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Microfluidics: Modeling, Mechanics and Mathematics by Bastian E. Rapp

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Chapter 15

Analytical Solutions to the Navier-Stokes Equation

15.1 Hydrostatics and Aerostatics

15.1.1 Hydrostatics: Incompressible Fluids

A particularly simple but very important case of fluid mechanics is the hydrostatic state. In hydrostatics, we assume the density of the fluid to be constant, thus we usually consider only incompressible fluids. Furthermore, changes of temperature are usually ignored. Because the fluid is not moving, we effectively have only one unknown field variable (see section 10.1.1), which is the pressure p. The increase of pressure can be induced either by external forces acting on the resting liquid or by the liquid’s weight itself. In the following, we consider a fluid column parallel to the z-axis (see Fig. 15.1 ...

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