Question: 6) Consider the system shown below in which a rod is contained within a coaxial cylinder. The system is aligned vertically. The rod has a

6) Consider the system shown below in which a rod is contained within a coaxial cylinder. The system is aligned vertically. The rod has a radius R1 and the outer cylinder has a radius of R2. The region between the rod and outer cylinder contains an incompressible Newtonian liquid that has a density and viscosity . The rod is being moved in the positive z-direction at a constant velocity V while the outer cylinder is stationary. Assume the liquid is in steady fully developed laminar flow and there is no pressure gradient acting on the liquid in the direction in which the rod is moving. (a) Write the simplified forms of the Continuity and Navier-Stokes Equations in cylindrical coordinates that will be used for solving for the velocity profile in the liquid. (b) Write the applicable boundary conditions that will be used to solve for the velocity profile. (c) Solve for the velocity profile z in terms of r,R1,R2,V,2g and . (d) Assume the rod has a radius RI=3cm and the cuter cylinder has a radius RZ=6cm. At steadystate, the rod is being moved in the positive z-direction at a constant velocity V=2.0cm/s. The liquid has a density =1260kg/m3 and viscosity =1.8Pas. Calculate the magnitude and direction of the viscous force per unit length in units of N/m acting on the rod surface

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