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: McGraw-Hill Education
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Question

the answer should be:  V2= -(P0-PL/2μL)(dx-x^)+Ux/d

A Newtonian fluid with viscosity μf and density Of is contained between two infinite horizontal parallel planes (separated by a distance d as shown below). The fluid flows laminarly under the action of a pressure gradient and the velocity U of the upper plane (the bottom plane is fixed). A manometer (with fluid density pm and viscosity μm) is connected between two points L apart along the bottom plane and indicates a differential reading of Ah. Using the coordinate system depicted in the figure below, calculate the velocity distribution in terms of known variables by performing a shell balance. What value must U have so that the frictional drag force on the upper plate is zero? Sketch the velocity profile for this last case (i.e., zero frictional drag force on the upper plate). Note to use t = − μ dVz dx d Pf 土 Ah L Pm ✗ Z
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Transcribed Image Text:A Newtonian fluid with viscosity μf and density Of is contained between two infinite horizontal parallel planes (separated by a distance d as shown below). The fluid flows laminarly under the action of a pressure gradient and the velocity U of the upper plane (the bottom plane is fixed). A manometer (with fluid density pm and viscosity μm) is connected between two points L apart along the bottom plane and indicates a differential reading of Ah. Using the coordinate system depicted in the figure below, calculate the velocity distribution in terms of known variables by performing a shell balance. What value must U have so that the frictional drag force on the upper plate is zero? Sketch the velocity profile for this last case (i.e., zero frictional drag force on the upper plate). Note to use t = − μ dVz dx d Pf 土 Ah L Pm ✗ Z
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