Bernoulli's principle is derived from which law?

• A. Archimedes' Principle
• B. Law of Conservation of Mass
• C. Newton's Second Law of Motion
• D. Coulomb's Law

Answer: (C)

The main idea is applying Newton's second law to a small fluid element as it moves along a streamline in steady, incompressible, inviscid flow. Forces on the element come from pressure at its faces and from gravity; as the element speeds up or slows down, its acceleration is tied to these forces via F = ma. When you balance pressure forces with the element’s acceleration and integrate along the streamline, you arrive at Bernoulli’s equation, which states that p + 1/2 ρv^2 + ρgz remains constant along a streamline. This directly explains why speed increases as pressure decreases in regions of faster flow.

The other choices aren’t what this derivation relies on. Archimedes’ principle explains buoyancy, not the pressure-velocity-energy relationship. The law of conservation of mass governs how much stuff flows, not the energy balance along a streamline. Coulomb’s law deals with electrostatic forces, unrelated to fluid flow.