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 1 •
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).
03:00
Coherent Anti-Stokes Raman Spectroscopy to Visualize Myelinated Neurons in Mouse Brain Tissue
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2025
Source: McCullagh, E. A., et al. Coherent Anti-Stokes Raman Spectroscopy (CARS) Application for Imaging Myelination in Brain Slices. J. Vis. Exp. (2022)The video demonstrates fluorescence and Coherent Anti-Stokes Raman Spectroscopy (CARS) imaging to visualize neuronal architecture in rodent brain tissue. Nissl staining labels cell bodies by binding to ribosomal RNA, while CARS imaging targets lipid-rich myelin through laser-induced signals. Overlaying the fluorescence and CARS images provides a...
01:06
Divergence and Stokes' Theorems
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2025
The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental theorem of calculus. The divergence theorem and Stokes' theorem are in a way similar to each other; The divergence theorem relates to the dot product of a vector, while Stokes' theorem relates to the curl of a vector. Many applications in physics and engineering make use of the divergence and Stokes' theorems, enabling us to write numerous physical laws...
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.