Daniel Bernoulli, an 18th-century Swiss mathematician and physicist, made groundbreaking contributions to fluid mechanics. His principle states that as the velocity of a fluid increases, its pressure decreases. This fundamental relationship can be observed in a simple pipe with varying cross-sections, where fluid flows faster through the narrow section while experiencing lower pressure.
Bernoulli's equation mathematically expresses the conservation of energy in fluid flow. The equation states that the sum of pressure energy, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline. The pressure term P represents the static pressure, the kinetic term one-half rho v squared represents the dynamic pressure, and the potential term rho g h represents the gravitational potential energy per unit volume.
Bernoulli's principle is based on several key assumptions that limit its applicability. First, the fluid must be incompressible with constant density. Second, the flow must be steady with no time variations. Third, the fluid must be inviscid with no viscosity effects. Fourth, the analysis applies only along a single streamline. In reality, all fluids have some viscosity and compressibility, which causes deviations from the ideal behavior predicted by Bernoulli's equation.
The Venturi effect perfectly demonstrates Bernoulli's principle. In a pipe with a constricted section, fluid velocity increases in the narrow throat while pressure decreases. Using the continuity equation and Bernoulli's equation, we can calculate the exact pressure and velocity changes. For example, with an inlet area of 0.1 square meters and throat area of 0.05 square meters, if the inlet velocity is 2 meters per second, the throat velocity doubles to 4 meters per second, while the pressure drops from 101,325 pascals to 95,325 pascals.
Bernoulli's principle has numerous practical applications in everyday life and engineering. Airplane wings generate lift because air flows faster over the curved upper surface than the flat lower surface, creating a pressure difference of 500 to 1000 pascals. Carburetors use the Venturi effect where fast-moving air creates low pressure to draw fuel into the airstream with typical velocity ratios of 3 to 1. Spray bottles work by compressed air creating a low-pressure zone that lifts liquid through a tube, with pressure drops ranging from 200 to 500 pascals.