As shown in the figure on the right, oil with viscosity = 0.13 Ns/ m2 and density r = 0.87 kg/m3 is forced through a narrow gap between two concentric cylinders with of radii, R1 = 5 cm, R2 = 5.2 cm, and length L = 1 m, where the inner cylinder rotates at w1 = 100 rpm (the outside cylinder is stationary). For this problem, you can neglect gravity and the length of the entrance region. Also, you can assume constant density and viscosity as well as axis-symmetry even when there is rotation (i.e., not a function of q) and steady fully developed flow (i.e., not a function of z). a. Obtain an expression for the oil velocity distribution inside the gap, where the pressure difference between the inlet and outlet is DP = P(z = 0) - P(z = L). b. Calculate the torque required to rotate the inside cylinder