.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fluid_engineering/plot_fluid_engineering_benchmark.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_fluid_engineering_plot_fluid_engineering_benchmark.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_fluid_engineering_plot_fluid_engineering_benchmark.py:


Poiseuille profile and volume flow
==================================

Integrate the laminar parabolic velocity profile over a circular cross section
and compare it with the volume-flow helper. The radius dependence is fourth power.

.. GENERATED FROM PYTHON SOURCE LINES 8-26



.. image-sg:: /api/gallery/fluid_engineering/images/sphx_glr_plot_fluid_engineering_benchmark_001.png
   :alt: plot fluid engineering benchmark
   :srcset: /api/gallery/fluid_engineering/images/sphx_glr_plot_fluid_engineering_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    from scipy.integrate import trapezoid

    from engineeringkit.fluid_engineering import poiseuille_flow

    radius, length, mu, dp = 0.005, 1, 0.001, 10
    r = np.linspace(0, radius, 10001)
    v = dp * (radius**2 - r**2) / (4 * mu * length)
    Q = poiseuille_flow(dp, radius, length, mu)
    assert np.isclose(trapezoid(2 * np.pi * r * v, r), Q, rtol=1e-7)
    assert np.isclose(poiseuille_flow(dp, 2 * radius, length, mu), 16 * Q)
    fig, ax = plt.subplots()
    ax.plot(r * 1000, v)
    ax.set(xlabel="radial position [mm]", ylabel="axial speed [m/s]")

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.062 seconds)


.. _sphx_glr_download_api_gallery_fluid_engineering_plot_fluid_engineering_benchmark.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/fluid_engineering/plot_fluid_engineering_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_fluid_engineering_benchmark.ipynb <plot_fluid_engineering_benchmark.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_fluid_engineering_benchmark.py <plot_fluid_engineering_benchmark.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_fluid_engineering_benchmark.zip <plot_fluid_engineering_benchmark.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_