Viscous Flow Theory




 3L-0T-0L-0D (9 Credits)


Course Content:

Introduction: stress-deformation relation, vector and tensor, vorticity and circulation, derivation of Navier-Stokes equations; Exact solutions: Couette flow, Hagen-Poiseuille flow, Stokes problems; Complex variable and Potential flow, Two-dimensional boundary layer: Blassius solution, Kármán-Pohlhausen method, effect of pressure gradient, separation and control, Waltz’s-Quadrature formula; Flow instability: concept of small-perturbations, linearized stability of parallel viscous flows, Orr-Sommerfeld equation; Turbulent boundary layers: Reynolds stress tensor, energy cascade, mixing length hypothesis, universal law of wall, fully developed turbulent flow through a pipe and channel, power law and effect of wall roughness; Compressible flow: condition of compressibility, subsonic, supersonic and hypersonic flows, shock and Mach waves, shock-boundary layer interactions; Special topics: Transition and turbulence, fluid-solid interaction, free-surface flow, bio-fluids, non-Newtonian flows, CFD and Measurements (optional and limited to any one).

Lecturewise Breakup (based on 50min per lecture):

I. Introduction: (3 Lectures)

Fluid Properties, Definition of Continuum, Examples of Viscous Flow Phenomena, Laminar and Turbulent Flow, Vector and Tensor notation, Lagrangian/Eulerian Methods, Streamline, Path line, Streak line, Material Derivative and acceleration, Strain Rate, Translation, Rotation and Distortion of Fluid Element, Vorticity and Circulation.

II. Fundamental Equations of Viscous Flow: (5 Lectures)

Conservation of Mass, Momentum and Energy, Finite Volume Approach, Derivation of Continuity Equation: conservative and non conservative form, Derivation of Navier-Stokes (N-S) equations for Compressible Flow, Stokes Hypothesis. Incompressible form of N-S equations.

III. Exact Solutions: (7 Lectures)

Parallel Flow in a Straight Channel, Couette Flow,  Lubrication Theory, Hagen-Poiseuille Flow, Unsteady Parallel Flow, Stokes Problems, Similarity Solution and Creeping Flow, Complex variable and Potential flow.

IV. Boundary Layer Theory: (6 Lectures)

Derivation of 2-D Boundary Layer Equations, Displacement, Momentum and Energy Thickness, Order of Magnitude Analysis, Shape Factor, Momentum-Integral Approach, Boundary Layer Separation, Effect of Pressure Gradient, Boundary Layer Control by Suction and Blowing, Blassius Solution of Boundary Layer Equation, Kármán-Pohlhausen Method for Non-Zero Pressure Gradient, Holsten and Bohlen Method (Modified Pohlhausen Method), Waltz’s-Quadrature Formula and Example Problems.

V. Flow Instability: (4 Lectures)

Instability, Concept of Small-Perturbations, Linearized Stability of Parallel Viscous Flows, Orr-Sommerfeld Equation, Neutral Stability Curve, Boundary Layer Transition qver a Flat Plate.

VI. Turbulent Boundary Layers: (6 Lectures)

Introduction to Turbulent Flows, Features of Turbulence, Energy Cascade, Mean and Fluctuating Components, Derivations of Reynolds Averaged Navier-Stokes Equations, Reynolds Stress Tensor, Turbulent Boundary Layer Equations, Eddy Viscosity and Mixing Length Hypothesis, Universal Law of Wall, Laminar Sublayer, Power Law for Turbulent Boundary Layer, Skin Friction Coefficient, Turbulent Boundary Layer with Pressure Gradient, Quadrature Formula and Example Problems.

VII. Internal Flows: (3 Lectures)

Fully Developed Turbulent Flow through a Pipe and Channel, Use of Log Law and Power Law, Derivation of Coefficient of Friction for Turbulent Pipe Flow, Moody Diagram, Hydrodynamic Smooth and Rough Pipe and Example Problems.

VIII. Compressible Flows: (5 Lectures)

Introduction and Definition, Limiting Condition of Compressibility, Subsonic, Supersonic and Hypersonic Flows, Mach Angle, Propagation of Small Disturbances, Formation of Shock, Shock Waves, Normal Shock Relations, Oblique Shock, Compression and Expansion Waves, Reflection and Interaction of Shocks, Expansion Waves, Shock-Boundary Layer Interactions and Example Problems.

IX. Special Topics: (3 Lectures)

Transition and turbulence, fluid-solid interaction, free-surface flow, bio-fluids and non-Newtonian flows, CFD and Measurements (optional and limited to any one topic).


  1. Fluid Mechanics by Pijush K. Kundu, Ira M. Cohen, David R Dowling (Academic Press)

  2. Fluid Mechanics by Frank M White (McGraw-Hill)

  3. Viscous Fluid Flow by Frank M White (McGraw-Hill)

  4. Boundary Layer Theory by H Sctllichting (McGraw-Hill)