Problem 2. (10 pts.) Show that for fully developed, steady-state, laminar flow in the z-direction for an incompressible fluid into and out of a horizontal tube of constant circular cross-section, v(vn^)dS=0. Do this by solving the surface integrals for the flow into and out of the tube. Hints for Approach: Treat this as a 2-D problem in the cylindrical coordinate system, z-r, with vz=vze^z. Note that the overall surface integral represents the sum of the surface integral for the flow into the tube at z=0 plus the surface integral for the flow out of the tube at z=L. Note: First use the condition of v=0 for an incompressible fluid to show that vz=f(z). Based on this condition, you should be able to then show that v(vn^)dS=0 for this type of flow system. Note that this can be shown very simply in a way that does not even require actually solving the surface integrals