Lecture on Fluid Dynamics and Bernoulli's Principle

Introduction to Fluid Dynamics

• Objective: Explore the behavior of air and water flow in different scenarios.
• Initial Observation: When creating strong airflow between two balls suspended on threads, instead of moving apart, they attract each other.

Experiment 1: Airflow Between Two Balls

• Setup: Balls suspended on threads with airflow blown between them.
• Observation: Balls get attracted to each other and rotate.
• Question: Why doesn't the airflow push them apart?

Experiment 2: Funnel and Rubber Ball

• Setup: Rubber ball placed in a funnel with airflow.
• Observation: The ball is sucked into the funnel and remains even when inverted.
• Conclusion: Airflow appears to have a suction effect rather than a pushing effect.

Experiment 3: Water Flow and Tennis Ball

• Setup: Tennis ball placed next to running water.
• Observation: Ball sticks to water and hangs on an inclined thread.
• Implication: Fast-moving gases or liquids exhibit counterintuitive properties.

Explanation Through Bernoulli's Principle

• Variable Cross-section Pipe: As pipe narrows, water flow speed increases.
• Pressure Dynamics:
  • Decreased cross-section -> increased speed requires force according to Newton’s second law.
  • Pressure in wider part > pressure in narrower part.
  • Counterintuitive drop in pressure in narrow sections.
• Bernoulli's Principle: Discovered by Daniel Bernoulli, states that as the speed of fluid increases, its pressure decreases.

Demonstrating Bernoulli’s Principle

• Narrow Neck Pipe: Made from two plastic glasses.
• Blowing Air:
  • Pressure at exit = atmospheric pressure.
  • Inside narrow neck = pressure lower than atmospheric.
• Pressure Sensor:
  • Shows pressure decrease by 5 kPa (50 cm of water column).
  • Colored water test shows a 30 cm rise under pressure changes.

Advanced Demonstrations

• Water Sprayer: Enhanced airflow pressure creates a sprayer effect.
• Plastic Bottle Experiment:
  • Attached to the pipe, decreased internal pressure crumples the bottle by atmospheric pressure.

Mathematical Explanation

• Fluid Flow in Pipes: Volume entering (V) and exiting pipe with pressure difference P1-P2 does mechanical work.
• Energy Conservation:
  • Conversion of pressure difference to kinetic energy.
  • Velocity head (ρv²/2) remains constant.

Venturi Tube and Flow Measurement

• Venturi Tube: Measures speed and volume of gas/fluid through differential pressure.
• Practical Application:
  • Device measures 12 L of air/sec; with 3 cm² section, air speed is 40 m/s.
• Industrial Scale: Larger Venturi tubes used for gas flow measurement with minimal pressure loss.

Conclusion

• Summary: Bernoulli's principle provides a foundation for understanding the behavior of fluids in motion, explaining phenomena that at first seem counterintuitive, like the attraction of balls in airflow and the suction effect in funnels.