Consider the horizontal, laminar flow of a non-Newtonian fluid (K = 2 Pas n and n = 0.35) that is subjected to a constant pressure gradient of 500 Pa/m in a pipe of circular cross-section (radius R = 5 cm). Performing a momentum balance on an annular fluid element (length dz and thickness dr) leads to the differential equation (DE) d dr (rrz) = r dp dz , (4) where r is the radial coordinate. The no-slip boundary condition applies at the pipe wall, whereas the strain rate vanishes at r = 0. The apparent viscosity for this fluid is related to its strain rate via () = K n1 (5) where K and n are positive constants 1. Using the ODE given in the question i.e., Equation (4) above, solve (i.e., integrate) it simultaneously with the appropriate shear stress-shear strain relationship from r = 0 to r = +R with r = 0.5 cm, where r = 0 corresponds to the pipe centreline, to compute the velocity profile of the fluid. Of course, use Euler integration. Report the velocities in tabulated form at each node in SI units. Compute the RMSE. [15 marks] 2. Repeat the calculation using r = 0.1 cm. [15 marks] 3. Comment on the RMSEs calculated in 1 and 2 aboveprovide brief explanations of any similarities or differences. [5 marks