Newton, Euler equation and Navier-Stokes equation of fluid mechanics (2)
Why does Newton emphasis that a force must be derived from the phenomena of motions?
Because this is the best and the most accurate method, with which we can directly find the true causes and reasons (in Newton’s word, causes and reasons are just forces) of the motions.
Euler, Navier and Stokes do not follow Newton’s rule, and want to use pressure forces to describe all kinds of phenomena of fluid motions, this is a big mistake, nobody can guaranty that pressure forces are true causes and reasons of all kinds of fluid motions, because pressure forces are not derived from phenomena of fluid motions.
According to Newton’s rule, the forces, which will be used to describe all kinds of fluid motions, must be derived from the phenomena of fluid motions.
So Euler equation and Navier-Stokes equation are useless.
Newton is a Giant, so we must strictly follow him.
In mechanics, we just care about forces and motions, motions and forces, different kinds of forces produce different kinds of motions and different kinds of motions need different kinds of forces.
In mechanics, we just care forces, we do not need differential equations; we just see a gravity force when we see the solar system, we just see a centripetal force when we see hurricanes, and we just see a centripetal force and electromagnetic forces when we see sunspots, or in Newton’s word, we can derive a centripetal force from the phenomena of the fluid motions of hurricanes, and then we can use this centripetal force, and magnetic forces, to demonstrate the plasmas motions of the sunspots.
Batchelor, G. K. 1994 An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge.
Newton, I. 1686 Principia, Daniel Adee, New York (republished in 1848).
