What does Bernoulli's Equation mathematically represent?

Bernoulli's Equation mathematically represents the conservation of energy in fluid flow. It describes how the total mechanical energy of a fluid remains constant along a streamline, comprising kinetic energy, potential energy, and pressure energy. Bernoulli's principle states that when a fluid moves through a system, if the speed of the fluid increases, the pressure within the fluid decreases, assuming no energy is added or lost due to work done on or by the fluid.

This principle is foundational in fluid mechanics, as it highlights the dynamics of fluid flow in various scenarios, such as pipe flow or air over wings. The equation captures the interplay between speed (kinetic energy), elevation (potential energy), and pressure energy, thus illustrating how energy is conserved within fluid systems. It exemplifies how energy transformations occur within a fluid without external influences, which is critical for understanding various fluid dynamic applications.