Syllabus

Syllabus#

Course Duration: 16 Weeks

Course Description#

This course introduces the fundamental principles of fluid mechanics, focusing on the behavior of incompressible fluids. Topics include fluid statics, kinematics, and dynamics, with an emphasis on differential analysis, including the Navier-Stokes equations and Bernoulli’s equation. Students will apply these principles to solve practical engineering problems.

Week-by-Week Outline#

Weeks 1-2: Introduction to Fluid Mechanics and Properties#

  • Prerequisites: Math and physics

  • Definition of fluids and distinction between solids and fluids.

  • Continuum hypothesis: fluid as a continuum.

  • Common physical quantities and units.

  • Fluid properties: density, viscosity, surface tension.

  • Ideal gas law

  • No-slip condition

  • Types of flows: laminar and turbulent

  • Flow classification: laminar vs. turbulent, steady vs. unsteady, uniform vs. non-uniform

Lab: Measurement of basic fluid properties (density, viscosity, surface tension).

Week 3: Fluid Kinematics#

  • Lagrangian vs. Eulerian descriptions of fluid motion.

  • Velocity and acceleration fields.

  • Concept of vorticity and circulation.

  • Streamlines, streaklines, and pathlines.

  • Velocity potential and stream function.

  • Flow classification: rotational vs. irrotational, incompressible vs. compressible.

Week 4: Fluid Statics#

  • Hydrostatic equation: \(\frac{dp}{dz} = -\rho g\).

  • Gauge vs. absolute pressure, vacuum pressure, and pressure head.

  • Pressure variation in incompressible and compressible static fluids.

  • Barometers, piezometers, and manometers.

  • Hydrostatic pressure forces on plane surfaces: resultant force and center of pressure.

  • Hydrostatic pressure on curved surfaces: decomposition into horizontal and vertical components.

  • Applications: pressure forces on submerged surfaces, dams, and gates.

  • Buoyancy force and Archimedes’ principle.

  • Stability of floating and submerged bodies: metacentric height and applications (ships, submarines).

  • Manometry errors: capillary effects and density variation.

Optional Enrichment:

  • Hydrostatics in rotating fluids (free surface of a rotating liquid, paraboloid shape).

  • Applications to engineering systems (hydraulic presses, storage tanks, ship stability).

Midterm

Week 5: Navier–Stokes Equations#

  • Review of Newton’s second law and its application to fluids.

  • Forces in fluid flow: pressure, body forces, and viscous forces.

  • Derivation of the Navier–Stokes equations for incompressible flow.

Week 6: Bernoulli’s Equation and Energy Conservation#

  • Derivation of Bernoulli’s equation from the Euler equations for steady, incompressible, inviscid flow.

  • Physical interpretation of Bernoulli’s equation as energy conservation.

  • Practical applications of Bernoulli’s equation (nozzles, flow meters, venturi tubes).

  • Limitations and conditions for Bernoulli’s equation.

Weeks 7-8: Control Volume Analysis and Integral Conservation Laws#

  • Introduction to the Reynolds Transport Theorem (RTT) as the bridge between system and control volume approaches.

  • Application of RTT to derive the integral conservation equations:

    • Continuity equation (conservation of mass).

    • Momentum equation (linear and angular momentum).

    • Energy equation (first law of thermodynamics for control volumes).

  • Assumptions and simplifications: steady flow, uniform flow, one-dimensional approximations.

  • Applications of integral analysis to engineering systems:

    • Jet propulsion and rocket thrust.

    • Forces on bends and nozzles in piping systems.

    • Turbines and pumps (energy transfer).

    • Flow over control surfaces and aerodynamic forces.

Midterm

Weeks 9-10: Dimensional Analysis and Similarity#

  • Concept of dimensional homogeneity and the importance of nondimensionalization in fluid mechanics.

  • The Buckingham Pi theorem: procedure to identify dimensionless groups.

