Syllabus
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Course Code: MMATH21-411 Course Name: Elective V) Advanced Fluid Mechanics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Wave motion in a Gas. Speed of sound in a gas. Equation of motion of a Gas. Subsonic, sonic and supersonic flows. Isentropic gas flow, Flow through a nozzle. Shock waves. | |
| 2 | Stress components in a real fluid. Relation between Cartesian components of stress. Translational motion of fluid element. Rate of strain quadric and principal stresses.
Transformation of rates of strains. Stress analysis in fluid motion. Relations between stress and strain rate. The co-efficient of viscosity and laminar flow. Newtonian and non-Newtonian fluids. Navier-Stokes equations of motion. Equations of motion in cylindrical and spherical polar coordinates. |
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| 3 | Some solvable problems in viscous flow: Steady motion between parallel planes, Steady flow through tube of uniform cross-section (Poiseuille Flow), Steady flow between concentric rotating cylinders. Steady viscous flow in tubes of uniform cross-section: Uniqueness theorem; Flow through tubes of uniform elliptic, equilateral triangular and rectangular cross-sections. Diffusion of vorticity. Energy dissipation due to viscosity. Steady flow past a fixed sphere. Unsteady flow over a flat plate. Flow in convergent and divergent chennals. | |
| 4 | Dynamical similarity. Dimensional analysis. Buckingham -theorem and its applications to viscous and compressible fluid flow. Reynolds number, Weber Number, Mach Number, Froude Number, Eckert Number . Prandtl boundary layer theory, Boundary layer thickness, Boundary layer equation in two-dimensions. The boundary layer flow over a flat plate (Blasius solution). Characteristic boundary layer parameters. Karman integral equations. Karman-Pohlhausen method. |
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