Please solve part (a) and (b) Bfluiediufinite volume of fluidarmuud the cyliuderRde care fal :theseoften in Plauy withere b.2s xt r-),lichO caivcylindri'cal coordinates B. Figure B shows a horizontal cross section of a long vertical cylinder of radiusR that is rotated steadily counterclockwise with an angular velocity o in a verylarge volume of a Newtonian liquid of viscosity u and density p. The liquidextends effectively to infinity, where it may be considered at rest. The axis ofthe cylinder coincides with the z axis of a cylindrical coordinate system. Thisis a laminar, steady state flow without gravity effects.(a) Identify which velocity components of a cylindrical coordinate system arezero for this flow.(b) Formulate the continuity equation for this flow, compute the result andcomment on the result of your analysis.(c) Formulate the momentum equation for this flow in the axial direction,explain which terms cancel, give the result of your analysis and expresswhat you learn from this result.

The cylinder will rotate inside the liquid with angular velocity which will be constant .The layer next to cylinder will have highest velocity. As the layers increase the velocity decreases and its almost null at last layer of fluid. There is only tangential velocity in this system and this is existing because the cylinder is rotating in the liquid. There is only tangential velocity present in the system. The direction of tangential velocity is radial direction. The other two direction velocity components are zero. The tangential velocity is uϕ The velocity in direction of r and z will be zero The incompressible continuity equation ∂(rur)r∂r+∂(uϕ)r∂ϕ+∂(uz)r∂z=0ur=0uz=0∂(uϕ)r∂ϕ=0 We will integrate the above obtained equation ∂∂ϕ∫(uϕ)dϕ=0ϕ→0⇒ ∂∂ϕ=ddϕ∫d(uϕ)dϕdϕ=∫0 dϕuϕ=crw=c As w is constant uϕ will be constant for particular radius of rotation r Final answers a) r direction velocity and z direction velocity are zero b)As w is constant uϕ will be constant for particular radius of rotation r