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Back HW#2 QUESTION1/60pts] 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 T&R Porous media flow R N.B. All your answers must be expressed in terms of µ, U₁, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region. (b) What is the expression of the average velocity in the open region? (c) Is the assumption of a linear velocity profile in the open region acceptable when this region Tuatifi 1:

Back HW#2 QUESTION1/60pts] 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 T&R Porous media flow R N.B. All your answers must be expressed in terms of µ, U₁, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region. (b) What is the expression of the average velocity in the open region? (c) Is the assumption of a linear velocity profile in the open region acceptable when this region Tuatifi 1:

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Back HW#2 QUESTION1/60pts] 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 T&R Porous media flow R N.B. All your answers must be expressed in terms of µ, U₁, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region. (b) What is the expression of the average velocity in the open region? (c) Is the assumption of a linear velocity profile in the open region acceptable when this region Tuatifi 1:
Transcribed Image Text:Back HW#2 QUESTION1/60pts] 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 T&R Porous media flow R N.B. All your answers must be expressed in terms of µ, U₁, a, R and dP/dx. (a) Use the continuity and Navier-Stokes equations to determine the expression of the velocity in the open region. (b) What is the expression of the average velocity in the open region? (c) Is the assumption of a linear velocity profile in the open region acceptable when this region Tuatifi 1:
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