 Resident-weighted transit time in a layered flow

Without transverse exchange, a particle chosen uniformly from pore volume samples each streamline's transit time with resident-volume weight. This differs from the flux-weighted residence time in a porous layer, which samples at the inlet proportionally to $v$. For constant porosity and a linear positive velocity $v=v_0+(v_1-v_0)y/H$, the two means are $L\log (v_1/v_0)/(v_1-v_0)$ and $2L/(v_0+v_1)$, respectively. Their limits agree for uniform velocity.