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Continuum mechanics is a branch of mechanics that deals with the deformation of and transmission of forces through materials modeled as a continuous medium (also called a continuum) rather than as discrete particles. Continuum mechanics deals with deformable bodies, as opposed to rigid bodies. A continuum model assumes that the substance of the ...
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. [ 1 ] : 3 It has applications in a wide range of disciplines, including mechanical , aerospace , civil , chemical , and biomedical engineering , as well as geophysics , oceanography , meteorology , astrophysics ...
1643 – Evangelista Torricelli provides a relation between the speed of fluid flowing from an orifice to the height of fluid above the opening, given by Torricelli's law. He also builds a mercury barometer and does a series of experiments on vacuum. [1] 1650 – Otto von Guericke invents the first vacuum pump. [1]
The Knudsen number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation. If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no ...
The Navier–Stokes equations assume that the fluid being studied is a continuum (it is infinitely divisible and not composed of particles such as atoms or molecules), and is not moving at relativistic velocities. At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the ...
Leonhard Euler is credited of introducing both specifications in two publications written in 1755 [3] and 1759. [4] [5] Joseph-Louis Lagrange studied the equations of motion in connection to the principle of least action in 1760, later in a treaty of fluid mechanics in 1781, [6] and thirdly in his book Mécanique analytique. [5]
In mathematics, the Navier–Stokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...
Flux F through a surface, dS is the differential vector area element, n is the unit normal to the surface. Left: No flux passes in the surface, the maximum amount flows normal to the surface.