Problem 2 - For a homework problem in ENGR 315 Sparky had to determine the velocity profile of a fully-developed laminar Newtonian fluid through an annulus that has a pressure gradient in the direction of flow (z direction). Unfortunately Sparky's dog ate the homework solution except for the page with the final solution. Sparky remembers the starting equations were the mass conservation and Navier-Stokes equations. The final solution Sparky remembers was the following: d p v₂ (r) =. 4μ dr r² In r Help Sparky out by checking the solution shown above by using the mass conservation and Navier-Stokes equations and the appropriate boundary conditions. Is Sparky's solution correct? If Sparky's solution is incorrect what is the correct solution? The final solution once the integration constant equations are determined can be tedious. As a minimum define the velocity equations in terms of integration constants, the two equations used to determine the integration constants and document in words how the final solution would be determined. This should provide enough data to determine if Sparky's solution is correct or not. Only providing the response with respect to the correctness of the equation is not sufficient. Some justification is required.

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)

5th Edition

ISBN:9781305084766

Author:Saeed Moaveni

Publisher:Saeed Moaveni

Chapter18: Mathematics In Engineering

Section: Chapter Questions

Problem 19P

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Transcribed Image Text:Problem 2 - For a homework problem in ENGR 315 Sparky had to determine the velocity profile of a fully-developed laminar Newtonian fluid through an annulus that has a pressure gradient in the direction of flow (z direction). Unfortunately Sparky's dog ate the homework solution except for the page with the final solution. Sparky remembers the starting equations were the mass conservation and Navier-Stokes equations. The final solution Sparky remembers was the following: d p v₂ (r) =. 4μ dr r² In r Help Sparky out by checking the solution shown above by using the mass conservation and Navier-Stokes equations and the appropriate boundary conditions. Is Sparky's solution correct? If Sparky's solution is incorrect what is the correct solution? The final solution once the integration constant equations are determined can be tedious. As a minimum define the velocity equations in terms of integration constants, the two equations used to determine the integration constants and document in words how the final solution would be determined. This should provide enough data to determine if Sparky's solution is correct or not. Only providing the response with respect to the correctness of the equation is not sufficient. Some justification is required.

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