= Question 4 Water flows vertically and at a constant rate in a pipe of length L, as shown in Figure 4. The pipe consists of a circular outer pipe of radius R and a central rod of radius R/4. The walls of the outer pipe are coated with Teflon so that the water does not wet the surface (negligible shear). The inner rod is not coated, so that the water does wet the surface. The walls are non-porous. The inlet and outlet of the pipe are exposed to atmosphere, such that the inlet and outlet static pressures are the same. Assuming that L/R >> 10 and that the flow is laminar and axisymmetric, determine the following. ! P = P 28 2R P out =P Teflon coated cylinder uncoated rod g Figure 4: Schematic of vertical pipe with central rod. (a) A formula for the radial distribution of the radial velocity component v. (b) A formula for the radial distribution of the vertical velocity component Uz. (c) The force per unit length (magnitude and direction) acting on the inner rod.