Équations

1821 · Best.-Nr. 43864 — Paris Crochard 1821. Without wrappers. In 'Annales de Chimie et de Physique' Volume 19 Cahier 3. Titlepage to vol. 19. Pp. 225-335. Navier's paper: pp. 244-260. Verso of titlepage with small stamps. Clean and fine. First appearance of Navier's famous paper in which he describes the relations between fluid flow and friction giving the FUNDAMENTAL EQUATIONS OF THE MATHEMATICAL THEORY OF ELASTICITY. The full paper was not published until 1828. Stokes's analysis of the internal friction of fluids was published in 1845 and as he was not familiar with the French litterature of mathematical physics he derived independently his own equations which accounts for the double-name ofthe equations. "The Navier-Stokes equation is now regarded as the universal basis of fluid mechanics no matter how complex and unpredictable the behavior of its solutions may be. It is also known to be the only hydrodynamic equation that is compatible with the isotropy and linearity of the stress-strain relation." Olivier Darrigol."Navier studied the motion of solid and liquid bodies deriving the partial differential equations to which he applied Fourier's methods to find particular solutions. This theoretical research led him to formulate the well-known equation identified with his name and that of Stokes. Navier viewed bodies as made up of particles which are close to each other and which act on each other by means of two opposing forces - one of attraction and one of repulsion - which when in a state of equilibrium cancel each otherout. The repelling force resulted from the caloric that a body possessed. When equilibrium is disturbed in a solid a restoring force acts which is proportional to the change in distance between the particles."DSB X p. 4."The equations are useful because they describe the physics of many things of academic and economic interest. They may be used to model the weather ocean currents water flow in a pipe and air flow around a wing. The Navier-Stokes equations in their full and simplified forms help with the design of aircraft and cars the study of blood flow the design of power stations the analysis of pollution and many other things. Coupled with Maxwell's equations they can be used to model and study magnetohydrodynamics. "Wikipedia. unknown