Flow through permeable tubes where the wall leakage is computed as part of the solution according to a membrane law has been considered only in terms of simplified one- and two-dimensional models that ignore the radial pressure gradient.
In fact, Marshall and Trowbridge (1974) derive a remarkable exact solution of the Stokes equation for a permeable tube of infinite length and compare their solution with the approximate solution I rederive in my paper with good agreement. The pressure is assumed to be constant outside the tube.
I inadvertently missed the opportunity to compare my boundary-element solution for a finite test section with the Marshall and Trowbridge (1974) solution for an infinite tube.