An approximate analytical solution for the fluid dynamics of laminar flow in a porous tube

An approximate solution for the fluid dynamics of flow through a porous tube, such as encountered in the cross-flow filtration process, is presented. Conservation of mass for the entire unit combined with the assumptions of quadratic variation of pressure along the length of the unit and local validity of the Hagen–Poiseuille law results in simplified expressions for the pressure and axial and radial velocity profiles. A finite element solution to the Navier–Stokes equations is used to compare the resulting expressions to the only other approximate analytical solution found in the literature. The results indicate that all three analyses are within 0.5% of each other for laminar flow in a long porous tube.