Unit 1 Fluid Mechanics Basics

• Review of Basic Concepts and Fluid Properties:  Basic laws of fluid motion: Continuity
• momentum, and 6 15 GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Master of Engineering Level: PG Subject Code : ME02000541 Subject Name : Advanced Fluid Mechanics w.e.f. 2024-25 https://syllabus.gtu.ac.in/ Page 2 of 6 energy equations.  Internal stresses and external forces on fluid elements.  Concepts of vorticity and circulation.  Velocity potential and stream function.  Analysis of irrotational flow
• Governing Equations of Fluid Flow:  Navier-Stokes equations: Derivation and physical significance.  Exact solutions for simple flow cases: Plane Poiseuille and Couette flow.  Energy equation for fluid flows with thermal effects

Unit 2 Dynamics of Ideal and Real Flows

8 lecture hours

• Ideal Fluid Motion:  Euler’s equation of motion: Derivation and applications.  Generalized Bernoulli equation: Interpretation and applications in ideal fluid flows.  Principle of superposition and its application in potential flows
• Boundary Layer Theory:  Prandtl’s boundary layer equations.  Laminar boundary layer over a flat plate: Blausius solution.  Approximation methods for boundary layer equations.  Momentum integral methods: Holstein and Bohlen method.  Thermal boundary layer theory and Reynolds analogy

Unit 3 Turbulence and Stability

8 lecture hours

• Transition to Turbulence:  Introduction to hydrodynamic stability theory.  Orr-Sommerfeld equation: Basic principles and results from stability studies.  Factors affecting transition from laminar to turbulent flow
• Turbulent Flow Fundamentals:  Reynolds stress tensor: Definition and importance.  Phenomenological theories: Prandtl’s mixing length and eddy viscosity concepts.  Universal velocity distribution: Logarithmic law of the wall and wake.  Energy cascade and Kolmogorov’s theory

Unit 4 Gas Dynamics

• One-Dimensional Isentropic Flow:  Basic equations for isentropic flow in ducts. 8 20 GUJARAT TECHNOLOGICAL UNIVERSITY Program Name: Master of Engineering Level: PG Subject Code : ME02000541 Subject Name : Advanced Fluid Mechanics w.e.f. 2024-25 https://syllabus.gtu.ac.in/ Page 3 of 6  Choking phenomenon in isentropic flows.  Design and operation of nozzles and diffusers under varying pressure ratios.  Performance of real nozzles and applications
• Normal Shocks:  Governing equations for shock waves: Conservation of mass
• momentum, and energy.  Rankine-Hugoniot relations and Prandtl relations.  Weak and strong shocks: Thickness of shocks.  Effects of normal shocks on converging-diverging nozzle performance
• Oblique Shocks and Expansion Waves: Formation and analysis of oblique shocks.  Prandtl-Meyer expansion waves and applications

Unit 5 Advanced Applications in Fluid and Gas Dynamics

5 lecture hours

• Flow in Constant Area Ducts with Friction (Fanno Flow):  Governing equations and working formulas.  Choking phenomena due to friction.  Effects on performance of long ducts
• Flow in Constant Area Ducts with Heat Transfer (Rayleigh Flow):  Governing equations and thermodynamic implications.  Applications of Rayleigh flow in heat-exchanger designs
• Case Studies and Advanced Applications:  Real-world applications in aerospace and automotive engineering.  Numerical techniques for solving compressible flow problems