Answered: Plate 1 Fluid Plate 2 Navier-Stokes…

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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Transcribed Image Text:Plate 1 +y Fluid +X Vol Plate 2 Navier-Stokes Equations - A Newtonian fluid is confined between two broad parallel vertical plates, separated by a distance B. The plate on the left is stationary, while the one on the right is moving upward at a constant velocity, vo. a. Assuming the flow is laminar, determine the simplified form of the Navier- Stokes equation for the steady-state, fully developed velocity profile in the fluid. Cartesian coordinates (x, y, z): Jvx at 2V, + Vx ax P (avy at joy + x ax av. JV: + Vx Jx ət JU, + Dy ay avy + Dy ay JU: + Oy Jy 20, + V₂ Jz jvy + V: Jz az ap ax ap əy ap + 2²0x2²0 2²0₂ + 3 əz² +μ əx² öx² [200 บ dy² + ởy² 2²₂ 2²₂ ay² + + + 3] + pox + poy + pg: b. For a system like this, it is important that the velocity (vo) is large enough to counteract the effect of gravity, otherwise the fluid will start to flow downward. For a system where the distance between plates is 1mm, the fluid is an oil with a density of 900kg/m³ and viscosity of 50mPa s, what is the minimum upward velocity of the moving plate so that all the fluid moves upward? (You may assume that the pressure drop term is negligible compared to the gravitational force term) If vo is set at this minimum value, what is the fluid velocity midway between the plates?

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