1. Consider a tangential laminar flow of an incompressible fluid in the space between two coaxial cylinders. The inner cylinder rotates at an angular velocity, i and the outer cylinder is stationary. a) Making reasonable assumptions simplify the equations of change to get the differential equations for the velocity distribution. b) Specify the necessary boundary conditions and solve for the velocity profile. c) Calculate the torque acting on the outer cylinder. d) The torque indicated by a Couette viscometer is 0.01Nm. If the diameter of the inner cylinder is 100mm, the annular gap is 1mm, the length is 120mm, and the inner cylinder rotates at 40rpm, determine the viscosity of the fluid contained in the viscometer. 2. For fully developed, laminar flow of a power-law fluid in a tube, the velocity profile is given by vz=n+13n+1vz[1(Rr)nn+1] a) Derive the governing equation for the forced convection heat transfer in a circular tube. b) State your assumptions and reduce the governing equation in terms of bulk temperature of fluid. c) Calculate Nusselt number (Nu) for large z, assuming a constant heat flux at the wall. d) Verify your result for n=1, the Newtonian case