Navier Stokes Equations
Navier Stokes Equations - Related Videos
01:28
Navier–Stokes Equations
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2025
For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
01:20
Stokes' Law
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2025
Viscous forces, like friction, are intermolecular forces that resist the relative motion of molecules over each other. When a solid body moves through a liquid, viscous forces drag it in the opposite direction. The force's magnitude depends on the solid's shape and size, as well as its speed and the liquid's coefficient of viscosity, density and temperature. The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...
12:21
Stimulated Stokes and Antistokes Raman Scattering in Microspherical Whispering Gallery Mode Resonators
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Cited by 2 •
2016
Efficient generation of nonlinear phenomena related to third order optical non-linear susceptibility Χ(3) interactions in triply resonant silica microspheres is presented in this paper. The interactions here reported are: Stimulated Raman Scattering (SRS), and four wave mixing processes comprising Stimulated Anti-stokes Raman Scattering (SARS).
03:10
Chemical Equations
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2020
Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are called reactants, and their formulas are placed on the left side of the equation. The substances generated by the reaction are called products, and their formulas are placed on the right side of the equation. Plus signs (+) separate individual reactant and product formulas, and an arrow (→) separates the reactant and product (left and right)...
02:59
The Nernst Equation
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2020
Nonstandard Reaction Conditions The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous. Discharge of this cell, however, results in a change in the reactant concentration and a steady decrease of the cell potential. At...
FAQs
The governing balance compares fluid inertia with pressure gradients, viscous stresses, and external body forces. Inertia represents the tendency of moving fluid to retain its motion, while pressure and viscosity alter that motion and body forces add external influence. Their relative effects determine the resulting velocity field, making the balance central to predicting how flow responds to operating conditions.
These variables describe different aspects of the flow state and may vary across space and time. Velocity indicates motion, pressure contributes to the force balance, density characterizes the fluid distribution, and temperature captures thermal variation. Tracking them together allows the equations to support analyses involving ordinary fluid motion as well as heat and mass transport.
Engineers turn to computational fluid dynamics when the equations do not yield an analytical solution for the flow being studied. The computational approach provides a way to analyze the governing relationships under specified initial and boundary conditions. This is especially useful for engineering systems where predicting flow behavior, transport, or flow-induced forces requires more than a closed-form result.
A particular flow requires initial and boundary conditions in addition to the governing equations. These conditions specify how the fluid state is constrained at the beginning of the analysis and along relevant boundaries. Engineers combine them with the selected fluid variables, pressure effects, viscous stresses, and external body forces to obtain a flow prediction rather than an unspecified set of possibilities.
In engineering design, the equations provide a framework for examining fluid motion and the resulting pressure, velocity, and flow-induced forces in systems such as pipelines, pumps, aircraft, and turbines. Analyses can help evaluate how operating conditions influence performance and loads. When direct analytical treatment is unavailable, computational fluid dynamics supports these design and assessment tasks.
Their use extends to predicting turbulence, heat and mass transport, and forces produced by flowing fluids. These outcomes connect fluid analysis to thermal behavior, material transport, and mechanical loading in engineered systems. Consequently, the equations are relevant not only to velocity and pressure calculations but also to assessing how flow interacts with equipment and surrounding structures.