Fluid Dynamics

Syllabus Details

• Unit I:(Coordinate Systems and Vector Calculus) Relation between cartesian coordinate systems to cylindrical polar coordinates and to spherical polar coordinates. Representation of vectors from one coordinate system to another coordinate system. Derivation of Curl, grad and divergence in cylindrical and spherical coordinate systems.
• Unit II:(Governing Equations and Kinematics) Continuum hypothesis, forces acting on a fluid, stress tensor, analysis of relative motion in the neighborhood of a point, Euler’s theorem, equation of continuity, Reynolds transport theorem, conservation of mass, material surface, momentum equation.
• Unit III:(Vorticity and Two-Dimensional Irrotational Flows) Stream lines, Bernoulli’s theorem, energy equation, circulation, Kelvin’s circulation theorem, vorticity, Lagrange’s theorem on permanence of vorticity, two dimensional irrotational flow of an incompressible fluid, Milne-Thomson circle theorem, Blasius’ theorem, flow past an airfoil, the Joukowski transformation, theorem of Joukowski and Kutta.
• Unit IV:(Axisymmetric Flows and Viscous Incompressible Flows) Axisymmetric flows, Stokes stream function, Butler’s sphere theorem, flows due to source, doublet, uniform flow past a sphere, irrotational three dimensional flow, Weiss’ sphere theorem. Constitutive equations for incompressible fluids, derivation of Navier-Stokes equations, unidirectional flows, Poiseuille flow, Couette flow, Stokes first and second problems, stagnation point flows, dynamical similarity and Reynolds number.
• Unit V:(Low Reynolds Number Flows and Boundary Layer Theory) Flows at low Reynolds number, axisymmetric flow of a viscous fluid, uniform flow past a sphere at low Reynolds number, torque and drag on a sphere due to a uniform flow, Prandtl model for boundary layer, boundary layer equation, solution for a flow past a plate.

Course Learning Objective

1. Define basic properties and laws that govern fluid motion, study kinematics and dynamics of fluids using these laws.
2. Study the fluid properties and relationships between physical quantities.
3. Understand the principles of conservation of mass, balance of momentum and energy applied to fluid motions.
4. Formulate physical properties in the form of mathematical equations.
5. Study the properties of fluids and the applications of the principles of fluid mechanics.
6. Study different types of flows, their governing equations, examples illustrating such flows and the properties of physical quantities associated with such flows.

Recommended Books

1. Batchelor, G. K. An Introduction to Fluid Mechanics. Cambridge University Press, 1993
2. Happel, J. and Brenner, H. Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965
3. Schlichting, H. and Gersten, K. Boundary-Layer Theory. with contributions by Egon Krause and Herbert Oertel, Jr., translated from the ninth German edition by Katherine Mayes, 8th revised and enlarged ed. Springer-Verlag, Berlin, 2000
4. Landau, L. D. and Lifshitz, E. M. Fluid Mechanics. Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., 1959
5. Kambe, T. Elementary Fluid Mechanics. World Scientific Publishing Co. Pvt. Ltd., Hackensack, NJ, 2007
6. O’Neill, M. E. and Chorlton, F. Ideal and Incompressible Fluid Dynamics. Ellis Horwood Series: Mathematics and its Applications, Ellis Horwood Ltd., Chichester; Halsted Press (John Wiley & Sons, Inc.), New York, 1986
7. Chorin, A. J. and Marsden, J. E. A Mathematical Introduction to Fluid Mechanics. 3rd ed. Texts in Applied Mathematics, 4, Springer-Verlag, New York, 1993