Basic Equations of Hydrodynamics

Abstract

As we shall see, the basic equations of hydrodynamics for liquids and gases are obtained by modifying the basic equations of elastodynamics.

The tensor surface n(τn) = −1 of hydrostatic pressure is a sphere. This law was probably discovered by Pascal (1624–1662).

The first two papers of Euler (1707–1783) about equilibrium and motion of fluids appeared in 1755…

Bernoulli’s equation represents the most important theorem in hydrodynamics. It was discovered in 1738 by Daniel Bernoulli (1700–1782), even before Euler’s equations were known, by using an argument which can be regarded as an early version of the energy conservation law ….

Today we consider the equation of Navier (1822) and Stokes (1845) as basic for the representation of all properties of fluids. In the technology of the nineteenth century, however, it was the conviction that there exists a deep gap between mathematical—physical hydrodynamics and technological hydraulic. This gap was closed by the profound experimental and theoretical work of the British engineer and physicist Osborne Reynolds (1842–1912). He worked with a colored fluid thread in a glass tube. For a small diameter d and a small velocity V the thread moved on a straight line (laminar flow). For large d or large V irregular side motions of the thread occurred (turbulent flow). Only by applying the aspects of a similarity law, was Reynolds able to obtain some systematics.

Arnold Sommerfeld (1944)