Fluid Mechanics Course

Lesson 1 • Nature and Classification of Fluids

Defines fluids, distinguishes liquids from gases, and introduces Newtonian vs. non-Newtonian behavior. Sets the conceptual baseline for all subsequent analysis.

Lesson 2 • The Continuum Hypothesis

Explains the continuum assumption and its validity limits using the Knudsen number. Justifies the macroscopic approach used throughout the course.

Lesson 3 • Dimensional Analysis Basics

Introduces dimensions, units, and the Buckingham Pi theorem for forming dimensionless groups. Provides tools used in every experimental and analytical chapter.

Lesson 1 • Pressure Concepts and Measurement

Defines absolute, gauge, and vacuum pressure and introduces manometry. Connects pressure measurement to real instrumentation used in labs and industry.

Lesson 2 • Buoyancy, Flotation, and Stability

Applies Archimedes' principle and evaluates metacentric height for floating bodies. Provides stability criteria used in naval and offshore engineering.

Lesson 3 • Forces on Curved Surfaces

Resolves horizontal and vertical components of hydrostatic force on curved boundaries. Extends plane-surface methods to cylindrical and spherical geometries.

Lesson 4 • Hydrostatic Pressure Distribution

Derives the hydrostatic equation and applies it to incompressible and compressible fluids. Builds the pressure-depth relationship used in force calculations.

Lesson 1 • Flow Description Methods

Contrasts Lagrangian and Eulerian descriptions and defines material derivative. Establishes the mathematical framework for all kinematic and dynamic analysis.

Lesson 2 • Flow Classification and Patterns

Classifies flows as laminar or turbulent, rotational or irrotational, and 1D through 3D. Guides selection of appropriate governing equations in later chapters.

Lesson 3 • Flow Visualization Concepts

Defines streamlines, streaklines, and pathlines and relates them under steady conditions. Connects mathematical definitions to experimental visualization techniques.

Lesson 1 • Reynolds Transport Theorem

Converts system-based conservation laws to control-volume form via the Reynolds Transport Theorem. This theorem underpins every integral conservation equation in the course.

Lesson 2 • Angular Momentum Equation

Extends momentum analysis to rotating systems such as turbines and sprinklers. Provides the torque-angular momentum relationship for turbomachinery applications.

Lesson 3 • Linear Momentum Equation

Applies Newton's second law to control volumes to find forces on pipes, bends, and nozzles. Includes body forces, pressure forces, and momentum flux terms.

Lesson 4 • Continuity Equation

Applies mass conservation to fixed and moving control volumes for compressible and incompressible flows. Establishes velocity-area relationships used in duct and nozzle analysis.

Lesson 1 • Energy Equation for Real Flows

Extends Bernoulli to include pump work, turbine work, and head losses. Enables full energy budgeting for real piping and hydraulic systems.

Lesson 2 • Bernoulli Equation Applications

Solves flow rate, velocity, and pressure problems in nozzles, orifices, and Venturi meters. Demonstrates direct engineering use of the Bernoulli equation.

Lesson 3 • Flow Measurement Devices

Analyzes Venturi meters, orifice plates, flow nozzles, and rotameters using energy principles. Connects theory to calibration and uncertainty in industrial measurement.

Lesson 1 • Laminar Flow in Pipes

Derives the Hagen-Poiseuille velocity profile and pressure drop for fully developed laminar flow. Establishes the baseline viscous flow solution for comparison with turbulent cases.

Lesson 2 • Minor Losses in Pipe Systems

Quantifies head losses through fittings, valves, bends, and expansions using loss coefficients. Completes the head-loss toolkit needed for full system analysis.

Lesson 3 • Pump and System Curve Matching

Constructs system curves and overlays pump performance curves to find the operating point. Covers pump selection, series/parallel pump arrangements, and cavitation avoidance.

Lesson 4 • Pipe Network Analysis

Solves series, parallel, and branching pipe networks using continuity and energy equations. Introduces iterative methods for multi-loop network problems.

Lesson 1 • Boundary Layer Separation

Explains adverse pressure gradients, separation points, and wake formation. Connects separation to pressure drag and stall in aerodynamic applications.

Lesson 2 • Boundary Layer Fundamentals

Defines boundary layer thickness, displacement thickness, and momentum thickness. Introduces the physical mechanism of viscous retardation near solid surfaces.

Lesson 3 • Laminar Boundary Layer Analysis

Applies the Blasius solution and von Kármán integral method to flat-plate laminar flow. Provides analytical drag predictions for streamlined surfaces.

Lesson 4 • Drag and Lift on Bodies

Calculates total drag and lift using drag/lift coefficients for common shapes. Applies results to vehicle aerodynamics, structural wind loads, and airfoil design.

Lesson 1 • Fanno and Rayleigh Flow

Models adiabatic flow with friction (Fanno) and frictionless flow with heat transfer (Rayleigh). Provides tools for analyzing combustion chambers and long gas pipelines.

Lesson 2 • Isentropic Flow with Area Change

Derives area-velocity and area-Mach relations for isentropic duct flow. Explains the converging-diverging nozzle and the role of the throat in choking.

Lesson 3 • Thermodynamic Foundations for Compressible Flow

Reviews ideal gas law, isentropic relations, and speed of sound derivation. Establishes the thermodynamic tools required for all compressible flow calculations.

Lesson 4 • Oblique Shocks and Expansion Waves

Analyzes oblique shock geometry using the theta-beta-Mach relation and Prandtl-Meyer expansion. Extends shock analysis to two-dimensional supersonic flow fields.