Course
Fluid Mechanics
Brief history of fluid mechanics, Fluids and their properties, Concepts of viscosity, thermal conductivity, mass diffusivity, compressibility and surface tension, Molecular considerations of the same. Hydrostatics – center of pressure, center of buoyancy and meta centre, ISA. Tensor calculus (Cartesian Tensors). Eulerian and Lagrangian methods of describing fluid motion, streamlines, streack lines and path lines. Kinematics of fluids – translation, rotation and deformation, circulation, Green’s Stokes theorems. Derivation of governing equations for mass, momentum, energy in the differential and integral forms and their specialization for inviscid and potential flow. Equations in non-inertial frames. Bernoulli’s equation. One-dimensional flow. Laminar flows like Couette flow and Hagen-Poiseuille flow, flow in bearings and boundary layers. Dimensional analysis Viscous flow over a flat plate and in pipes – transition, turbulent flow, skin friction and losses in pipes
Course structure & Assessments
4 credit course, weekly online assignments, 2 in-person invigilated quizzes, 1 in-person invigilated end term exam For details, visit Academics.
| Week 1 | Basics of Fluid Mechanics: • Introduction to fluid mechanics • Fluid and its properties • Dimensions and units • Dimensional analysis |
| Week 2 | Fluid statics (1): • Governing equation • Force on a submerged surface • Buoyancy: stability and metacenter |
| Week 3 | Fluid Statics (2): • Application: U-tube manometer • International Standard Atmosphere |
| Week 4 | Kinematics of Fluid Flow (1): • Eulerian and Lagrangian description of fluid flow • Flowlines: Pathlines, streamlines and streaklines • Cartesian tensor notation |
| Week 5 | Kinematics of Fluid Flow (2): • Velocity gradient tensor: Strain rate and vorticity • Vorticity, circulation and irrotational flow |
| Week 6 | Governing Equations of Fluid Flow (1): • Conservation of mass: Integral form • Reynolds transport theorem |
| Week 7 | Governing Equations of Fluid Flow (2): • Conservation of mass: differential form • Continuity equation in cartesian coordinates • Streamfunction • Ideal Flows |
| Week 8 | Governing Equations of Fluid Flow (3): • Conservation of linear momentum: Integral form • Stress tensor and surface traction • Stress-strain (rate) relationship |
| Week 9 | Governing Equations of Fluid Flow (4): • Conservation of linear momentum: differential form • Navier-Stokes equations in cartesian coordinates |
| Week 10 | Governing Equations of Fluid Flow (5): • Bernoulli equation • Conservation of linear momentum in a non-inertial frame of reference |
| Week 11 | Application of Equations of Fluid Flow: • Couette flow • Flow past a flat plate: boundary layers |
| Week 12 | Application of Equations of Fluid Flow: • Flow though circular pipes • Friction factor and losses |