  • Key dimensionless numbers in fluid mechanics:

    • Reynolds number (inertia vs. viscous forces).

    • Froude number (inertia vs. gravity forces).

    • Mach number (inertia vs. compressibility effects).

    • Weber number (inertia vs. surface tension).

    • Strouhal number (unsteady vs. convective inertia).

  • Modeling and similarity: geometric, kinematic, and dynamic similarity.

  • Applications in wind tunnel testing, hydraulic modeling, and prototype scaling.

Weeks 11-12: Differential Analysis of Fluid Flow#

  • Conservation of mass: continuity equation in differential form.

  • Conservation of momentum: revisiting the Navier–Stokes equations for incompressible flow.

  • Application of differential equations to simple 1D and 2D flows.

  • Exact solutions of Navier–Stokes for simple cases: Couette flow, Poiseuille flow, stagnation flow.

  • Concept of boundary conditions for viscous flows (no-slip, symmetry, far-field).

  • Velocity potential and stream function.

Lab: Computational exploration of Couette and Poiseuille flows using Python.

Midterm

Weeks 13-14: Viscous Flow and Internal Flow in Pipes#

  • Laminar vs. turbulent flow: Hagen–Poiseuille equation for laminar flow, transition criteria (Reynolds number).

  • Head loss in pipes: Darcy–Weisbach equation and empirical correlations.

  • Use of the Moody chart and friction factor correlations (Blasius, Colebrook–White equation).

  • Minor losses: fittings, bends, valves, expansions, and contractions.

  • Energy equation for pipe systems: combining major and minor losses.

  • Pipe networks:

    • Series and parallel pipe systems.

    • Conservation of mass and energy at junctions (Hardy Cross method).

    • Iterative and numerical methods for solving complex pipe networks.

    • Use of computational tools for large networks.

Week 15: Boundary Layers and External Flow#

  • Introduction to boundary layer concept: definition and physical significance.

  • Laminar vs. turbulent boundary layers.

  • Blasius solution (flat plate) and order-of-magnitude estimates.

  • Boundary layer thickness, displacement thickness, and momentum thickness.

  • Boundary layer separation and wake formation.

  • Drag: skin friction drag vs. pressure drag.

  • Lift generation: Kutta–Joukowski theorem (conceptual introduction).

  • Applications to external flow over cylinders, spheres, and airfoils.

Week 16: Turbomachinery#

  • Introduction to turbomachinery: classification (pumps, turbines, compressors, fans).

  • Basics of compressible flow: speed of sound, Mach number, and compressibility effects.

  • Compressible flow regimes: subsonic, transonic, supersonic, and their relevance in turbomachinery.

  • Euler’s turbine equation and energy transfer between fluid and rotor.

  • Performance analysis of pumps, turbines, and compressors (head, efficiency, specific speed).

  • Cavitation: causes, effects on performance, and design strategies to mitigate it.

  • Performance curves and characteristic maps: interpretation and applications.

  • Case studies: hydraulic turbines for hydropower, axial compressors in jet engines.

Midterm

Assessments#

  • 3 Laboratory Reports (in-lab experiments and computational): 14%

  • Midterm Exams (4): 76%

  • Free-topic presentation / experiment: 10%

Material#

  • Cengel, Yunus A., and John M. Cimbala. Fluid Mechanics: Fundamentals and Applications. McGraw-Hill, 2018. [CC18]

  • White, Frank M. Fluid Mechanics. McGraw-Hill, 2016. [Whi16]

  • Munson, Bruce R., Donald F. Young, Theodore H. Okiishi, and Wade W. Huebsch. Fundamentals of Fluid Mechanics. Wiley, 2012. [MYOH12]

  • Shames, Irving H. Mechanics of Fluids. McGraw-Hill, 2003. [Sha03]

  • Fox, Robert W., Alan T. McDonald, and Philip J. Pritchard. Introduction to Fluid Mechanics. Wiley, 2011. [FMP11]

Contents