Answered: As shown in Figure A, two immiscible,…

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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Attaching question and figure, please solve a,b,c and then i will post it once again for the remaining parts.

Transcribed Image Text:As shown in Figure A, two immiscible, incompressible liquids are flowing in the x-direction (streamwise direction) in a horizontal thin slit of length L and width W under the influence of a horizontal pressure gradient ( Po – P1/L). The fluid flow rates are adjusted, so that the slit is half filled with liquid I (the less dense phase) and half filled with liquid II (the more dense phase). The liquids are flowing sufficiently slowly that no instabilities occur - that is, the interface remains exactly planar. This is a steady state flow of two Newtonian liquids with constant viscosities and densities, which is studied in Cartesian coordinates. Gravitational effects are not important. (a) Identify the streamwise, transverse and spanwise direction of the flow (b) Identify which velocity component is non zero for this flow problem (c) Formulate the continuity equation for both phases and check what information you obtain (d) Formulate the momentum conservation eq. in the spanwise direction and check what information you obtain (for both phases) (e) Formulate the momentum conservation equation in the transverse direction and check what information you obtain (for both phases) (f) Formulate the momentum conservation equation in the streamwise direction and determine the velocity profiles as well as the shear stress (for both phases) (g) Draw a figure with the resulting velocity profiles and the shear stress. How is the position of zero shear stress associated with the profile of the velocities? А.