.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_04_darcy_law.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_hydrology_plot_04_darcy_law.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_hydrology_plot_04_darcy_law.py:


Darcy's law (1856)
==================

Henry Darcy built sand filters for the fountains of Dijon and measured the
flow through a vertical column of sand under different heads. The discharge
was proportional to the head lost across the column divided by its length,
with a constant that depends on the sand, now the hydraulic conductivity. The
example repeats the experiment: heads read on the manometers combine elevation
and pressure, every sand gives a straight line through the origin, and water
in the pores moves faster than the flux by the inverse porosity.

.. GENERATED FROM PYTHON SOURCE LINES 13-35



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_04_darcy_law_001.png
   :alt: Darcy: flux is proportional to the head gradient
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_04_darcy_law_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.constants import GRAVITY
    from earthsciencekit.hydrology import darcy_flux, hydraulic_head, seepage_velocity

    length = 1.0  # m of sand
    pressure_top = 1000 * GRAVITY * np.linspace(0.5, 10, 12)  # Pa above the sand
    head_top = hydraulic_head(length, pressure_top, 1000, GRAVITY)
    head_bottom = hydraulic_head(0.0, 0.0, 1000, GRAVITY)  # free outflow at the base
    gradient = (head_bottom - head_top) / length
    fig, ax = plt.subplots()
    for conductivity, sand in [(1e-3, "coarse sand"), (3e-4, "medium sand"), (5e-5, "fine sand")]:
        flux = darcy_flux(conductivity, gradient)
        assert np.allclose(np.polyfit(-gradient, flux, 1), [conductivity, 0], atol=1e-12)
        ax.plot(-gradient, flux * 1e3, "o-", label=f"{sand}, K = {conductivity:g} m/s")
    assert np.isclose(seepage_velocity(darcy_flux(1e-3, -1), 0.35), 1e-3 / 0.35)
    ax.set(xlabel="head loss per unit length [1]", ylabel="Darcy flux [mm/s]", title="Darcy: flux is proportional to the head gradient")
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.085 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_04_darcy_law.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/hydrology/plot_04_darcy_law.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_04_darcy_law.ipynb <plot_04_darcy_law.ipynb>`

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

      :download:`Download Python source code: plot_04_darcy_law.py <plot_04_darcy_law.py>`

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

      :download:`Download zipped: plot_04_darcy_law.zip <plot_04_darcy_law.zip>`


.. only:: html

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

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