def Matsumoto_1974(mp, rhop, dp, rhog, D, Vterminal=1):
    r'''Calculates saltation velocity of the gas for pneumatic conveying,
    according to [1]_. Also described in [2]_.

    .. math::
        \mu = 0.448 \left(\frac{\rho_p}{\rho_f}\right)^{0.50}\left(\frac{Fr_p}
        {10}\right)^{-1.75}\left(\frac{Fr_s}{10}\right)^{3}

    .. math::
        Fr_s = \frac{V_{salt}}{\sqrt{gD}}

    .. math::
        Fr_p = \frac{V_{terminal}}{\sqrt{gd_p}}

    .. math::
        \mu = \frac{m_p}{\frac{\pi}{4}D^2V \rho_f}

    Parameters
    ----------
    mp : float
        Solid mass flow rate, [kg/s]
    rhop : float
        Particle density, [kg/m^3]
    dp : float
        Particle diameter, [m]
    rhog : float
        Gas density, [kg/m^3]
    D : float
        Diameter of pipe, [m]
    Vterminal : float
        Terminal velocity of particle settling in gas, [m/s]

    Returns
    -------
    V : float
        Saltation velocity of gas, [m/s]

    Notes
    -----
    Model is rearranged to be explicit in terms of saltation velocity
    internally.
    Result looks high, something may be wrong.
    For particles > 0.3 mm.

    Examples
    --------
    >>> Matsumoto_1974(mp=1., rhop=1000., dp=1E-3, rhog=1.2, D=0.1, Vterminal=5.24)
    19.583617317317895

    References
    ----------
    .. [1] Matsumoto, Shigeru, Michio Kara, Shozaburo Saito, and Siro Maeda.
       "Minimum Transport Velocity for Horizontal Pneumatic Conveying."
       Journal of Chemical Engineering of Japan 7, no. 6 (1974): 425-30.
       doi:10.1252/jcej.7.425.
    .. [2] Jones, Peter J., and L. S. Leung. "A Comparison of Correlations for
       Saltation Velocity in Horizontal Pneumatic Conveying." Industrial &
       Engineering Chemistry Process Design and Development 17, no. 4
       (October 1, 1978): 571-75. doi:10.1021/i260068a031
    '''
    A = pi/4*D**2
    Frp = Vterminal/(g*dp)**0.5
    Frs_sorta = 1./(g*D)**0.5
    expression1 = 0.448*(rhop/rhog)**0.5*(Frp/10.)**-1.75*(Frs_sorta/10.)**3
    expression2 = mp/rhog/A
    return (expression2/expression1)**(1/4.)
def Matsumoto_1974 ( mp , rhop , dp , rhog , D , Vterminal = 1 ) : A = pi / 4 * D ** 2 Frp = Vterminal / ( g * dp ) ** 0.5 Frs_sorta = 1. / ( g * D ) ** 0.5 expression1 = 0.448 * ( rhop / rhog ) ** 0.5 * ( Frp / 10. ) ** - 1.75 * ( Frs_sorta / 10. ) ** 3 expression2 = mp / rhog / A return ( expression2 / expression1 ) ** ( 1 / 4. )
r'''Calculates saltation velocity of the gas for pneumatic conveying,
    according to [1]_. Also described in [2]_.

    .. math::
        \mu = 0.448 \left(\frac{\rho_p}{\rho_f}\right)^{0.50}\left(\frac{Fr_p}
        {10}\right)^{-1.75}\left(\frac{Fr_s}{10}\right)^{3}

    .. math::
        Fr_s = \frac{V_{salt}}{\sqrt{gD}}

    .. math::
        Fr_p = \frac{V_{terminal}}{\sqrt{gd_p}}

    .. math::
        \mu = \frac{m_p}{\frac{\pi}{4}D^2V \rho_f}

    Parameters
    ----------
    mp : float
        Solid mass flow rate, [kg/s]
    rhop : float
        Particle density, [kg/m^3]
    dp : float
        Particle diameter, [m]
    rhog : float
        Gas density, [kg/m^3]
    D : float
        Diameter of pipe, [m]
    Vterminal : float
        Terminal velocity of particle settling in gas, [m/s]

    Returns
    -------
    V : float
        Saltation velocity of gas, [m/s]

    Notes
    -----
    Model is rearranged to be explicit in terms of saltation velocity
    internally.
    Result looks high, something may be wrong.
    For particles > 0.3 mm.

    Examples
    --------
    >>> Matsumoto_1974(mp=1., rhop=1000., dp=1E-3, rhog=1.2, D=0.1, Vterminal=5.24)
    19.583617317317895

    References
    ----------
    .. [1] Matsumoto, Shigeru, Michio Kara, Shozaburo Saito, and Siro Maeda.
       "Minimum Transport Velocity for Horizontal Pneumatic Conveying."
       Journal of Chemical Engineering of Japan 7, no. 6 (1974): 425-30.
       doi:10.1252/jcej.7.425.
    .. [2] Jones, Peter J., and L. S. Leung. "A Comparison of Correlations for
       Saltation Velocity in Horizontal Pneumatic Conveying." Industrial &
       Engineering Chemistry Process Design and Development 17, no. 4
       (October 1, 1978): 571-75. doi:10.1021/i260068a031