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LaTeX Math Block
 c(p) \equiv 0 \Leftrightarrow  \frac{d \rho}{ dp} = 0 

This also implies that material balance equation:

LaTeX Math Block
\frac{\partial \rho}{\partial t} + \nabla (\rho \, {\br u}) = 0

simplifies to:

LaTeX Math Block
 \nabla ({\br u}) = 0