cylinder of diameters 0.475 cm to 7.62 cm, L/D from 8 to 127.Transition
    between ranges is not smooth. If outside of range, no warning is given.
    Formulas are presented similarly in [3]_ and [4]_, but only [4]_ shows
    the transition formula.

    Examples
    --------
    >>> Nu_vertical_cylinder_Eigenson_Morgan(0.7, 2E10)
    230.55946525499715

    References
    ----------
    .. [1] Eigenson L (1940). Les lois gouvernant la transmission de la chaleur
       aux gaz biatomiques par les parois des cylindres verticaux dans le cas
       de convection naturelle. Dokl Akad Nauk SSSR 26:440-444
    .. [2] Morgan, V.T., The Overall Convective Heat Transfer from Smooth
       Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and
       J.P. Hartnett, V 11, 199-264, 1975.
    .. [3] Popiel, Czeslaw O. "Free Convection Heat Transfer from Vertical
       Slender Cylinders: A Review." Heat Transfer Engineering 29, no. 6
       (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
    .. [4] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
       Vertical Cylinders." In Natural Convection from Circular Cylinders,
       23-42. Springer, 2014.

def Nu_vertical_cylinder_Eigenson_Morgan(Pr, Gr, turbulent=None):
    r'''Calculates Nusselt number for natural convection around a vertical
    isothermal cylinder according to the results of [1]_ correlated by [2]_,
    presented in [3]_ and in more detail in [4]_.

    .. math::
        Nu_H = 0.48 Ra_H^{0.25},\; 10^{9} < Ra

        Nu_H = 51.5 + 0.0000726 Ra_H^{0.63},\; 10^{9} < Ra < 1.69 \times 10^{10}

        Nu_H = 0.148 Ra_H^{1/3} - 127.6 ,\; 1.69 \times 10^{10} < Ra

    Parameters
    ----------
    Pr : float
        Prandtl number [-]
    Gr : float
        Grashof number [-]
    turbulent : bool or None, optional
        Whether or not to force the correlation to return the turbulent
		 result; will return the laminar regime if False; leave as None for
        automatic selection

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

    Notes
    -----
    Author presents results as appropriate for both flat plates and cylinders.
    Height of 2.5 m with diameters of 2.4, 7.55, 15, 35, and 50 mm. Another
    experiment of diameter 58 mm and length of 6.5 m was considered.
    Cylinder of diameters 0.475 cm to 7.62 cm, L/D from 8 to 127.Transition
    between ranges is not smooth. If outside of range, no warning is given.
    Formulas are presented similarly in [3]_ and [4]_, but only [4]_ shows
    the transition formula.

    Examples
    --------
    >>> Nu_vertical_cylinder_Eigenson_Morgan(0.7, 2E10)
    230.55946525499715

    References
    ----------
    .. [1] Eigenson L (1940). Les lois gouvernant la transmission de la chaleur
       aux gaz biatomiques par les parois des cylindres verticaux dans le cas
       de convection naturelle. Dokl Akad Nauk SSSR 26:440-444
    .. [2] Morgan, V.T., The Overall Convective Heat Transfer from Smooth
       Circular Cylinders, in Advances in Heat Transfer, eds. T.F. Irvin and
       J.P. Hartnett, V 11, 199-264, 1975.
    .. [3] Popiel, Czeslaw O. "Free Convection Heat Transfer from Vertical
       Slender Cylinders: A Review." Heat Transfer Engineering 29, no. 6
       (June 1, 2008): 521-36. doi:10.1080/01457630801891557.
    .. [4] Boetcher, Sandra K. S. "Natural Convection Heat Transfer From
       Vertical Cylinders." In Natural Convection from Circular Cylinders,
       23-42. Springer, 2014.
    '''
    Ra = Pr*Gr
    if turbulent or (Ra > 1.69E10 and turbulent is None):
        return 0.148*Ra**(1/3.) - 127.6
    elif 1E9 < Ra < 1.69E10 and turbulent is not False:
        return 51.5 + 0.0000726*Ra**0.63
    else:
        return 0.48*Ra**0.25