2-78 A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius R,rotating at angulas velocity (rotation rate) , and a stationary outer cylinder of inside radius Ro. In the tiny gap between the two cylind chs is the fluid of viscosity . The length of the cylinders (inmo the page in Fig. P2-78) is L. L is large such that end effeen are negligible (we can treat this as a two-dimensional prob. lem). Torque (T) is required to rotate the inner cylinder at constant speed. (a) Showing all of your work and algebra, genero ate an approximate expression for T as a function of the other variables. (b) Explain why your solution is only an approxi. mation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radius Ro were to increase, all else staying the same)