Can pressure do work in an incompressible flow? -- CFD Online Discussion Forums

January 15, 2018, 12:48	Can pressure do work in an incompressible flow?	#1
toodles New Member Join Date: Dec 2015 Posts: 27 Rep Power: 10	I am trying to analyze the energy equation for incompressible flows. I start with N-S and dot it with the velocity vector: $\bigg( \rho \frac{D\mathbf{u}}{Dt} - \nabla^2 \mathbf{u} + \nabla p \bigg) \cdot \mathbf{u} = 0$ Then I get something like $1/2 \rho \frac{\partial \mathbf{u}^2}{\partial t} - \Phi + \mathbf{u}\cdot \nabla p = 0$ I am interested in the work due to pressure term. Can this be nonzero if the flow is divergence free? Using identities it can be rewritten as $\mathbf{u} \cdot \nabla p = -p \nabla \cdot \mathbf{u} + \nabla \cdot (p\mathbf{u})$ Obviously, the first term on the RHS is 0 if the flow is divergence free, but what is the second term? I am having trouble visualizing this one physically. When is it or isn't it equal to 0? I am having trouble understanding how pressure could do work on an incompressible flow. Any elucidation or thoughts would be very appreciated.

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