Inner pressure is constant
==========================

Bernoulli's equation applied to an ideal liquid specifies that the inner pressure of the
fluid is constant at all points along a streamline.

**Conditions:**

#. The fluid must be :ref:`ideal <ideal_fluid_def>`.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Bernoulli%27s_principle#Simplified_form>`__.

.. py:currentmodule:: symplyphysics.laws.hydro.inner_pressure_is_constant

.. py:data:: time

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

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: inner_pressure

    Inner pressure of the fluid at a chosen point in space as a function of :attr:`~time`.
    See :ref:`Inner pressure is sum of pressures`.

Symbol:
    :code:`p_inner(t)`

Latex:
    :math:`p_\text{inner}{\left(t \right)}`

Dimension:
    :code:`pressure`


.. py:data:: law

    :code:`Derivative(p_inner(t), t) = 0`


    Latex:
        .. math::
            \frac{d}{d t} p_\text{inner}{\left(t \right)} = 0