= Pore velocity
{title2=$v=q/\phi$}
= Interstitial velocity
{synonym}
<Pore velocity> is the <fluid> <velocity> averaged over pore volume relative to the solid framework. For uniform <porosity> $\phi$, full saturation and all pores participating, $\mathbf v=\mathbf q/\phi$, with <Darcy velocity> $\mathbf q$ defined per bulk area. The identity follows from volume averaging: extending the relative <fluid> <velocity> by zero in the solid gives a bulk average equal to the pore fraction times the pore-volume average. It does not assert that every local passage has open area $\phi A$ or identical speed.
In a uniform advective model, travel over length $L$ takes $L/v=\phi L/q$. If some pore volume is inaccessible to transport, the corresponding estimate uses <effective porosity> $\phi_e$ and $v=q/\phi_e$. A connected but nearly stagnant passage can exchange solute slowly, so even this mean does not describe all arrival times. <Flux-weighted residence time in a porous layer> explains one precise averaging convention.https://books.gw-project.org/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/chapter/darcys-law/{ref}
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