Course Details:
This is an introduction to the basic ideas of physics of fluids and the application to the wealth of macroscopic phenomena. The important thing to learn from this course is how to reason about physics, both qualitatively and quantitatively.
Module 1: Continuous matter
• Molecules, Continuum Approximation, Newtonian Mechanics, Reference Frames.
Module 2: Fluids at Rest
• Pressure: The pressure field, hydrostatics, bulk modulus, applications (Earth’s homo-entropic atmosphere, Sun’s convective envelope).
• Buoyancy and stability: Archimedes’ principle, stability of floating body.
• Hydrostatic shapes: Fluid interfaces in hydrostatic equilibrium, the centrifugal force, the tides.
• Surface Tension: Soap bubbles, pressure discontinuity, The Rayleigh-Plateau instability, contact angle, meniscus at a flat wall, meniscus in a cylindrical tube, applications (sessile drops and captive bubbles; pendant drops and tethered bubbles).
Modules 3: Fluids in Motion
• Continuum Dynamics: The velocity field, incompressible flow, mass conservation.
• Nearly ideal flow: Euler equation, collapse of a spherical cavity, steady incompressible ideal flow, vorticity, circulation, potential flow, cylinder in uniform crosswind, sphere in a uniform stream, d Alembert’s paradox.
• Compressible flow: Steady compressible flow, Laval nizzle.
• Viscosity: Shear viscosity, velocity driven planer flow, incompressible Newtonian fluids.
• Channels and pipes: Steady, incompressible, viscous flow, pressure-driven channel flow, gravity driven planer flow, Laminar pipe flow, turbulent pipe flow, Laminar cylindric flow, secondary flow and Taylor vortices.
• Creeping flow: Stokes flow, flow around a solid ball, Beyond stokes Law, Lubrication.
• Rotating Fluids: Fictitious forces, steady flow in a rotating system, The Ekman layer, steady bathtub vortex.
• Computational fluid dynamics: Unsteady, incompressible flow, temporal discritization, spatial discritization, Laminar channel entry flow.
Textbook:
• Physics of Continuous matter, B. Lautrup.
References:
• Elementary Fluid Dynamics, by D. J. Acheson.