Bernoulli's Principle

One quarter of a millennium ago, Daniel Bernoulli pioneered the use of kinetic theory that molecules moved and bumped things. He also knew that flowing fluids pressed less, but he did not connect these ideas logically. In Hydrodynamica, Daniel's logic that flow reduced pressure was obscure, and his formula was awkward. Daniel's father Johann, amid controversy, improved his son's insight and presentation in Hydraulica. This research was centered in St. Petersburg where Leonhard Euler, a colleague of Daniel and a student of Johann, generalized a rate-of-change dependence of pressure and density on speed of flow. Bernoulli's principle for liquids was then formulated in modern form for the first time.

In this same group of scientists was d'Alembert, who found paradoxically that fluids stopped ahead of obstacles, so frictionless flow did not push.

Progress then seems to have halted for about a century and a half until Ludwig Prandtl or one of his students solved Euler's equation for smooth streams of air in order to have a mathematical model of flowing air for designing wings. Here, speed lowers pressure more than it lowers density because expanding air cools, and the ratio of density times degrees-kelvin divided by pressure is constant for an ideal gas.

More turbulent flow, as in atmospheric winds, requires an alternative solution of Euler's equation because mixing keeps air-temperature fixed.