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Introductory Fluid Mechanics For Physicists And Mathematicians
Geoffrey Pert
Synopsis "Introductory Fluid Mechanics For Physicists And Mathematicians"
This Text Will Introduce The Core Ideas Of Fluid Mechanics Using Both Theoretical And Experimental Methods. The Approach Will Be Through Physics And Analytic Methods. Empirical Methods As Used In Engineering Will Be Introduced When Necessary If Analytic Methods Are Intractable. The First Part Of The Book Will Deal With Incompressible Fluids. The Properties Of Ideal Flow And Irrotational Flow Will Be Explored To Introduce The Concepts Of Uniqueness And Existence Stemming From Laplaces Equation. Complex Variables Will Be Used To Develop Solutions In This Approximation. An Introduction Will Be Given To The Basic Design Of Aerofoils. The Stresses And Strain Rates Resulting From Viscosity Will Be Introduced Leading To The Navier - Stokes Equation. Boundary Layers And Separation Are A Consequence. The Underlying Structure Of Turbulence Will Be Treated In An Elementary Fashion And Dimensional Analysis Will Be Used To Derive Empirical Relations To Calculate The Flow Through Pipes And Boundary Layers. A Brief Introduction To Convective Heat Transfer Will Examine Forced Convection In Pipes And Boundary Layers. The Second Part Will Deal With Compressible Flow. It Will Be Argued That Compressible Flow Is Mainly Ideal. A Brief Discussion Of Sound Waves Will Lead To The Ideas Of Mach Lines And Characteristics. Two Important Problems Involving Characteristics Will Be Solved To Illustrate The Power Of The Method: Namely The Expansion Of Gas Behind A Piston And The Flow Around A Corner. Characteristics Will Be Used To Describe The Failure Of Ideal Flow In Compression And The Consequent Generation Of Shock Waves. Shock Waves Will Be Investigated In Some Depth, Both In Their Structure And Consequences, And Their Effects On Aerofoils. The Pertubation Method For Compressible Flow Will Be Introduced And Used To Develop Approximations For Compressible Flow Around Wings In Subsonic And Supersonic Flight. The Treatment Of Flows With Heat Release, Namely Deflagrations And Detonations, Will Be Considered. Finally An Outline Of The Method Of Similarity Will Be Given To Show How To Treat Flow Involving Compression And Rarefaction In Symmetric Systems With Particular Examples
