Answered: Please give detailed explanations and…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Please give detailed explanations and show your work clearly - I will be using this to study for an upcoming exam. Please do as much as you can but don't worry if you cannot complete the entire problem. Thank you!

Transcribed Image Text:Problem 2 Water of constant density p flows down an inclined straight pipe, which has a circular cross section of radius R. There is no pump driving the flow and flow is fully developed. The angle between the pipe and the horizontal plane is a constant 4. The viscosity of water is a constant u. a) Simplify the Navier Stokes equations to a form that can be solved with paper & pencil by using appropriate assumptions and arguments. b) Solve the simplified equation to obtain the velocity profile by using appropriate boundary conditions. c) By using surface integral of viscous stress, compute the viscous drag on the pipe wall for every unit length of the pipe in the axial direction. d) By using force balancing on a control volume, compute the viscous drag on the pipe wall for every unit length of the pipe in the axial direction, and compare the results in c) and d). e) Compute the viscous stress on a cross-section area, that is a control surface normal to the pipe wall, at (r = R/2, 0 = 0) %3D

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