Fluid Mechanics Lecture Notes

Definition of a Fluid

• Fluid: A substance or collection of particles that move and change shape under an external shearing stress.
• Common Forms: Gases and liquids are typical representations of fluids.

Conservation Principles

• Key Principles: Conservation of mass, Newton’s second law (instead of momentum), and the first and second laws of thermodynamics.

Common Fluid Properties

• Density: Mass per unit volume.
• Specific Volume: Inverse of density.
• Specific Weight: Density times the gravity constant.
• Specific Gravity: Ratio between the density of the fluid and the density of water.
• Ideal Gas Equation: (P/\rho = RT)

Viscosity

• Importance: A critical property in fluid mechanics.
• No-slip Condition: Fluid velocity is zero at the contact surface.
• Shear Strain Rate: Velocity change per unit distance (dy).
• Newtonian Fluids: Fluids that have a linear relationship between shear stress and shear strain rate.
• Viscosity (µ): Dynamic viscosity is a constant for Newtonian fluids; units are Pa·s or kg/(m·s).

Kinematic Viscosity

• Definition: Dynamic viscosity divided by the density of the fluid.
• Units: m²/s

Example Problem

• Situation: A snowmobile on ice with a thin water film.
• Parameters:
  • Water film thickness: 14 microns
  • Contact area: 960 cm²
  • Constant speed: 40 km/h
• Calculation:
  • Shearing stress (τ): Dynamic viscosity of water times the shear strain rate (du/dy).
  • Force Calculation: Shearing stress equals force over area.
  • Viscosity of Water: 1.787 mPa·s at 0°C.
  • Required Thrust Force: 136.2 N

Additional Resources

• Links to further examples and lectures are available in the lecture description.