Froude number formula
=====================

The Froude number is based on the speed-to-length ratio as defined by Froude. It has
some analogy with the :ref:`Mach number <Mach number is flow speed over speed of sound>`,
but it is not frequently used in the field of theoretical fluid dynamics. It relates the
inertia forces in a system to the effects due to gravity, in other words, it is related
to the tendency of the fluid to make `gravity waves <https://en.wikipedia.org/wiki/Gravity_wave>`__.

**Notation:**

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

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Froude_number>`__.
#. `ScienceDirect <https://www.sciencedirect.com/topics/engineering/froude-number>`__.

..
    TODO: rename file

.. py:currentmodule:: symplyphysics.laws.hydro.froude_number

.. py:data:: flow_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.flow_speed`.

Symbol:
    :code:`u`

Latex:
    :math:`u`

Dimension:
    :code:`velocity`


.. py:data:: characteristic_length

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

Symbol:
    :code:`l_c`

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

Dimension:
    :code:`length`


.. py:data:: froude_number

    :attr:`~symplyphysics.symbols.classical_mechanics.froude_number`.

Symbol:
    :code:`Fr`

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

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`Fr = u / sqrt(g * l_c)`


    Latex:
        .. math::
            \text{Fr} = \frac{u}{\sqrt{g l_\text{c}}}