ME 50900 – Intermediate Fluid Mechanics

This is a GitHub repository for ME 50900 – Intermediate Fluid Mechanics at Purdue University, as taught by Prof. Ivan C. Christov. The repository mainly consists of Jupyter notebooks used for hands-on demos in lectures, continuous knowledge acquisition, problem-set solutions, and enrichment activities.

🚀 Getting started (rough grouping of notebooks based on course topics):

• Kinematics:

  • Flow visualization — quiver plots, streamlines, pathlines, streaklines.
  • Velocity field in polar coords — plotting planar (2D) velocity fields given in terms of polar velocity components.
  • Streamfunction in 2D — constructing, visualizing, and understanding streamfunctions for 2D flows in Cartesian coordinates.
  • Kinematics and the material derivative — given a flow field, going beyond flow visualization.

• Dynamics of unidirectional flows:

  • Combined PC flow — solution of combined Poiseuille–Couette flow generated by the combination of a pressure gradient and wall motion.
  • Startup PC flow — the full transient solution from rest for Poiseuille–Couette flow (to complement Combined PC Flow).
  • Slip flow in a channel — a pressure-driven flow with Navier slip in a 2D channel, arising from microfluidics.
  • Stokes' 1st problem — similarity solution for the flow caused by the impulsive motion of a plate.
  • Stokes' 2nd problem — post-transient solution for the flow caused by an oscillating plate.
  • Decay of an ideal vortex — similarity solution for the decay of a point load of vorticity at the origin.
  • Womersley flow — flow in a 2D channel and a 3D axisymmetric tube driven by a periodically pulsating pressure gradient, including animations.
  • Rectangular duct flow — Fourier series solution for pressure-driven flow in a 3D duct.

• Flow fields with two velocity components:

  • Asymptotic suction flow — a fully-developed flow field with two velocity components.
  • Ideal flows in 2D — having fun with functions of a complex variable.
  • Boundary layers — everything you need to know about Blasius' problem.
  • Stokes flows in 2D — having fun with the biharmonic equation in the plane, from Taylor's scraper to Moffatt's eddies.
  • Stokes flow past sphere — heavy-duty calculations in spherical coordinates.
  • Wavy channel flow — the pressure drop along a wavy channel from lubrication theory.
  • Slipper pad bearing — a classic application of Reynolds' lubrication equation.

• Dimensional analysis:

  • Dimensional analysis — Buckingham's $\Pi$ theorem is just the rank–nullity theorem in disguise.
  • Taylor and the bomb — how G. I. Taylor estimated the energetic yield of the Trinity test.

⚠️ The notebooks are unlikely to be robust and may require updates to run on different platforms, and as underlying Python libraries evolve.

📝 Also, checkout the handouts folder.

📚 Some resources for self-learning Jupyter, Python and $\LaTeX$:

• Google Colaboratory lets open Jupyter notebooks from GitHub and run them in the cloud from your browser: https://colab.research.google.com.

  • See the getting started with Markdown guide for how to write nice discussion between your computational cells in the Jupyter notebook.
  • More advanced programmers may find the following links useful: Introduction to Git in VS Code, Jupyter Notebooks in VS Code.

• Check out PY4E – Python for Everybody – for free materials for learning how to program in Python.

  • The first few lectures of ME 297 - Introduction to Data Science for Mechanical Engineers also cover getting started with Scientific Python.

• For all your math typesetting needs: D. F. Griffiths and D. J. Higham, Learning LaTeX, 2nd ed, SIAM.