Water at room temperature is pumped steadily through a wide, rectangular duct. a. Starting from the appropriate Navier-Stokes equations, generate a mathematical model for the velocity profile of the flow in the rectangular duct. List all necessary assumptions. b. Repeat part (a.) for flow of a fluid pumped through a cylindrical pipe. C. Compare the velocity profile in the rectangular duct with that in the cylindrical pipe. d. Plot the velocity profile in the rectangular duct and the cylindrical pipe on the same graph. Label the axes appropriately, with units. Hand-drawn or illegible graphs will not be graded. Make it clear which geometry each curve represents. Assume a pipe diameter of 0.005 [m], and the average velocity of the water is v. = 0.005 [m/s]. Try a scatter plot with velocity on the x axis, and position on the y axis (reverse of a typical chart)