Incompressible Fluid Flow

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Course Contents

1. Introduction
1.1 Compressibility of Fluids 1.2 Compressible and Incompressible Flows 1.3 Laminar and turbulent flows

2. Basic Concepts in Incompressible Flows
2.1 Definition of a fluid 2.2 Steady and unsteady flows 2.3 Streamlines and pathlines 2.4 Stream function, vorticity and circulation 2.5 Eulerian and Lagrangian formulations 2.6 Material derivative

3. The Incompressible Navier-Stokes Equations
3.1 Continuity equation – Eulerian formulation 3.2 Momentum equation – Lagrangian formulation 3.2.1 Forces acting on a fluid element and the stress tensor 3.3 Straining of a fluid element and the strain rate tensor 3.4 Relation between the deviatoric stress tensor and the strain rate tensor 3.5 Incompressible Navier-Stokes equations 3.6 Newtonian and Non-Newtonian fluids

4. Solutions to the Incompressible Navier-Stokes Equations
4.1 Mathematical nature of the incompressible Navier-Stokes equations 4.2 Boundary conditions 4.3 An illustrative example 4.4 Solutions to the incompressible Navier-Stokes equations

5. Potential Flows
5.1 Euler equation for inviscid flows 5.1.1 Bernoulli’s equation 5.1.2 Relation between Bernoulli’s equation and the first law of thermodynamics 5.2 Potential flows 5.2.1 Basic flows 5.2.2 Superposed flows 5.2.3 Conformal mapping 5.2.4 Flow in a sector

6. Laminar Boundary Layer Theory
6.1 Derivation of the boundary layer equations 6.2 Boundary layer flow over a flat plate with zero pressure gradient 6.2.1 Differential analysis – Principle of similarity 6.2.2 Integral analysis 6.2.3 Displacement and momentum thickness 6.3 Boundary layer flows with non-zero pressure gradient 6.3.1 Falkner-Skan similarity solutions 6.3.2 von Karman – Pohlhausen integral solution 6.4 Separation and drag 6.5 Other flows governed by the boundary layer equations 6.5.1 Free shear layer 6.5.2 2D laminar jet

7. Analytical Solutions to the Incompressible Navier-Stokes Equations
7.1 Parallel flow solutions 7.1.1 Couette-Poiseuille flow 7.1.2 Hagen-Poiseuille flow in a pipe 7.1.3 Flow between concentric rotating cylinders 7.1.4 Flow in convergent and divergent channels 7.2 Creeping flow solutions

8. Turbulent Flows
8.1 Reynolds averaging 8.2 Reynolds Averaged Navier Stokes (RANS) equations 8.3 Bouissenesq hypothesis
8.4 Turbulence modeling 8.5 Universal structure of the mean velocity profile in the turbulent boundary layer

9. Turbulent Internal Flows
9.1 Turbulent flow in a pipe 9.2 Effect of roughness 9.3 Moody’s chart 9.4 Drag reduction

10. Turbulent External Flows
10.1 Turbulent boundary layer over a flat plate with zero pressure gradient 10.1.1 Effect of roughness 10.2 Turbulent flows with non-zero pressure gradient 10.3 Drag reduction in external flows

Text/Reference Books

1. V. Babu, Fundamentals of Incompressible Fluid Flow.
2. F. M. White, Fluid Mechanics.
3. S Som, Gautam Biswas, S Chakraborty Introduction to Fluid Mechanics & Fluid Machines.
4. P. K. Kundu, I. M. Cohen, D. R. Dowling, Fluid Mechanics.