.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/aerodynamics/boundary_layer/plot_01_reynolds_similarity.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_boundary_layer_plot_01_reynolds_similarity.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_boundary_layer_plot_01_reynolds_similarity.py:


Reynolds' dimensionless number and wind-tunnel similarity
=========================================================

Osborne Reynolds' dye experiments (1883) showed that pipe flow turns
turbulent when :math:`\rho V D/\mu` exceeds a critical value, whatever the
individual fluid, speed or diameter. The same number
(:func:`~engineeringkit.aerodynamics.reynolds_number`) decides whether a
scale model reproduces full-scale flow: matching it at reduced size forces
higher speed or denser gas, which is why NACA built a pressurised
variable-density tunnel in 1923.

.. GENERATED FROM PYTHON SOURCE LINES 15-22

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.aerodynamics import isa_atmosphere, reynolds_number

    mu_air = 1.789e-5








.. GENERATED FROM PYTHON SOURCE LINES 23-25

From insects to airliners
-------------------------

.. GENERATED FROM PYTHON SOURCE LINES 25-40

.. code-block:: Python


    cases = {
        "fruit fly": (1.225, 1.0, 0.002),
        "sparrow": (1.225, 10.0, 0.05),
        "glider": (1.225, 30.0, 1.0),
        "light aircraft": (1.225, 60.0, 1.5),
        "airliner cruise": (float(isa_atmosphere(11000.0).density), 240.0, 6.0),
    }
    names, values = [], []
    for name, (rho, V, chord) in cases.items():
        Re = float(reynolds_number(rho, V, chord, mu_air))
        names.append(name)
        values.append(Re)
        print(f"{name:16s} Re = {Re:9.2e}")





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

 .. code-block:: none

    fruit fly        Re =  1.37e+02
    sparrow          Re =  3.42e+04
    glider           Re =  2.05e+06
    light aircraft   Re =  6.16e+06
    airliner cruise  Re =  2.93e+07




.. GENERATED FROM PYTHON SOURCE LINES 41-47

Matching Reynolds number in a 1/10-scale model
----------------------------------------------

At sea-level density the model must fly ten times faster than the
aircraft, which puts it in the compressible regime; raising the tunnel
pressure (and so the density) is the way out.

.. GENERATED FROM PYTHON SOURCE LINES 47-66

.. code-block:: Python


    full = float(reynolds_number(1.225, 60.0, 1.5, mu_air))
    pressure_ratio = np.linspace(1, 25, 100)
    model_speed = full * mu_air / (1.225 * pressure_ratio * 0.15)
    speed_20atm = full * mu_air / (1.225 * 20 * 0.15)
    print(f"required model speed at 1 atm: {model_speed[0]:.0f} m/s; at 20 atm: {speed_20atm:.0f} m/s")
    assert np.isclose(reynolds_number(1.225 * 20, speed_20atm, 0.15, mu_air), full)

    fig, axes = plt.subplots(1, 2, figsize=(10, 3.6))
    axes[0].barh(names, values)
    axes[0].set_xscale("log")
    axes[0].set(xlabel="chord Reynolds number", title="Reynolds numbers in flight")
    axes[1].plot(pressure_ratio, model_speed)
    axes[1].axhline(0.3 * 340, color="gray", ls="--", label="Mach 0.3")
    axes[1].set(xlabel="tunnel pressure [atm]", ylabel="model speed [m/s]", title="1/10 model, matched Re")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/aerodynamics/boundary_layer/images/sphx_glr_plot_01_reynolds_similarity_001.png
   :alt: Reynolds numbers in flight, 1/10 model, matched Re
   :srcset: /api/gallery/aerodynamics/boundary_layer/images/sphx_glr_plot_01_reynolds_similarity_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    required model speed at 1 atm: 600 m/s; at 20 atm: 30 m/s





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

   **Total running time of the script:** (0 minutes 0.292 seconds)


.. _sphx_glr_download_api_gallery_aerodynamics_boundary_layer_plot_01_reynolds_similarity.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/boundary_layer/plot_01_reynolds_similarity.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_reynolds_similarity.ipynb <plot_01_reynolds_similarity.ipynb>`

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

      :download:`Download Python source code: plot_01_reynolds_similarity.py <plot_01_reynolds_similarity.py>`

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

      :download:`Download zipped: plot_01_reynolds_similarity.zip <plot_01_reynolds_similarity.zip>`


.. only:: html

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

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