Fluid Dynamics

1. Governing Equations
   1. Conservation Laws
      1. Conservation of Mass (Continuity Equation)
         1. Derivation for Incompressible Flow
            1. Constant Density Assumption
            2. Simplifications for Fluid Domains
         2. Derivation for Compressible Flow
            1. Variable Density Consideration
            2. Relation to Thermodynamic Principles
         3. Application in Complex Geometries
      2. Conservation of Momentum (Navier-Stokes Equations)
         1. Navier-Stokes Equations for Incompressible Flow
            1. Simplified Form for Low-speed Flows
            2. Stream Function and Vorticity Formulations
         2. Navier-Stokes Equations for Compressible Flow
            1. Additional Energy and Pressure Terms
            2. Shock Wave Considerations
         3. Non-Newtonian Fluid Considerations
            1. Modifications for Shear-Dependent Viscosity
            2. Incorporation of Elastic Effects
         4. Understanding Non-dimensional Forms
            1. Influence of Reynolds Number
            2. Dimensionless Scale Analysis
         5. Solutions and Approximations
            1. Analytical Solutions for Simple Cases
            2. Numerical Solutions Through Computational Methods
      3. Conservation of Energy
         1. Total Energy Equation
            1. Internal, Kinetic, and Potential Energy
            2. Heat Transfer Considerations
         2. Thermal Energy Equation
            1. Coupling with Thermodynamics
            2. Effect of Heat Sources/Sinks
         3. Simplifications in Specific Scenarios
            1. Adiabatic Processes
            2. Isothermal Processes
         4. Thermodynamic Relationships
            1. First and Second Laws of Thermodynamics
            2. Entropy Generation and Efficiency
   2. Equation of State
      1. Definition and Role
         1. Relation between Pressure, Temperature, and Volume
         2. Ideal Gas Law as a Simplistic Model
      2. Complex Equations of State
         1. Van der Waals Equation for Real Gases
         2. Cubic and Other Polynomial Equations of State
      3. Application in Varying Conditions
         1. Supercritical and Hypersonic Flows
         2. Phase Changes and Multiphase Flow Situations
      4. Limitations and Assumptions
         1. Deviations from Ideal Behavior
         2. Comparisons with Empirical Data
   3. Bernoulli’s Equation
      1. Basic Formulation
         1. Assumptions of Inviscid Flow
         2. Influence of Pressure, Velocity, and Height
      2. Applications in Simple Systems
         1. Pipe Flow and Venturi Effect
         2. Fluid Measurement Devices, e.g., Pitot Tubes
      3. Corrections for Real Flow Conditions
         1. Losses due to Friction and Turbulence
         2. Inclusion of Viscous Effects
      4. Extensions and Derivations
         1. Bernoulli’s Equation for Compressible Flow
         2. Applications in Aerodynamics and Hydrodynamics
      5. Interpretation in Engineering Problems
         1. Energy Conservation in Moving Fluids
         2. Pressure Changes in Expanding and Contracting Geometries