Fluid Mechanics & Machines – Lecture 1 & 2 Comprehensive Notes

Lecture Context - Course: BMEE204L – Fluid Mechanics & Machines - Instructor: Dr. G. Vinayagamurthy (Associate Professor, CAMIT & School of Mechanical Engineering, VIT-Chennai) - Venue: Aerodynamics Laboratory - Lecture #: 1 & 2 (Fall 2025–26) – Date: 10-07-2025 ## Historical Evolution of Fluid Mechanics - Classical pioneers - Archimedes (c. 287–212 BC) – Buoyancy principle, hydrostatics. - Bernoulli (1667–1748) – Conservation of mechanical energy in flows. - Newton (1642–1727) – Viscous shear concept, laws of motion. - Leibniz (1646–1716) – Differential calculus; groundwork for continuum analysis. - Euler (1707–1783) – Euler’s equations for inviscid flow. - Navier (1785–1836) – Viscous term in motion equation. - Stokes (1819–1903) – Stokes flow, boundary-layer beginnings. - Reynolds (1842–1912) – Transition, Reynolds number. - Prandtl (1875–1953) – Modern boundary-layer theory. - Taylor (1886–1975) – Turbulence & dimensional analysis. - Importance: - Development of analytical, experimental and computational methods. - Shapes modern engineering, meteorology, oceanography and biomechanics. ## Real-World Applications of Fluid Mechanics ### Weather & Natural Flows - Climate modelling (NOAA GFDL CM2.1) - Surface‐air temperature change map (A1B scenario, 2050\text{s} vs 1971{-}2000). - Precipitation change contours: \pm 60\;\text{inches yr}^{-1} range shown. - Severe events: Hurricanes, tornados, downbursts. - Meteorological instrumentation, forecasting, wind loading on structures. ### Vehicles & Transportation - Aerodynamics of cars, trucks, cycles—drag reduction. - Hydrodynamics of boats, offshore racing; propulsion efficiency. - Aircraft & spacecraft – lift, stability, shock waves. ### Energy & Power - Power-plant steam/water circuits. - Wind-turbine blade design; Betz limit. - Ocean/tidal energy (AQUARET, 2008). ### Civil & Built Infrastructure - Tall towers (CN, Tokyo Skytree, Ostankino, Oriental Pearl, Berlin, Eiffel, Tokyo Tower) – vortex shedding, wind-induced sway. - Bridges – aeroelastic flutter (“bridge to sway” failures). - Urban planning – pollutant dispersion, street-canyon ventilation, satellite airflow mapping. ### Biomedical & Health Care - Hemodynamics: - Normal vs. narrowed (stenotic) vessel; pressure–flow interplay. - Blood-pump & ventricular assist device (VAD) design; avoiding hemolysis. - Temperature‐controlled injections (fluid–thermal interaction graph 20!\unicode{x2013}!26\,^{\circ}\text{C}). - Respiratory airflow; drug aerosol transport. ### HVAC (Heat-Ventilation-Air-Conditioning) - Airflow distribution, thermal comfort indices, duct sizing. ### Sports & Recreation - Water sports (surfing, rowing), auto racing, cycling—boundary layer control, drafting. - Offshore racing – planing hull hydrodynamics. ## Course Curriculum Snapshot (BMEE204L) ### Objectives - Apply hydrostatics, mass/momentum conservation, Euler & Bernoulli relations. - Understand fluid properties/behaviour in internal & external flows. - Quantify pipe losses; grasp boundary-layer theory. - Introduce pumps & turbines. ### Expected Outcomes 1. Interpret fluid properties & statics in engineering systems. 2. Describe flows via Lagrangian and Eulerian frames. 3. Formulate governing equations. 4. Analyse viscous pipe flow & losses. 5. Perform dimensional analysis. 6. Predict flow separation via boundary-layer concepts. 7. Evaluate hydraulic-machine performance. ### Module Synopsis - M1 Fluid Statics & Buoyancy (8 h) – Pascal’s law, manometry, forces on surfaces, stability of floating bodies. - M2 Fluid Kinematics (5 h) – Material derivative, stream/path/streak lines, \psi & \phi, Reynolds Transport Theorem. - M3 Fluid Dynamics (5 h) – Continuity, Euler/Bernoulli, venturi/orifice/Pitot, momentum equation, Navier–Stokes. - M4 Viscous Pipe Flow (6 h) – Laminar (Hagen–Poiseuille \Delta p=\frac{32\mu UL}{D^{2}}), turbulent (Darcy–Weisbach h_{f}=f\frac{L}{D}\frac{V^{2}}{2g}), Moody chart, minor losses. - M5 Dimensional Analysis (5 h) – Rayleigh, Buckingham \pi, similitude, model laws. - M6 Boundary Layer (5 h) – Thickness, momentum integral \theta\frac{dU*{e}}{dx}+\frac{d\theta}{dx}U*{e}=\frac{\tau*{w}}{\rho U*{e}}, separation, drag/lift, control. - M7 Hydraulic Machines (9 h) – Centrifugal pumps (head, priming, cavitation), Pelton/Francis/Kaplan turbines, specific speed N_{s}=N\sqrt{P}/H^{5/4}, draft tube, governing. - M8 Contemporary Issues (2 h) – Emerging technologies. ### Assessment Scheme - CAT-1 & CAT-2: 2\times15=30 marks. - Quiz-1: 10; Quiz-2: 10. - Assignment: 10. - FAT (Final): 40. ## Fundamental Concepts & Definitions - Fluid – Substance that experiences continuous deformation under any finite shear stress. This means that unlike solids, fluids will continuously flow as long as a shear stress is applied, no matter how small. They do not resist permanent shape change. - “Zero-memory” (ideal) vs. viscoelastic fluids (non-ideal). - Zero-memory fluids respond only to current stresses, while viscoelastic fluids exhibit time-dependent deformation, retaining some