Department of Mathematics
Certificate Course on
Incompressible Fluid Dynamics
(Hybrid Mode)
Course Duration : 42 Hours
Course Starting Date : 10. 12. 2024
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Course Description
Fluid Dynamics is an application area of the subject of Partial Differential Equations. In general terms, the subject of fluid dynamics deals with any physical problem that involves fluid flows. Some examples are flow of air past aircraft and automobiles, flow of blood in our vasculature, flow of air as we breathe, atmospheric flows, etc. This course will build from first principles, and after briefly considering the relatively simple fluid statics scenarios, will derive the integral as well as differential forms of equations that govern fluid dynamics. Different approximations (incompressible, irrotational, inviscid, and boundary layers) will be considered and the contexts in which each of these approximations are useful will be clearly elaborated upon. At the end of the course, students will be able to solve a range of problems analytically and will be ready to participate in projects in various application areas of fluid dynamics.
Course Instructor
Dr. Sanyasiraju V S S Yedida
Professor
Department of Mathematics
IIT MADRAS, Chennai
Pre-requisites
Eligibility: B.Sc. (Mathematics / Physics), M.Sc. (Mathematics / Physics), Research Scholars.
Course Objectives
- Students will be able to solve solve fluid statics and simple kinematics and dynamics problems involving pressure distributions and buoyancy.
- Students will be able to apply physical principles of mass conservation, Newton’s second law and energy conservation to derive the integral as well as differential forms of governing equations (dimensional as well as non-dimensional forms) of fluid mechanics and apply them to solve a range of physical problems.
- Students will be able to apply scaling principles to derive the boundary layer equations and apply boundary layer concepts to calculate drag in simple situations.
- Students will be able to solve problems in the incompressible-inviscid-irrotational regime and understand when it is reasonable to make these approximations.
Weekly Lecture Plan (Two 1.5 hrs lectures per week) Time: 2.00 pm – 3.30 pm
Week No. | Lecture Topic | COs Met | Tentative Dates |
1 | The concept of a fluid, Fluid as a continuum, Properties of the velocity field, Thermodynamic properties of a fluid, Viscosity and other secondary properties, Flow patterns: Streamlines, streak lines and path lines. | CO1 | 10.12.2024 and 13.12.2024 |
2 | Pressure distribution in a fluid: Pressure and pressure gradient, Equilibrium of a fluid element, Hydrostatic pressure distributions, Application to manometry, Hydrostatic forces on plane and curved surfaces and in layered fluids, Buoyancy and stability, Pressure distribution in rigid body motion, Pressure measurement. | CO1 | 17.12.2024 and 20.12.2024 |
3, 4, 5 | Differential relations for a fluid particle: The acceleration field of a fluid, Differential equations of mass conservation, linear momentum, angular momentum and energy, Boundary conditions, Stream function, Some illustrative incompressible viscous flows, | CO2 | 24.12.2024 and 27.12.2024 31.12.2024 and 03.01.2025 07.01.2025 and 10.01.2025 |
6, 7, 8 | Flow past immersed bodies: Reynolds number and geometry effects, Momentum integral estimates, Boundary layer equations, Flat plate boundary layer, Boundary layers with pressure gradient. | CO3 | 13.01.2025 and 17.01.2025 20.01.2025 and 23.01.2025 28.01.2025 and 31.01.2025 |
9, 10, 11 | Potential flows: Vorticity and irrotationality, Frictionless irrotational flows, Elementary plane flow solutions, Superposition of plane flow solutions, Plane flow past closed body shapes, Airfoil theory, Axisymmetric potential flow. | CO4 | 03.02.2025 and 07.02.2025 10.02.2025 and 14.02.2025 18.02.2025 and 21.02.2025 |
12, 13, 14 | Integral relations for a control volume: Basic physical laws of fluid mechanics, The Reynolds Transport Theorem, Conservation of mass, Linear momentum equation, Angular momentum theorem, Energy equation, Frictionless flow: Bernoulli equation. | CO2 | 25.02.2025 and 28.02.2025 04.03.2025 and 07.03.2025 11.03.2025 and 14.03.2025 |
Type of Evaluation | % Contribution in Grade |
Homework | 15 |
Project / Term Paper | 15 |
Mid Semester Exam | 30 |
End Semester Exam | 40 |
Course Duration : 42 Hours
Course Starting Date : 10. 12. 2024
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For Further Details
Sri. R. Soundararajan
Head, Department of Mathematics
Ph. No. 9840128824
Dr. N. Vishnu Ganesh
Assistant Professor
Ph. No. 9842408674
Email : [email protected]