What is Bernoulli's theorem based on?

Bernoulli's theorem is based on the conservation of energy — one of the most fundamental principles in all of physics. Stated by Swiss mathematician Daniel Bernoulli in 1738, the theorem describes the relationship between the pressure, velocity, and height of a fluid flowing through a pipe. The core idea is beautifully simple — in a steady, non-viscous, incompressible fluid flow, the total mechanical energy at every point along a streamline remains constant. When fluid speeds up, its pressure drops, and when it slows down, its pressure rises — energy simply converts from one form to another but never gets lost.

• Bernoulli's Equation: P + ½ρv² + ρgh = constant — where P is pressure, ρ is density, v is velocity, g is gravity, and h is height
• Energy Forms: The equation represents three forms of energy — pressure energy, kinetic energy (½ρv²), and potential energy (ρgh)
• Practical Application: Explains how aircraft wings generate lift — faster airflow over the curved upper surface creates lower pressure, pushing the wing upward
• Venturi Effect: Fluid speeds up when passing through a narrow section of pipe, causing pressure to drop — a direct application of Bernoulli's theorem
• Conditions: Theorem applies only to steady, non-viscous, incompressible fluid flow along a streamline — real fluids deviate slightly due to viscosity