def Froude_densimetric(V, L, rho1, rho2, heavy=True, g=g):
    """Calculates the densimetric Froude number :math:`Fr_{den}` for velocity
    `V` geometric length `L`, heavier fluid density `rho1`, and lighter fluid 
    density `rho2`. If desired, gravity can be specified as well. Depending on
    the application, this dimensionless number may be defined with the heavy
    phase or the light phase density in the numerator of the square root.
    For some applications, both need to be calculated. The default is to 
    calculate with the heavy liquid ensity on top; set `heavy` to False
    to reverse this.

    .. math::
        Fr = \\frac{V}{\\sqrt{gL}} \\sqrt{\\frac{\\rho_\\text{(1 or 2)}} 
        {\\rho_1 - \\rho_2}}

    Parameters
    ----------
    V : float
        Velocity of the specified phase, [m/s]
    L : float
        Characteristic length, no typical definition [m]
    rho1 : float
        Density of the heavier phase, [kg/m^3]
    rho2 : float
        Density of the lighter phase, [kg/m^3]
    heavy : bool, optional
        Whether or not the density used in the numerator is the heavy phase or
        the light phase, [-]
    g : float, optional
        Acceleration due to gravity, [m/s^2]

    Returns
    -------
    Fr_den : float
        Densimetric Froude number, [-]

    Notes
    -----
    Many alternate definitions including density ratios have been used.

    .. math::
        Fr = \\frac{\\text{Inertial Force}}{\\text{Gravity Force}}
        
    Where the gravity force is reduced by the relative densities of one fluid
    in another.
    
    Note that an Exception will be raised if rho1 > rho2, as the square root
    becomes negative.

    Examples
    --------
    >>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81)
    0.4134543386272418
    >>> Froude_densimetric(1.83, L=2., rho1=800, rho2=1.2, g=9.81, heavy=False)
    0.016013017679205096

    References
    ----------
    .. [1] Hall, A, G Stobie, and R Steven. "Further Evaluation of the 
       Performance of Horizontally Installed Orifice Plate and Cone 
       Differential Pressure Meters with Wet Gas Flows." In International 
       SouthEast Asia Hydrocarbon Flow Measurement Workshop, KualaLumpur,
       Malaysia, 2008.
    """
    if heavy:
        rho3 = rho1
    else:
        rho3 = rho2
    return V / (g * L) ** 0.5 * (rho3 / (rho1 - rho2)) ** 0.5
