Laminar Entry Problem in Porous Tubes

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Abstract
The inlet region for laminar flow in porous pipes with small injection or suction is analyzed numerically. Finite difference methods are developed and solutions obtained for the equations of fluid motion with two different wall boundary conditions: constant injection or suction velocity through the wall, and velocity through the wall proportional to local pressure. Solutions are found for both uniform and parabolic axial velocity profiles at the pipe inlet. The results are found to be in good agreement with the solution of Weissberg for the conditions of constant suction velocity and a parabolic inlet velocity profile. Hydrodynamic entrance lengths are found and are compared for uniform and parabolic inlet profiles in the presence of constant injection or suction.