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1. An incompressible Newtonian liquid is in steady laminar flow in a slit formed by two parallel vertical walls separated by a distance 2B. The walls have a length L and a width W. Since B

1. An incompressible Newtonian liquid is in steady laminar flow in a slit formed by two parallel vertical walls separated by a distance 2B. The walls have a length L and a width W. Since B

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
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1. An incompressible Newtonian liquid is in steady laminar flow in a slit formed by two parallel vertical walls separated by a distance 2B. The walls have a length L and a width W. Since B<W and B « L, edge and end effects are not important. The flow can be considered fully developed and the velocity will vary only in the x-direction. The pressure at the entrance is Po and at the exit PL. Fluid in Note the location of the coordinate system in which x = 0 is located midway between the two vertical surfaces. 2B - (a) Write the simplified form of the Navier-Stokes equation that will be used to solve for the velocity profile vz. (b) Write the two boundary conditions that will be used to obtain a solution for the velocity profile. (c) Obtain a solution for the velocity profile vz as a function of x in terms of Po, PL, P, g, µ, L and B. (d) Determine the maximum velocity and its location. (e) Obtain equations for the volumetric flow rate and average velocity. What is the relationship between the average and maximum velocity? ut Fluid out
Transcribed Image Text:1. An incompressible Newtonian liquid is in steady laminar flow in a slit formed by two parallel vertical walls separated by a distance 2B. The walls have a length L and a width W. Since B<W and B « L, edge and end effects are not important. The flow can be considered fully developed and the velocity will vary only in the x-direction. The pressure at the entrance is Po and at the exit PL. Fluid in Note the location of the coordinate system in which x = 0 is located midway between the two vertical surfaces. 2B - (a) Write the simplified form of the Navier-Stokes equation that will be used to solve for the velocity profile vz. (b) Write the two boundary conditions that will be used to obtain a solution for the velocity profile. (c) Obtain a solution for the velocity profile vz as a function of x in terms of Po, PL, P, g, µ, L and B. (d) Determine the maximum velocity and its location. (e) Obtain equations for the volumetric flow rate and average velocity. What is the relationship between the average and maximum velocity? ut Fluid out
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