.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/fluid_engineering/pipe_flow/plot_07_swamee_jain.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_pipe_flow_plot_07_swamee_jain.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_pipe_flow_plot_07_swamee_jain.py:


Swamee and Jain's explicit friction factor (1976)
=================================================

Colebrook's equation needs iteration, which was a nuisance on the first
programmable calculators. In 1976 Prabhata Swamee and Akalank Jain fitted
explicit formulas for all three of Moody's pipe problems. Their friction
factor,

.. math::

    f = \frac{0.25}{\left[\log_{10}\left(\frac{\varepsilon/D}{3.7} + \frac{5.74}{Re^{0.9}}\right)\right]^2},

(:func:`~engineeringkit.fluid_engineering.swamee_jain_friction_factor`)
stays close to Colebrook's over the range of engineering pipes. This
example maps the error and checks their explicit diameter formula against
an iterative solution.

.. GENERATED FROM PYTHON SOURCE LINES 21-32

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np
    from scipy import optimize

    from engineeringkit.fluid_engineering import (
        G,
        colebrook_friction_factor,
        darcy_head_loss,
        swamee_jain_friction_factor,
    )








.. GENERATED FROM PYTHON SOURCE LINES 33-35

Error against Colebrook
-----------------------

.. GENERATED FROM PYTHON SOURCE LINES 35-48

.. code-block:: Python


    Re = np.geomspace(5e3, 1e8, 60)
    rel = np.geomspace(1e-6, 0.05, 50)
    RE, REL = np.meshgrid(Re, rel)
    error = swamee_jain_friction_factor(RE, REL) / colebrook_friction_factor(RE, REL) - 1

    fig, ax = plt.subplots(figsize=(6.5, 4.2))
    mesh = ax.pcolormesh(Re, rel, 100 * error, shading="auto", cmap="RdBu_r", vmin=-3, vmax=3)
    ax.set(xscale="log", yscale="log", xlabel="Reynolds number", ylabel="relative roughness", title="Swamee-Jain error [%]")
    fig.colorbar(mesh)
    fig.tight_layout()
    print(f"largest error {100 * np.abs(error).max():.2f}%; median {100 * np.median(np.abs(error)):.2f}%")




.. image-sg:: /api/gallery/fluid_engineering/pipe_flow/images/sphx_glr_plot_07_swamee_jain_001.png
   :alt: Swamee-Jain error [%]
   :srcset: /api/gallery/fluid_engineering/pipe_flow/images/sphx_glr_plot_07_swamee_jain_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    largest error 2.99%; median 0.39%




.. GENERATED FROM PYTHON SOURCE LINES 49-58

The explicit diameter
---------------------

For a flow :math:`Q` over a length :math:`L` with head loss :math:`h_f`,

.. math::

    D = 0.66\left[\varepsilon^{1.25}\left(\frac{LQ^2}{gh_f}\right)^{4.75}
        + \nu Q^{9.4}\left(\frac{L}{gh_f}\right)^{5.2}\right]^{0.04}.

.. GENERATED FROM PYTHON SOURCE LINES 58-75

.. code-block:: Python


    nu, eps, Q, L, h_f = 1.0e-6, 0.045e-3, 0.05, 1000.0, 10.0
    D_sj = 0.66 * (eps**1.25 * (L * Q**2 / (G * h_f)) ** 4.75 + nu * Q**9.4 * (L / (G * h_f)) ** 5.2) ** 0.04


    def loss(D):
        v = Q / (np.pi * D**2 / 4)
        return darcy_head_loss(colebrook_friction_factor(v * D / nu, eps / D), L, D, v)


    D_exact = optimize.brentq(lambda D: loss(D) - h_f, 0.05, 1.0)
    print(f"explicit D = {1e3 * D_sj:.1f} mm, iterative D = {1e3 * D_exact:.1f} mm")

    assert np.abs(error).max() < 0.03
    assert abs(D_sj / D_exact - 1) < 0.02

    plt.show()




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

 .. code-block:: none

    explicit D = 205.0 mm, iterative D = 202.2 mm





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

   **Total running time of the script:** (0 minutes 0.112 seconds)


.. _sphx_glr_download_api_gallery_fluid_engineering_pipe_flow_plot_07_swamee_jain.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/pipe_flow/plot_07_swamee_jain.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_07_swamee_jain.ipynb <plot_07_swamee_jain.ipynb>`

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

      :download:`Download Python source code: plot_07_swamee_jain.py <plot_07_swamee_jain.py>`

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

      :download:`Download zipped: plot_07_swamee_jain.zip <plot_07_swamee_jain.zip>`


.. only:: html

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

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