.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fluid_engineering/hydrostatics/plot_02_stevin_hydrostatic_paradox.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_hydrostatics_plot_02_stevin_hydrostatic_paradox.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_hydrostatics_plot_02_stevin_hydrostatic_paradox.py:


Stevin's hydrostatic paradox (1586)
===================================

In *De Beghinselen des Waterwichts* (1586) Simon Stevin showed that the
force of water on the bottom of a vessel depends only on the depth and the
area of the bottom, not on how much water the vessel holds:
:math:`p = \rho g h` (:func:`~engineeringkit.fluid_engineering.hydrostatic_pressure`).
He went on to find the force on a sloping or vertical wall, the first
problem of engineering hydrostatics. This example fills three vessels of
different shape to the same depth, then computes the thrust on a dam face
and where it acts (:func:`~engineeringkit.fluid_engineering.hydrostatic_force_plane`,
:func:`~engineeringkit.fluid_engineering.center_of_pressure_depth`).

.. GENERATED FROM PYTHON SOURCE LINES 17-28

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.fluid_engineering import (
        G,
        center_of_pressure_depth,
        hydrostatic_force_plane,
        hydrostatic_pressure,
        pressure_head,
    )








.. GENERATED FROM PYTHON SOURCE LINES 29-35

Three vessels, one base force
-----------------------------

Each vessel has a 0.01 m² base and holds water 0.5 m deep. A flared vessel
holds five times the water of a narrow-necked one, yet the force on the
base is the same; the side walls carry the difference.

.. GENERATED FROM PYTHON SOURCE LINES 35-42

.. code-block:: Python


    rho, depth, base = 998.0, 0.5, 0.01
    volumes = {"narrow neck": 0.002, "straight": 0.005, "flared": 0.010}
    base_force = hydrostatic_pressure(rho, depth) * base
    for name, V in volumes.items():
        print(f"{name:>11}: water weighs {rho * G * V:5.1f} N, force on base {base_force:.1f} N")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    narrow neck: water weighs  19.6 N, force on base 48.9 N
       straight: water weighs  48.9 N, force on base 48.9 N
         flared: water weighs  97.9 N, force on base 48.9 N




.. GENERATED FROM PYTHON SOURCE LINES 43-49

A dam face
----------

Water 30 m deep stands against a vertical dam 1 m wide. The pressure grows
linearly with depth, so the thrust is that at mid-depth times the area and
acts two thirds of the way down. A 30 m column is about 3 atmospheres.

.. GENERATED FROM PYTHON SOURCE LINES 49-66

.. code-block:: Python


    H, width = 30.0, 1.0
    F = hydrostatic_force_plane(rho, H / 2, H * width)
    y_p = center_of_pressure_depth(H / 2, H * width, width * H**3 / 12)
    print(f"thrust {F / 1e6:.2f} MN per metre, acting {y_p:.1f} m below the surface")
    p_base = hydrostatic_pressure(rho, H)
    print(f"pressure at the base {p_base / 1e3:.0f} kPa = {pressure_head(p_base, 13546.0):.2f} m of mercury")

    y = np.linspace(0, H, 50)
    fig, ax = plt.subplots(figsize=(5, 4))
    ax.fill_betweenx(y, 0, hydrostatic_pressure(rho, y) / 1e3, alpha=0.4)
    ax.axhline(y_p, color="k", ls="--", label=f"centre of pressure, {y_p:.0f} m")
    ax.invert_yaxis()
    ax.set(xlabel="pressure [kPa]", ylabel="depth [m]", title="Pressure on a dam face")
    ax.legend()
    fig.tight_layout()




.. image-sg:: /api/gallery/fluid_engineering/hydrostatics/images/sphx_glr_plot_02_stevin_hydrostatic_paradox_001.png
   :alt: Pressure on a dam face
   :srcset: /api/gallery/fluid_engineering/hydrostatics/images/sphx_glr_plot_02_stevin_hydrostatic_paradox_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    thrust 4.40 MN per metre, acting 20.0 m below the surface
    pressure at the base 294 kPa = 2.21 m of mercury




.. GENERATED FROM PYTHON SOURCE LINES 67-69

Stevin's result: the thrust on the vertical face is half the force the
same area would carry lying flat at the full depth.

.. GENERATED FROM PYTHON SOURCE LINES 69-75

.. code-block:: Python


    assert np.isclose(F, 0.5 * hydrostatic_pressure(rho, H) * H * width)
    assert np.isclose(y_p, 2 * H / 3)
    assert np.isclose(base_force, rho * G * depth * base)

    plt.show()








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

   **Total running time of the script:** (0 minutes 0.030 seconds)


.. _sphx_glr_download_api_gallery_fluid_engineering_hydrostatics_plot_02_stevin_hydrostatic_paradox.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/hydrostatics/plot_02_stevin_hydrostatic_paradox.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_stevin_hydrostatic_paradox.ipynb <plot_02_stevin_hydrostatic_paradox.ipynb>`

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

      :download:`Download Python source code: plot_02_stevin_hydrostatic_paradox.py <plot_02_stevin_hydrostatic_paradox.py>`

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

      :download:`Download zipped: plot_02_stevin_hydrostatic_paradox.zip <plot_02_stevin_hydrostatic_paradox.zip>`


.. only:: html

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

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