Bernoulli’s principle

Bernoulli’s Principle Experiment For Schools, Teachers, and Students

The Bernoulli principle states that for an incompressible, non-viscous fluid in steady flow, the sum of its pressure energy, kinetic energy, and potential energy per unit volume is constant. This principle explains the relationship between a fluid’s velocity and pressure in different regions of flow.

Theory

1. Mathematical Expression
   The Bernoulli equation is given by:
   P + 1/2 ρ v² + ρ g h = constant

   where:

   • P: Pressure of the fluid (Pa)
   • ρ: Density of the fluid (kg/m³)
   • v: Velocity of the fluid (m/s)
   • g: Acceleration due to gravity (m/s²)
   • h: Height of the fluid above a reference point (m)
2. Key Concepts
   • As the velocity of a fluid increases, its pressure decreases, and vice versa.
   • The principle applies to steady, incompressible, and non-viscous fluid flow.
   • In horizontal flow (h = constant), Bernoulli’s principle simplifies to:
     P + 1/2 ρ v² = constant

Applications of Bernoulli Principle

1. Flight Mechanics
   Explains lift generation on airplane wings where air moves faster over the curved upper surface, reducing pressure and creating lift.
2. Venturi Effect
   Used in devices like carburetors and Venturi meters, where fluid velocity increases and pressure decreases in a constricted section of a pipe.
3. Sports Applications
   Explains the swing of a ball in sports such as cricket, baseball, or soccer, where differential air pressure causes the ball to curve.
4. Pipelines
   Ensures efficient fluid transport through pipelines by predicting pressure and velocity changes.

Example of Ball Swinging

In sports like cricket or soccer, Bernoulli’s principle explains the swing of a ball. When a bowler delivers a cricket ball with a spin, the air flows faster on one side (due to the spin) and slower on the other side. According to Bernoulli’s principle:

Lower Pressure + Higher Velocity (spinning side) → Higher Pressure + Lower Velocity (non-spinning side)

This pressure difference causes the ball to move sideways, resulting in a curved trajectory.

For instance:

• In cricket, reverse swing occurs when the ball’s rough side affects air velocity differently from the smooth side, creating a significant pressure difference.
• In soccer, a player can bend a free kick by applying spin, exploiting Bernoulli’s principle for a dramatic curve.

Real-Life Uses

• Designing efficient wings for airplanes to achieve optimal lift.
• Developing sports strategies for using spin to curve the ball.
• Creating efficient piping systems and Venturi-based flow devices.
• Designing carburetors to mix air and fuel efficiently.

Observations

• Faster fluid flow leads to lower pressure (e.g., above airplane wings).
• Higher pressure is observed in regions of slower fluid velocity.
• Curved paths of spinning objects demonstrate the pressure differential created by Bernoulli’s principle.
• The principle applies only to steady, non-viscous, and incompressible flows.