Shreyas Mandre

Associate Professor
Mathematics Institute, University of Warwick

Fluid Dynamics

A university course in fluid dynamics for undergraduates in Maths and Physics. (Some version of this is taught at Warwick as MA3D1 and at Brown as ENGN0810.)

The HTML and PDF lecture notes may be found at this link.

Here is the learning material, including recordings of videos made in the unusual year of 2020:

1. Preliminaries  
2. Mathematical modelling of fluid flow  
      2.1   Definition of a fluid   (online notes)   (video)   (handwritten notes)
      2.2   Fluids in continuum mechanics   (online notes)   (video)   (handwritten notes)
      2.3   Properties of fluids   (online notes)   (video)   (handwritten notes)
      2.4   Lagrangian and Eulerian descriptions   (online notes)   (video)   (handwritten notes)
      2.5   Flow visualization   (online notes)   (video)   (handwritten notes)
      2.6   Deformation of infinitesimal fluid elements   (online notes)   (video)   (handwritten notes)
      2.7   Conservation laws in continuum mechanics   (online notes)   (video)   (handwritten notes)
      2.8   Conservation of mass   (online notes)   (video)   (handwritten notes)
      2.9   Conservation of momentum   (online notes)   (video)   (handwritten notes)
      2.10   Conservation of angular momentum   (online notes)   (video)   (handwritten notes)
      2.11   Constitutive laws   (online notes)   (video)   (handwritten notes)
      2.12   Boundary and initial conditions   (online notes)   (video)   (handwritten notes)
3. One dimensional flows  
      3.1   Steady one-dimensional flows   (online notes)   (video)   (handwritten notes)
      3.2   Unsteady one-dimensional flows   (online notes)   (video)   (handwritten notes)
4. Dimensional analysis  
      4.1   Dimensional analysis   (online notes)   (video)   (handwritten notes)
5. Hydrostatics and Bernoulli equations  
      5.1   Hydrostatics   (online notes)   (video)   (handwritten notes)
      5.2   The Bernoulli equations   (online notes)   (video)   (handwritten notes)
      5.3   Applications of Bernoulli equation   (online notes)   (video)   (handwritten notes)
6. Potential flow  
      6.1   Potential flow - general considerations   (online notes)   (video)   (handwritten notes)
      6.2   Elementary potential flows   (online notes)   (video)   (handwritten notes)
      6.3   Derived potential flows   (online notes)   (video)   (handwritten notes)
      6.4   Force on immersed bodies   (online notes)   (video)   (handwritten notes)
      6.5   Flow around an airfoil   (online notes)   (video)   (handwritten notes)
7. Boundary layers  
      7.1   Qualitative description of the flow   (online notes)  
      7.2   Derivations of the Prandtl boundary layer equations   (online notes)   (video)   (handwritten notes)
      7.3   Self-similar flow past flat plate and drag on a flat plate   (online notes)   (video)   (handwritten notes)