Viscosity and Fluid Dynamics Lecture Notes

Key Concepts

• Empty Box & Lid Experiment
  • Demonstrates fluid resistance when a lid is moved over a fluid-filled container.
  • Without fluid, the lid moves with constant speed.
  • With fluid, the lid slows down and stops due to viscous resistance.

Fluid Properties

• Viscous Resistance
  • Caused by adhesive forces between the lid and the fluid.
  • Top layer of fluid moves with the lid, creating a velocity gradient.
  • Bottom layer of fluid does not move, causing drag on the lid.

Key Definitions

• Viscous Force (Fv)
  • Depends on:
    • Area: Area of the lid in contact with the fluid.
    • Speed: Faster movement increases viscous force.
    • Depth (D): Inversely proportional to the depth of fluid.
    • Viscosity (η): Measure of a fluid's resistance to flow.

Viscosity

• Coefficient of Viscosity (η)
  • Indicates how resistant a fluid is to flow (how thick it is).
  • Example values:
    • Honey/corn syrup: high viscosity
    • Water: low viscosity
    • Gases: even lower viscosity.

Units of Viscosity

• Viscosity Units:
  • Pascals seconds (Pa·s) or poise (P).
  • 1 poise = 0.1 Pa·s.
  • Example: Water at 0°C has a viscosity of about 1.8 mPa·s (or cP).

Temperature Effects

• Viscosity is temperature-dependent:
  • Colder temperatures increase viscosity (e.g., engine oil in cold weather).
• Specific examples:
  • Water (0°C): 1.8 mPa·s
  • Blood: 3-4 mPa·s
  • Air: 0.018 cP
  • Engine oil: around 200 cP.

Newtonian vs Non-Newtonian Fluids

• Newtonian Fluid:
  • Viscosity is constant regardless of flow speed.
• Non-Newtonian Fluid:
  • Viscosity changes with flow speed.

Poiseuille's Law

• Definition: Equation to calculate volume flow rate of a fluid through a tube.
• [ Q = \frac{\Delta P \cdot \pi R^4}{8ηL} ]
  • Where:
    • Q: Volume flow rate (m³/s)
    • ΔP: Pressure differential (P1 - P2)
    • R: Radius of the tube
    • η: Viscosity
    • L: Length of the tube.

Key Points of Poiseuille's Law

• Flow rate is directly proportional to pressure difference and radius to the fourth power.
• Flow rate is inversely proportional to viscosity and length of the tube.
• Assumes laminar flow and Newtonian fluids.

Conclusion

• Understanding viscosity and fluid dynamics is crucial for medical and engineering applications.
• Poiseuille's Law provides a practical way to analyze fluid flow in various contexts.