VO is a function of r.Small r refers to the variable r, as in the radial direction in the cylindrical coordinates. Capital R refers to the radius of the outer cylinder and is a constant. Radius of the inner cylinder is defined as kR, where k (kappa) is also a constant.In part (a), you are tasked to verify that the profile given in Eqn 1 is correct. You are evaluating the equation at two locations (outer cylinder, inner cylinder).Recall that angular velocity is w (omega), and w # Ve. VO refers to the local linear velocity in the 0 direction (i.e., tangential velocity).In part (b), you can ignore the resulting negative sign. You are looking for an expression of the magnitude of the shear rate o (sigma) at the inner cylinder. In Example 1.2 we replaced a cylindrical problem with a linear approximation. Thevelocity distribution for this flow, taking the cylindrical character into accountV₁ = ∞ (₁ ²²₂ ²) · ( ²² - , )1-kwhere R is the radius of the outer cylinder, r is the local radius, k = Finner cylinder / R, and @is the angular velocity of the inner cylinder.(a) Verify that this distribution shows a zero velocity at the radius of the outer, non-movingcylinder and shows V₂ = kR at the surface of the inner, rotating cylinder.(b) The shear rate in cylindrical coordinates, for a fluid whose velocity depends only on r(equivalent to dV/ dy in rectangular coordinates), is given by6=cal) = rshear rate cylindricalcoordinates0=w (₁²2ddrShow that for the above velocity distribution, the shear rate at the surface of the innercylinder is given by1-k²Ve(-;-)(c) Show that the shear rateis12.26/s, which is 1.15 times the value for the flat approximation in Example 1.2. The

Answered: In Example 1.2 we replaced a…

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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VO is a function of r.

Small r refers to the variable r, as in the radial direction in the cylindrical coordinates. Capital R refers to the radius of the outer cylinder and is a constant. Radius of the inner cylinder is defined as kR, where k (kappa) is also a constant.

In part (a), you are tasked to verify that the profile given in Eqn 1 is correct. You are evaluating the equation at two locations (outer cylinder, inner cylinder).

Recall that angular velocity is w (omega), and w # Ve. VO refers to the local linear velocity in the 0 direction (i.e., tangential velocity).

In part (b), you can ignore the resulting negative sign. You are looking for an expression of the magnitude of the shear rate o (sigma) at the inner cylinder.