A fluid of viscosity μ flows in the horizontal cylinder (radius R) shown in the figure under a constant pressure gradient dP/dx. Flow R TaR The inner core of the cylinder is filled with a porous material. The flow in this porous region is slow and assumed to be a plug-type flow such that the velocity is constant and everywhere the same inside the porous region. Denote this velocity by Uo. The flow in the open (non-porous) region is steady, Newtonian, incompressible and axisymmetric. It will be assumed that only the axial (x) component of the velocity is non-zero. Open flow Porous media flow N.B. All your answers must be expressed in terms of u, Uo, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region.

A fluid of viscosity μ flows in the horizontal cylinder (radius R) shown in the figure under a constant pressure gradient dP/dx. Flow R TaR The inner core of the cylinder is filled with a porous material. The flow in this porous region is slow and assumed to be a plug-type flow such that the velocity is constant and everywhere the same inside the porous region. Denote this velocity by Uo. The flow in the open (non-porous) region is steady, Newtonian, incompressible and axisymmetric. It will be assumed that only the axial (x) component of the velocity is non-zero. Open flow Porous media flow N.B. All your answers must be expressed in terms of u, Uo, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region.

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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