.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fluid_engineering/measurement/plot_02_venturi_meter.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_measurement_plot_02_venturi_meter.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_measurement_plot_02_venturi_meter.py:


Venturi's tube (1797)
=====================

Giovanni Battista Venturi reported in 1797 that water flowing through a
contraction drops in pressure at the narrowest point and recovers most of
it in a gentle expansion. Clemens Herschel turned the effect into the
Venturi water meter in 1887: continuity and Bernoulli's equation give the
flow from the pressure drop between inlet and throat,
:math:`Q = C_d A_2\sqrt{2\Delta p/[\rho(1 - (A_2/A_1)^2)]}`
(:func:`~engineeringkit.fluid_engineering.venturi_flow`). This example
draws the pressure along a meter and reads the flow back from it.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.fluid_engineering import bernoulli_pressure, continuity_velocity, venturi_flow








.. GENERATED FROM PYTHON SOURCE LINES 22-28

Pressure along the meter
------------------------

A 150 mm pipe narrows to a 75 mm throat over 0.2 m and widens again over
0.6 m, carrying 30 L/s of water. Without losses the pressure follows the
area.

.. GENERATED FROM PYTHON SOURCE LINES 28-44

.. code-block:: Python


    rho, Q, p_in = 998.0, 0.030, 200e3
    x = np.linspace(0, 1.0, 201)
    d = np.interp(x, [0, 0.1, 0.3, 0.35, 0.95, 1.0], [0.15, 0.15, 0.075, 0.075, 0.15, 0.15])
    A = np.pi * d**2 / 4
    v = continuity_velocity(A[0], Q / A[0], A)
    p = bernoulli_pressure(p_in, rho, v[0], v)

    fig, ax = plt.subplots(figsize=(6, 4))
    ax.plot(x, p / 1e3)
    ax.set(xlabel="position [m]", ylabel="pressure [kPa]", title="Ideal pressure along a Venturi meter")
    fig.tight_layout()

    dp = p[0] - p.min()
    print(f"throat speed {v.max():.2f} m/s, pressure drop {dp / 1e3:.1f} kPa")




.. image-sg:: /api/gallery/fluid_engineering/measurement/images/sphx_glr_plot_02_venturi_meter_001.png
   :alt: Ideal pressure along a Venturi meter
   :srcset: /api/gallery/fluid_engineering/measurement/images/sphx_glr_plot_02_venturi_meter_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    throat speed 6.79 m/s, pressure drop 21.6 kPa




.. GENERATED FROM PYTHON SOURCE LINES 45-50

Reading the flow
----------------

The meter inverts the pressure drop. A real tube reads about 2% low
because of friction, which the discharge coefficient corrects.

.. GENERATED FROM PYTHON SOURCE LINES 50-59

.. code-block:: Python


    A1, A2 = A[0], A.min()
    print(f"ideal meter: {1e3 * venturi_flow(dp, rho, A1, A2):.2f} L/s")
    print(f"with C_d = 0.98: {1e3 * venturi_flow(dp, rho, A1, A2, 0.98):.2f} L/s")

    assert np.isclose(venturi_flow(dp, rho, A1, A2), Q)
    assert np.isclose(p[-1], p_in) and np.isclose(v.max(), 4 * v[0])

    plt.show()




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

 .. code-block:: none

    ideal meter: 30.00 L/s
    with C_d = 0.98: 29.40 L/s





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

   **Total running time of the script:** (0 minutes 0.025 seconds)


.. _sphx_glr_download_api_gallery_fluid_engineering_measurement_plot_02_venturi_meter.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/measurement/plot_02_venturi_meter.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_02_venturi_meter.ipynb <plot_02_venturi_meter.ipynb>`

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

      :download:`Download Python source code: plot_02_venturi_meter.py <plot_02_venturi_meter.py>`

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

      :download:`Download zipped: plot_02_venturi_meter.zip <plot_02_venturi_meter.zip>`


.. only:: html

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

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