.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/hydrology/plot_11_theis_well_solution.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_11_theis_well_solution.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_11_theis_well_solution.py:


Theis's well solution (1935)
============================

Charles Theis noticed that groundwater flow to a well obeys the same equation
as heat conduction, and borrowed the solution for a line sink. The drawdown
grows without limit as the well takes water from storage, at a rate fixed by
the transmissivity, and every observation well falls on one type curve when
the drawdown is plotted against ``t / r**2``.

.. GENERATED FROM PYTHON SOURCE LINES 11-32



.. image-sg:: /api/gallery/hydrology/images/sphx_glr_plot_11_theis_well_solution_001.png
   :alt: Drawdown keeps growing, One type curve W(u)
   :srcset: /api/gallery/hydrology/images/sphx_glr_plot_11_theis_well_solution_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.hydrology import theis_drawdown, well_function

    rate, transmissivity, storativity = 0.02, 5e-3, 2e-4
    time = np.logspace(1, 6, 200)
    fig, (left, right) = plt.subplots(1, 2, figsize=(9, 4))
    for radius in (5.0, 20.0, 80.0):
        drawdown = theis_drawdown(rate, transmissivity, storativity, radius, time)
        u = radius**2 * storativity / (4 * transmissivity * time)
        assert np.allclose(drawdown, rate / (4 * np.pi * transmissivity) * well_function(u))
        left.semilogx(time / 3600, drawdown, label=f"r = {radius:g} m")
        right.loglog(time / radius**2, drawdown, lw=4 - radius / 40, label=f"r = {radius:g} m")
    left.set(xlabel="time since pumping began [h]", ylabel="drawdown [m]", title="Drawdown keeps growing")
    right.set(xlabel="t / r^2 [s/m^2]", ylabel="drawdown [m]", title="One type curve W(u)")
    left.legend()
    fig.tight_layout()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.474 seconds)


.. _sphx_glr_download_api_gallery_hydrology_plot_11_theis_well_solution.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_11_theis_well_solution.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_11_theis_well_solution.ipynb <plot_11_theis_well_solution.ipynb>`

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

      :download:`Download Python source code: plot_11_theis_well_solution.py <plot_11_theis_well_solution.py>`

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

      :download:`Download zipped: plot_11_theis_well_solution.zip <plot_11_theis_well_solution.zip>`


.. only:: html

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

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