Apparent weight of a fully submersed body in fluid
==================================================

The *Archimedean force* acting on a body fully submersed in a fluid is equal to the weight of the
fluid displaced by the body. It can be derived that the weight of the body submersed in the fluid
is proportional to its weight in vacuum and also depends on the ratio of the fluid density and body
density.

**Notes:**

#. Positive apparent weight means that the body is sinking, whereas negative apparent weight means
   that the body is floating to the surface.

**Conditions:**

#. The body is completely *submersed* in the fluid.

**Links:**

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

..
    TODO: rename law

.. py:currentmodule:: symplyphysics.laws.hydro.weight_in_fluid_via_ratio_of_densities

.. py:data:: weight_in_fluid

    Apparent weight of the body submersed in the fluid. See :attr:`~symplyphysics.symbols.classical_mechanics.force`.

Symbol:
    :code:`W_fl`

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

Dimension:
    :code:`force`


.. py:data:: weight_in_vacuum

    Weight of the body in vacuum, i.e. its true weight. See :attr:`~symplyphysics.symbols.classical_mechanics.force`.

Symbol:
    :code:`W_vac`

Latex:
    :math:`W_\text{vac}`

Dimension:
    :code:`force`


.. 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:: body_density

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

Symbol:
    :code:`rho_b`

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

Dimension:
    :code:`mass/volume`


.. py:data:: law

    :code:`W_fl = W_vac * (1 - rho_fl / rho_b)`


    Latex:
        .. math::
            W_\text{fl} = W_\text{vac} \left(1 - \frac{\rho_\text{fl}}{\rho_\text{b}}\right)