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Section 6: Viscous Flows | |
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| 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 Navier-Stokes equations; summary of the governing equations and boundary conditions for incompressible flows and constant-density flows; boundary conditions for viscous flows. | |||||||||||
| 6.2 | Comments on the character of the Navier-Stokes equations at low and high Reynolds numbers; laminar flows and their stability; turbulence. | |||||||||||
| 6.3 | Some truly inertia-free flows: Steady, laminar fully developed pipe flows; laminar Couette flows with and without pressure gradient. | |||||||||||
| 6.4 | (Almost) inertia-free flows. Criteria for quasi-steady, locally-fully-developed (quasi-parallel) laminar flow. Examples: Flows in various converging and diverging channels, free-surface 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 | ||||||||||||
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Special 2.25 notes by A. Sonin: (i) Equation of Motion for Viscous Fluids [PDF] and (ii) Criteria for inertia-free and locally fully-developed flows Fay, Chapter 6 |
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Problem Set Section 6 |
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| Problem 6.3 | ||||||||||||
| Problem 6.6 | ||||||||||||
| Problem 6.10 | ||||||||||||
| Problem 6.13 | ||||||||||||
| Problem 6.16 | ||||||||||||
| Problem 6.20 | ||||||||||||
| Problem 6.22 | ||||||||||||
| Problem 8.3 | ||||||||||||
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