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Neglecting the non-linear term in the Navier-Stokes equations simplifies the analysis, often leading to linear models that are easier to solve and analyze. This approximation is typically valid in conditions where the flow is dominated by viscous forces, such as in low Reynolds number flows. However, this simplification may not accurately capture the dynamics of turbulent or high-speed flows, where non-linear interactions play a crucial role. Thus, the decision to neglect non-linear terms depends on the specific flow regime being studied.

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What has the author Y-N Kim written?

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To derive the Navier-Stokes equations in spherical coordinates, we start with the general form of the Navier-Stokes equations in Cartesian coordinates and apply the transformation rules for spherical coordinates ((r, \theta, \phi)). This involves expressing the velocity field, pressure, and viscous terms in terms of the spherical coordinate components. The continuity equation is also transformed accordingly to account for the divergence in spherical coordinates. Finally, we reorganize the resulting equations to isolate terms and ensure they reflect the physical properties of fluid motion in a spherical geometry.


Derivation of navier-stokes equation for a cylindrical coordinates for a compressible laminar flow?

it is easy you can see any textbook........


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The answer depends on the nature of the equation. Mathematicians are still not able to solve the Navier-Stokes equations, for example. In fact there is a million dollar (US) prize if you can figure out a general solution. The equations are not simply mathematical contrivances to create a challenge: they deal with fluid flow and are used for studying the flow of liquids inside a pipe, or air-flow over a plane's wings and so on.


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