Aerodynamics Lecture 2: Flow Variables

Introduction

• Recap from last lecture:
  • Difference in perspective from fluid mechanics.
  • Body forces, balancing forces, empirical quantities, and flow properties.
• Focus of current lecture:
  • Dive into flow variables and their physical meaning.
  • Understand how they generate forces on objects.

Key Flow Variables

• Velocity:
  • Bulk fluid quantity, represented by u, v, w for x, y, z directions.
  • Units: distance/time.
  • Considered macroscopically using the Eulerian point of view.
• Pressure:
  • Molecular quantity, force per area.
  • Force from fluid molecules impacting surfaces.
  • Pressure difference across a surface generates force.
• Density:
  • Represented by ρ, units: mass/volume.
  • Number of molecules within a fixed volume.
  • Density gradients lead to force across surfaces.
• Temperature:
  • Represented by T or θ, dimensionless (Kelvin/Celsius).
  • Average kinetic energy of molecules.
  • Temperature differences across surfaces can create forces.
• Viscosity:
  • Dynamic viscosity (μ), units: force∙time/area.
  • Kinematic viscosity (ν), dynamic viscosity normalized by density.
  • Molecular property, represents fluid friction.

Flow Situations and Assumptions

• Incompressible and Inviscid Flow:
  • Density constant, viscosity negligible.
  • Dominated by velocity and pressure (e.g., Bernoulli equation).
• Incompressible Flow with Viscosity:
  • Surfaces and boundary layers make viscosity important (Navier-Stokes equations).
• Compressible and Viscous Flow:
  • Complex to solve, often requires simulations and measurements.

Molecular and Macroscopic Considerations

• Forces generated at molecular level but examined macroscopically.
• Continuum assumption applies; molecular interactions create macroscopic forces.

Relation through Ideal Gas Law

• Pressure, density, temperature are interrelated.
• Change in one affects the others.

Summary

• Discussed main flow variables: velocity, pressure, density, temperature, viscosity.
• Relationship of flow variables to force generation.
• Next lecture: General body forces in aerodynamics.