A wire-coating die essentially consists of a cylindrical wire of radius KR moving horizontally at a constant velocity V along the axis of a cylindrical die of radius R. If the pressure in the die is uniform, then the Newtonian fluid of constant viscosity and density flows through the narrow annular region solely by the drag due to the motion of the wire (and is referred to as Couette flow). Neglect end effects and assume an isothermal system.

A. Find an expression for the steady state velocity profile in the annular region of the die from N-S equation.

B. Obtain the mass flow rate through the annular die region.