Basic Fluid Mechanics and CFD

Basic Fluid Mechanics and CFD Anything related to the general theory of fluid flows and their computation

The role of pressure for incompressible flows

Posted July 1, 2013 at 11:34 by sbaffini (NuTBox)
Updated December 21, 2016 at 10:11 by sbaffini

If we consider the continuity and momentum equations for a general compressible fluid:

$\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0$

$\frac{\partial}{\partial t}\left( \rho u_i \right) + \frac{\partial}{\partial x_j} \left[ \rho u_i u_j + p \delta_{ij} - \tau_{ji} \right] = 0$

taking the time derivative of the first one and the divergence of the second one:
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