AMAT 42393: Fluid Dynamics

Course Code  : AMAT 42393

Title         : Fluid Dynamics

Pre-requisites : PMAT 41343

Learning Outcomes:

At the end of this course the student will

• Identify fluid flow motions and their properties

• formulate equations of motions based on three conservation laws

• simplify equations of motions considering flow characteristics and apply them in real world problems

• identify appropriate boundary conditions

• make use of complex analysis for two-dimensional fluid motions

• distinguish the dominant terms through dimensional analysis

• Analyze and interpret the 3D flow problems.

Course Content:

Vector Analysis Review:

• Orthogonal curvilinear coordinates, Gradient, Divergence and curl.

Basic Principles of Fluid Dynamics: 

• Fluids and fluid flow variables, Stream lines and path lines, Lagrangian and Euler approaches for describing fluid motions, Reynold’s Transport Theorem, conservation of mass (equation of continuity), momentum and energy

Newtonian fluid: 

• Inviscid and viscous fluids, Euler’s equation of Motion, Vorticity, irrotational motion under conservative forces, Bernoulli’s equation

Boundary condition: 

• Inlet and outlet conditions, no slip condition, pressure boundary conditions, radial and axisymmetric boundary conditions.

Flow in Pipes: 

• Laminar flow in pipes, Pressure drop and head loss, flows in non-circular and inclined pipes.

Two-Dimensional Motion: 

• Stream function and plotting stream lines, Complex potential, Sources and sinks, Vortices, Doublets and image systems, Milne-Thompson theorem.

Axi-symmetric Motion: 

• Stokes’ stream function in three dimensional flows.

Three-Dimensional Motion: 

• Irrotational motion, Laplace’s Equation, Spherical Harmonics, Flow of a stream past a fixed sphere, Motion of a sphere in a fluid, Impulsive motion.

Dimensional Analysis and modeling : 

• Nondimensionalization of equations

Method of Teaching and Learning :  A combination of lectures, classroom discussions and group projects.

Assessment : Based on tutorials, tests, presentations and end of course Examination.

Recommended Reading :

1. Ruban, A.I. & Gajjar, J.S.B. (1 st Ed., 2014). Fluid Dynamics (classical fluid dynamics), Oxford.

2. Cengel, Y.A. & Cimbala, J.M. (2006). Fluid Mechanics (Fundamentals and Applications), McGraw Hill.

3. Feistauer, M. (1993). Mathematical Methods in Fluid Dynamics, Chapman and Hall/CRC.

4. Chorin, A.J. & Marsden, J.E. (2012). A Mathematical Introduction to Fluid Mechanics, Springer Science & Business Media.

5. Henningson, D.H. & Berggren, B. (2005). Fluid Dynamics Theory and Computation, Stockholm.

6. Chorlton, F. (2005). Textbook of Fluid Dynamics, CBS Publishers & Distributors