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Momentum: the drag experienced by a rain drop as it falls in the atmosphere is an example of momentum diffusion (the rain drop loses momentum to the surrounding air through viscous stresses and decelerates). The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are
In order to find the weak form of the Navier–Stokes equations, firstly, consider the momentum equation [20] + + = multiply it for a test function , defined in a suitable space , and integrate both members with respect to the domain : [20] + + = Counter-integrating by parts the diffusive and the pressure terms and by using the Gauss' theorem ...
A continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids. Classical Momentum is a vector quantity : it has both magnitude and direction.
A general momentum equation is obtained when the conservation relation is applied to momentum. When the intensive property φ is considered as the mass flux (also momentum density), that is, the product of mass density and flow velocity ρu, by substitution into the general continuity equation:
As written in the Cauchy momentum equation, the stress terms p and τ are yet unknown, so this equation alone cannot be used to solve problems. Besides the equations of motion—Newton's second law—a force model is needed relating the stresses to the flow motion. [ 12 ]
For example, the structure of electron shells and subshells in chemistry is significantly affected by the quantization of angular momentum. Quantization of angular momentum was first postulated by Niels Bohr in his model of the atom and was later predicted by Erwin Schrödinger in his Schrödinger equation .
The compressible Euler equations consist of equations for conservation of mass, balance of momentum, and balance of energy, together with a suitable constitutive equation for the specific energy density of the fluid. Historically, only the equations of conservation of mass and balance of momentum were derived by Euler.
Defining equation (physical chemistry) List of electromagnetism equations; List of equations in classical mechanics; List of equations in fluid mechanics; List of equations in gravitation; List of equations in nuclear and particle physics; List of equations in wave theory; List of photonics equations; List of relativistic equations