A pipe has a porous section of length L as shown in the figure. Velocity at the start of this section of V0. If fluid leaks into the pipe through the porous section at a volumetric rate per unit area q(x/L)2, what will be axial velocity in the pipe at any „x‟? Assume incompressible one dimensional flow i.e., no gradients in the radial direction ?

Question

Accepted Answer

VX = V0 + (4/3) q (x3/L2D). The change in velocity is found by integrating the leakage rate over the length L. The correct integration yields the form shown in option D.