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Substituting

LaTeX Math Block Reference
anchornabla_rho
 into
LaTeX Math Block Reference
anchorpre_filnal
 and reducing the density 
LaTeX Math Inline
body\rho(p)
 one arrives to:

LaTeX Math Block
anchorpre_filnal
alignmentleft
\rho \, \phi \, c_t  \cdot \frac{\partial p}{\partial t} + \nabla 
\, ( \rho \,
 {\bf u}  
+ c \cdot ( {\bf u} \, \nabla p) = \rho \, \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k)
LaTeX Math Block
anchorqk
alignmentleft
\int_{\Sigma_k} \, {\bf u} \,  d {\bf A} = q_k(t)


See also

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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model / Single-phase pressure diffusion @model

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