Grashof number
==============

The Grashof number (Gr) is a dimensionless number which approximates the ratio of the
buoyancy to viscous forces acting on a fluid. It arises in situations involving natural convection
and is analogous to the Reynolds number.

**Notation:**

#. :math:`g` (:code:`g`) is :attr:`~symplyphysics.quantities.acceleration_due_to_gravity`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Grashof_number#Definition>`__.

.. py:currentmodule:: symplyphysics.laws.thermodynamics.grashof_number

.. py:data:: grashof_number

    :attr:`~symplyphysics.symbols.thermodynamics.grashof_number` of the fluid.

Symbol:
    :code:`Gr`

Latex:
    :math:`\text{Gr}`

Dimension:
    :code:`dimensionless`


.. py:data:: volumetric_expansion_coefficient

    Volumetric (see :attr:`~symplyphysics.symbols.classical_mechanics.volume`) :attr:`~symplyphysics.symbols.thermodynamics.thermal_expansion_coefficient` of the body.

Symbol:
    :code:`alpha_V`

Latex:
    :math:`\alpha_{V}`

Dimension:
    :code:`1/temperature`


.. py:data:: surface_temperature

    :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the surface of the fluid.

Symbol:
    :code:`T_s`

Latex:
    :math:`T_\text{s}`

Dimension:
    :code:`temperature`


.. py:data:: bulk_temperature

    Average :attr:`~symplyphysics.symbols.thermodynamics.temperature` of the inside of the fluid.

Symbol:
    :code:`T_b`

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

Dimension:
    :code:`temperature`


.. py:data:: characteristic_length

    :attr:`~symplyphysics.symbols.basic.characteristic_length` of the fluid body.

Symbol:
    :code:`l_c`

Latex:
    :math:`l_\text{c}`

Dimension:
    :code:`length`


.. py:data:: kinematic_viscosity

    :attr:`~symplyphysics.symbols.thermodynamics.kinematic_viscosity` of the fluid.

Symbol:
    :code:`nu`

Latex:
    :math:`\nu`

Dimension:
    :code:`area/time`


.. py:data:: law

    :code:`Gr = g * alpha_V * (T_s - T_b) * l_c^3 / nu^2`


    Latex:
        .. math::
            \text{Gr} = \frac{g \alpha_{V} \left(T_\text{s} - T_\text{b}\right) l_\text{c}^{3}}{\nu^{2}}