A viscometer measures a fluid's viscosity. One type of viscometer is a rotational viscometer; its design consists of two concentric cylinders with a thin layer of the fluid in between them. The outer cylinder is fixed while the inner cylinder is spun by an external force. You surmise that the torque needed to turn the inner cylinder is a function of the fluid's viscosity (and other parameters). In the figure, the fluid is depicted in grey. a) Find the governing nondimensional groups for this system. Assume that the torque T is a function of the inner Di and outer diameter Do, the length of the cylinders L, the angular velocity of the inner cylinder , and the fluid's density , and viscosity . Choose L, and as your scaling variables. b) Before building the full-scale system, you decide to build a model that is 31 the size. Given the full-scale system angular velocity 1, what angular velocity 2 does the model need to operate at to achieve dynamic similarity? Assume the fluid properties are the same for both systems. c) What is the ratio between the torques on the two systems, T2T1