Bernoulli’s Principle

Bernoulli’s principle is derived from the principle of conservation of energy applied to an ideal fluid in motion. The equation’s three terms represent different forms of energy per unit volume. The term \(p\) is the static pressure, representing the internal energy of the fluid. The term \(\frac{1}{2}\rho v^2\) is the dynamic pressure, which is the kinetic energy of the fluid in motion. The final term, \(\rho gh\), is the hydrostatic pressure, representing the fluid’s potential energy due to its elevation \(h\) in a gravitational field \(g\). The principle asserts that the sum of these three terms remains constant along a single streamline.

It is crucial to understand the assumptions under which Bernoulli’s principle is valid: the flow must be steady (velocity at a point does not change with time), incompressible (density is constant), and inviscid (no frictional forces from viscosity). These are significant limitations, meaning the principle is an idealization. In real-world applications, viscous effects can cause energy losses that are not accounted for in the basic equation.

While often used to provide a simplified explanation for aerodynamic lift—where air traveling faster over the curved upper surface of a wing creates lower pressure compared to the flatter bottom surface—this is an incomplete picture. A full explanation of lift also requires considering Newton’s third law and the deflection of air downwards (downwash). Nevertheless, Bernoulli’s principle provides a powerful and intuitive tool for a first-order analysis of many fluid dynamics phenomena, from measuring flow rates with a Venturi meter to understanding how a perfume atomizer works.