Submerged volume of floating body via density ratio
===================================================

If a body is fully or partially submerged in a fluid, an Archimedes force
starts acting on it from the fluid pushing it in the opposite direction of
the gravity force.

The ratio of the body's volume submerged in a fluid to its total volume
depends on the ratio of the densities of the body and the fluid.

**Conditions:**

#. :math:`\rho \le \rho_\text{fl}`, so the body must be floating. See below for the
   description of the symbols.
#. The body must be in static equilibrium.

**Links:**

#. `Physics LibreTexts, formula 10.3.17 <https://phys.libretexts.org/Bookshelves/University_Physics/Physics_(Boundless)/10%3A_Fluids/10.3%3A_Archimedes_Principle>`__.

.. py:currentmodule:: symplyphysics.laws.hydro.submerged_volume_of_floating_body_via_density_ratio

.. py:data:: submerged_volume

    :attr:`~symplyphysics.symbols.classical_mechanics.volume` submerged in the fluid, which is equal to the volume of the displaced
    fluid.

Symbol:
    :code:`V_fl`

Latex:
    :math:`V_\text{fl}`

Dimension:
    :code:`volume`


.. py:data:: body_volume

    Total :attr:`~symplyphysics.symbols.classical_mechanics.volume` of the body.

Symbol:
    :code:`V`

Latex:
    :math:`V`

Dimension:
    :code:`volume`


.. py:data:: body_density

    :attr:`~symplyphysics.symbols.basic.density` of the body.

Symbol:
    :code:`rho`

Latex:
    :math:`\rho`

Dimension:
    :code:`mass/volume`


.. py:data:: fluid_density

    :attr:`~symplyphysics.symbols.basic.density` of the fluid.

Symbol:
    :code:`rho_fl`

Latex:
    :math:`\rho_\text{fl}`

Dimension:
    :code:`mass/volume`


.. py:data:: law

    :code:`V_fl / V = rho / rho_fl`


    Latex:
        .. math::
            \frac{V_\text{fl}}{V} = \frac{\rho}{\rho_\text{fl}}