(a) Find the velocity distribution in the narrow annular region. (b) Find the mass rate of flow through the annular region. (c) Obtain the viscous force acting on the rod over the length L. (d) Show that the result in (n)
(a) Find the velocity distribution in the narrow annular region. (b) Find the mass rate of flow through the annular region. (c) Obtain the viscous force acting on the rod over the length L. (d) Show that the result in (n)
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:2B.7 Annular flow with inner cylinder moving axially (see Fig. 2B.7). A cylindrical rod of radius
KR moves axially with velocity v₂ = Vo along the axis of a cylindrical cavity of radius R as seen
in the figure. The pressure at both ends of the cavity is the same, so that the fluid moves
through the annular region solely because of the rod motion.
Fluid at modified
pressure
Rod of radius KR
moving with velocity vo
Cylinder of inside
radius R
Answers: (a) V₂
Vo
Fluid at modified
pressure Po
Fig. 2B.7 Annular flow with the inner cylinder moving axially.
(a) Find the velocity distribution in the narrow annular region.
(b) Find the mass rate of flow through the annular region.
(c) Obtain the viscous force acting on the rod over the length L.
(d) Show that the result in (c) can be written as a "plane slit" formula multiplied by a "curva-
ture correction." Problems of this kind arise in studying the performance of wire-coating dies.¹
In (r/R)
In
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Step 1: Stating the information from the diagram
VIEWStep 2: Finding the velocity distribution in the annular region by substituting Newton's law of viscosity
VIEWStep 3: By integral balance finding the mass flow rate through the annular region
VIEWStep 4: By substituting the velocity distribution equation finding the viscous force acting on the road.
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