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.

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

A fluid of viscosity u flows in the horizontal
cylinder (radius R) shown in the figure under
a constant pressure gradient dP/dx.
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.
Flow
Open
flow
aR
Porous
media flow
R
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.

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