Volume flux is constant
=======================

The product of the area and the fluid speed, which is called the *volume flux*, is constant
at all points along the tube of flow of an incompressible liquid. This equation is also
known as the *equation of continuity*.

**Conditions:**

#. The fluid is :ref:`ideal <ideal_fluid_def>`.

**Links:**

#. `Engineering LibreTexts, derivable from here <https://eng.libretexts.org/Bookshelves/Aerospace_Engineering/Fundamentals_of_Aerospace_Engineering_(Arnedo)/03%3A_Aerodynamics/3.01%3A_Fundamentals_of_fluid_mechanics/3.1.02%3A_Continuity_equation>`__.

.. py:currentmodule:: symplyphysics.laws.hydro.volume_flux_is_constant

.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: tube_area

    Cross-sectional :attr:`~symplyphysics.symbols.classical_mechanics.area` of the tube of flow as a function of :attr:`~time`.

Symbol:
    :code:`A(t)`

Latex:
    :math:`A{\left(t \right)}`

Dimension:
    :code:`area`


.. py:data:: flow_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.flow_speed` of the fluid as a function of :attr:`~time`.

Symbol:
    :code:`u(t)`

Latex:
    :math:`u{\left(t \right)}`

Dimension:
    :code:`velocity`


.. py:data:: law

    :code:`Derivative(A(t) * u(t), t) = 0`


    Latex:
        .. math::
            \frac{d}{d t} A{\left(t \right)} u{\left(t \right)} = 0