How did Leonhard Euler and Daniel Bernoulli help establish hydrodynamics?

In the 18th century, Leonhard Euler and Daniel Bernoulli established the foundations of hydrodynamics by applying the dynamic principles Isaac Newton developed for discrete particles to fluids, which they treated as continuous media.1

Daniel Bernoulli’s 1738 work, Hydrodynamica, was pivotal in defining the properties of fluid flow, specifically pressure, density, and velocity. He derived Bernoulli’s theorem, which states that for an ideal, steady-flowing fluid, the total mechanical energy—comprising pressure, gravitational potential energy, and kinetic energy—remains constant. This principle explains that in horizontal flow, a decrease in fluid pressure corresponds to an increase in fluid velocity.234

While the principle is named after Bernoulli, Euler also contributed significantly to its development, often arriving at similar conclusions independently. Together, they treated fluids as idealized, inviscid substances where viscosity and shear stresses are negligible. By establishing these mathematical relationships, they provided the framework for analyzing steady fluid motion, which remains essential to modern fluid mechanics and engineering.431