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e velocity profile Expression for the flow rate

e velocity profile Expression for the flow rate

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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fluid flow between parallel plates (Fig. 2) that are horizontal and a distance 2h apart. A constant pressure gradient is applied in the x-direction (dp/dx). The flow is fully developed laminar and steady. The plate width is denoted by B a) Simplify the governing equations b) Define the boundary conditions c) Determine the velocity profile d) Develop an expression for the flow rate Continuity Equation ap d + at əx Momentum Equations d'u dr P8x P8y P8z ə a (pu) + (pv) + (pw) = 0 dy əz др Əx + μ әр + м ду ap + M əz d²v dx² + azu dy d²v dy² + + d²u az² ²v əz² a²w dz² azw dzw + + ay² dx² www. p P ди Ət dv at aw at + u + u + u ди ax dv əx dw ax y + v + v g Fixed Fig. 2: Flow between parallel plates with a co- pressure gradient ди + v ду dv ду + w aw ду + W ди az dv + w əz dw u(y) əz #max 介介
Transcribed Image Text:fluid flow between parallel plates (Fig. 2) that are horizontal and a distance 2h apart. A constant pressure gradient is applied in the x-direction (dp/dx). The flow is fully developed laminar and steady. The plate width is denoted by B a) Simplify the governing equations b) Define the boundary conditions c) Determine the velocity profile d) Develop an expression for the flow rate Continuity Equation ap d + at əx Momentum Equations d'u dr P8x P8y P8z ə a (pu) + (pv) + (pw) = 0 dy əz др Əx + μ әр + м ду ap + M əz d²v dx² + azu dy d²v dy² + + d²u az² ²v əz² a²w dz² azw dzw + + ay² dx² www. p P ди Ət dv at aw at + u + u + u ди ax dv əx dw ax y + v + v g Fixed Fig. 2: Flow between parallel plates with a co- pressure gradient ди + v ду dv ду + w aw ду + W ди az dv + w əz dw u(y) əz #max 介介
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