Bernoulli’s Theorem and Its Applications

• Bernoulli’s Theorem states that for an incompressible, frictionless fluid, the total mechanical energy along a streamline is constant.

• Mathematically, P + 1/2 ρ v^2 + ρ g h = "constant"

here:

• P = static pressure
  

• ρ = fluid density

• v = fluid velocity

• g = acceleration due to gravity

• h = height above a reference point

Applications of Bernoulli’s Theorem:

1. Venturi meter: Measures fluid flow rate by using a constriction in the pipe.

2. Orifice Meter: Measures flow rate by reducing the cross-sectional area.

3. Pitot Tube: Measures fluid flow velocity by converting kinetic energy into potential energy.

4. Aircraft Design: Determines pressure distribution over wings.