Answered: 1. An incompressible Newtonian liquid…

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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Transport Phenomena Question

Answer a) and b)

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

Expert Solution

Step 1

The given diagram for the flow of fluid in a slit is:

Given conditions of the flow:

The flow is steady-state and laminar
The fluid is incompressible and Newtonian.
B<<W and B<<L. Thus, edge and end effects are not considered.
The flow is fully developed.
Velocity varies only in x-direction.
The entrance pressure is P₀ and the exit pressure is P_L.
x = 0 is located in the middle of the two vertical surfaces.

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