Consider two concentric cylinders with a newtonian liquid of constant density, r, and constant dynamic viscosity, µ, contained between them. the outer pipe, with radius, ro, is fixed while the inner pipe, with radius, ri, and mass per unit length, m, falls under the action of gravity at a constant speed. there is no pressure gradient within flow and no swirl velocity (i. e., tangential velocity) component. determine the vertical speed, v, of the inner cylinder as a function of the following (subset of) parameters: g, ro, ri, m, r, and µ. fixed outer cylinder with radius, ro movable inner cylinder with radius, ri, and mass per unit length, m annular region filled with liquid of density, r, and dynamic viscosity, µ v