final exam review problems

final exam review problems - Review Session Problem 1 A...

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Review Session Problem 1) A Newtonian fluid flows upwards in a pipe, then meets a solid cylinder concentric with the pipe rotating with angular velocity, Ω . The surfaces of the conical shell and cone are described by the equations on the diagram. a) We are interested in the flow around the junction of the pipe and cylinder, over 0 < z < L1+L2. (L1 and L2 are comparable to R1 and R2). Postulate the form of the velocity field v . That is, what components of the velocity are non‐zero, and what variables does each component depend on? b) Write the boundary conditions within the region 0 < z < L1. c) Write the boundary conditions within the region L1 < z < L2 d) Simplify the equations below by crossing out any terms you expect to be zero.
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Review Session Problem 1 Solution: a) So we’ll assume: Newtonian, incompressible, steady state, axisymmetric (no θ dependence). Postulate: v θ = v ( r , z ) v r = v r ( r , z ) v z = v z ( r , z ) P = P ( r , z ) b ) v z = finite at r = 0 for 0 < z < L 1 v r = 0 at r = 0 for 0 < z < L 1 v = 0 at r = 0 for 0 < z < L 1 v r = 0 at r = R for 0 < z < L 1 v z = 0 at r = R
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final exam review problems - Review Session Problem 1 A...

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