

Section 6: Viscous Flows  
6.1  The equation of motion for viscous flows. Surface stress; stress tensor; symmetry of the stress tensor; the equation of motion in terms of the stress tensor; the stress tensor for Newtonian fluids; the NavierStokes equations; summary of the governing equations and boundary conditions for incompressible flows and constantdensity flows; boundary conditions for viscous flows.  
6.2  Comments on the character of the NavierStokes equations at low and high Reynolds numbers; laminar flows and their stability; turbulence.  
6.3  Some truly inertiafree flows: Steady, laminar fully developed pipe flows; laminar Couette flows with and without pressure gradient.  
6.4  (Almost) inertiafree flows. Criteria for quasisteady, locallyfullydeveloped (quasiparallel) laminar flow. Examples: Flows in various converging and diverging channels, freesurface flows, and lubrication theory.  
6.5  Rayleigh's problem of the transient motion induced by a flat plate that moves in its own plane: an archetypal example of laminar viscous flow with significant inertial effects. The viscous diffusion time and its implications in various types of flows, including boundary layers in steady laminar flow.  
Reading  
Special 2.25 notes by A. Sonin: (i) Equation of Motion for Viscous Fluids [PDF] and (ii) Criteria for inertiafree and locally fullydeveloped flows Fay, Chapter 6 

Problem Set Section 6 

Problem 6.3  
Problem 6.6  
Problem 6.10  
Problem 6.13  
Problem 6.16  
Problem 6.20  
Problem 6.22  
Problem 8.3  