Flux-weighted residence time in a porous layer ($⟨\tau {⟩}_Q=V_{\mathrm{pore}}/Q$)

For steady incompressible flow with no stagnant volume, partition the layer into streamtubes of volume flux $dQ$. The pore volume in a streamtube is $\tau dQ$, so $\int \tau dQ=V_{\mathrm{pore}}$. This gives the mean residence time $V_{\mathrm{pore}}/Q$ even when individual path times vary widely. Streamfunction labels measure flux in two-dimensional flow, so they supply the correct weighting.