Similitude And Approximations In Engineering

ABOUT THE COURSE:This course introduces the tools required for computational and experimental investigations of complex phenomena. It introduces the beauty of similitude and self-similitude that lead to simplification of problems. The course is taught largely with examples and case studies in the area of fluid mechanics, heat transfer and viberations.INTENDED AUDIENCE: For all students and researchers in the area of fluid mechanics, solid mechanics and transport phenomenaPREREQUISITES: The full benefit will be obtained by those students who have basic knowledge of fluid mechanics.INDUSTRY SUPPORT: It forms the basis for experimental investigations in all engineering

Syllabus

Week 1: Introduction
Science and physical properties , Dimensions of physical quantities, Nature of quantitative investigations, Variables and parameters, Concept of similitudeWeek 2:Obtaining modelling rules from governing equations and boundary
conditions, Example include damped oscillations, Transient conduction in an infinite slab, viscous fluid flows, significance of Euler Froude and Reynolds numbersWeek 3:Obtaing modelling rules from classical dimensional analysis of Bridgeman ,
Simple examples, Dimensional Analysis of Centrifugal Pumps, Obtininf Kepler's law dimensionally, Supplementing dimensionalm analysis with physical knowledge. Huntley's extension, Directional analysis, Example: Free convectionWeek 4:Scale factor or law approach,
Inter-relationships between scale factors for kinematic dynamic quantities, Obtaining modelling and prediction rules through law approachWeek 5:Basis of approximations,
estimation, regular and irregular approximation, Examples include estimating time for baking potatoes, spreading of oil slick, flow pat an oscillation sphereWeek 6:Self-similarity:
Stokes first and second problems, nuclear explosion, Blasius and Falkner- Skan profilesWeek 7:Relaxation of modelling rules ,
Disregarding weak laws, Self-modelling; Sequential and segmented modelling, Regional modelling, directional modelling, Bypassing strong rules, restriction on generality, Simulating laws: dummy mass and dummy springs, Testing ship modelsWeek 8:Detailed Case Studies ,
Aerodynamic testing of tall Chimneys, Studying human voicing by slowing down motion and by making 10x models, Filtration