.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/forces/plot_01_bernoulli_dynamic_pressure.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_aerodynamics_forces_plot_01_bernoulli_dynamic_pressure.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_aerodynamics_forces_plot_01_bernoulli_dynamic_pressure.py:


Bernoulli's dynamic pressure and the pitot-static airspeed
==========================================================

Daniel Bernoulli's *Hydrodynamica* (1738) traded pressure for speed along a
streamline: :math:`p + \tfrac12\rho V^2` is constant. A pitot tube brings the
flow to rest and reads the total pressure; the static port reads :math:`p`;
their difference is the dynamic pressure
:math:`q = \tfrac12\rho V^2` from
:func:`~engineeringkit.aerodynamics.dynamic_pressure`. Inverting it gives the
airspeed, but only if the right density is used: the same pitot reading
means a higher true airspeed at altitude.

.. GENERATED FROM PYTHON SOURCE LINES 16-21

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import dynamic_pressure, isa_atmosphere








.. GENERATED FROM PYTHON SOURCE LINES 22-24

Dynamic pressure grows with the square of speed
-----------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 24-30

.. code-block:: Python


    V = np.linspace(0, 120, 121)
    rho_sl = float(isa_atmosphere(0.0).density)
    q = dynamic_pressure(rho_sl, V)
    print(f"q at 50 m/s, sea level: {float(dynamic_pressure(rho_sl, 50.0)):.1f} Pa")





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

 .. code-block:: none

    q at 50 m/s, sea level: 1531.3 Pa




.. GENERATED FROM PYTHON SOURCE LINES 31-37

The same pitot reading at altitude
----------------------------------

Inverting Bernoulli, :math:`V = \sqrt{2q/\rho}`. An airspeed indicator is
calibrated with sea-level density, so it shows the *equivalent* airspeed;
the true airspeed is larger by :math:`\sqrt{\rho_0/\rho}`.

.. GENERATED FROM PYTHON SOURCE LINES 37-56

.. code-block:: Python


    altitudes = np.array([0.0, 3000.0, 6000.0, 9000.0, 12000.0])
    rho = isa_atmosphere(altitudes).density
    q_reading = float(dynamic_pressure(rho_sl, 70.0))
    true_speed = np.sqrt(2 * q_reading / rho)
    for h, v in zip(altitudes, true_speed, strict=True):
        print(f"h = {h / 1e3:4.0f} km: indicated 70.0 m/s -> true {v:5.1f} m/s")
    assert np.allclose(dynamic_pressure(rho, true_speed), q_reading)

    fig, axes = plt.subplots(1, 2, figsize=(9, 3.5))
    axes[0].plot(V, q / 1e3)
    axes[0].set(xlabel="speed V [m/s]", ylabel="dynamic pressure q [kPa]", title="q = rho V^2 / 2 at sea level")
    axes[1].plot(altitudes / 1e3, true_speed, "o-")
    axes[1].axhline(70, color="gray", ls="--", label="indicated (sea-level calibration)")
    axes[1].set(xlabel="altitude [km]", ylabel="true airspeed [m/s]", title="Same pitot reading, thinner air")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_01_bernoulli_dynamic_pressure_001.png
   :alt: q = rho V^2 / 2 at sea level, Same pitot reading, thinner air
   :srcset: /api/gallery/aerodynamics/forces/images/sphx_glr_plot_01_bernoulli_dynamic_pressure_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    h =    0 km: indicated 70.0 m/s -> true  70.0 m/s
    h =    3 km: indicated 70.0 m/s -> true  81.3 m/s
    h =    6 km: indicated 70.0 m/s -> true  95.4 m/s
    h =    9 km: indicated 70.0 m/s -> true 113.5 m/s
    h =   12 km: indicated 70.0 m/s -> true 139.0 m/s





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

   **Total running time of the script:** (0 minutes 0.200 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_forces_plot_01_bernoulli_dynamic_pressure.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/aerodynamics/forces/plot_01_bernoulli_dynamic_pressure.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_bernoulli_dynamic_pressure.ipynb <plot_01_bernoulli_dynamic_pressure.ipynb>`

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

      :download:`Download Python source code: plot_01_bernoulli_dynamic_pressure.py <plot_01_bernoulli_dynamic_pressure.py>`

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

      :download:`Download zipped: plot_01_bernoulli_dynamic_pressure.zip <plot_01_bernoulli_dynamic_pressure.zip>`


.. only:: html

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

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