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Q9/ Tank draining with a power-law fluid. A very viscous non-Newtonian liquid in simple shear obeys the relation: T = C√s, where r is the shear stress, s is the strain rate (of a typical form Ovx/dy), and c is a constant. A uniform thin film of the liquid, of thickness h, flows steadily under gravity down a vertical plate. Show that the mass flow rate m per unit plate width is: m= p³gh 4c2 For a vertical plate from which the liquid is now draining, h will be a function of time and of the vertically downward distance x. Prove, by means of a suitable transient mass balance on a differential element, and using the above equation for m, that: ah p²g²h³ Əh A tank with vertical sides is initially full, and at t = 0 is rapidly drained of the liquid. If x is measured from the top of the tank, verify that the film thickness on the sides is given by Ət 1/3 h=

Q9/ Tank draining with a power-law fluid. A very viscous non-Newtonian liquid in simple shear obeys the relation: T = C√s, where r is the shear stress, s is the strain rate (of a typical form Ovx/dy), and c is a constant. A uniform thin film of the liquid, of thickness h, flows steadily under gravity down a vertical plate. Show that the mass flow rate m per unit plate width is: m= p³gh 4c2 For a vertical plate from which the liquid is now draining, h will be a function of time and of the vertically downward distance x. Prove, by means of a suitable transient mass balance on a differential element, and using the above equation for m, that: ah p²g²h³ Əh A tank with vertical sides is initially full, and at t = 0 is rapidly drained of the liquid. If x is measured from the top of the tank, verify that the film thickness on the sides is given by Ət 1/3 h=

Introduction to Chemical Engineering Thermodynamics
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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Q9/ Tank draining with a power-law fluid. A very viscous non-Newtonian liquid in simple shear obeys the relation: T = C√s, where r is the shear stress, s is the strain rate (of a typical form Ovx/dy), and c is a constant. A uniform thin film of the liquid, of thickness h, flows steadily under gravity down a vertical plate. Show that the mass flow rate m per unit plate width is: m= p³gh 4c2 For a vertical plate from which the liquid is now draining, h will be a function of time and of the vertically downward distance x. Prove, by means of a suitable transient mass balance on a differential element, and using the above equation for m, that: ah p²g²h³ Əh A tank with vertical sides is initially full, and at t = 0 is rapidly drained of the liquid. If x is measured from the top of the tank, verify that the film thickness on the sides is given by Ət 1/3 h=
Transcribed Image Text:Q9/ Tank draining with a power-law fluid. A very viscous non-Newtonian liquid in simple shear obeys the relation: T = C√s, where r is the shear stress, s is the strain rate (of a typical form Ovx/dy), and c is a constant. A uniform thin film of the liquid, of thickness h, flows steadily under gravity down a vertical plate. Show that the mass flow rate m per unit plate width is: m= p³gh 4c2 For a vertical plate from which the liquid is now draining, h will be a function of time and of the vertically downward distance x. Prove, by means of a suitable transient mass balance on a differential element, and using the above equation for m, that: ah p²g²h³ Əh A tank with vertical sides is initially full, and at t = 0 is rapidly drained of the liquid. If x is measured from the top of the tank, verify that the film thickness on the sides is given by Ət 1/3 h=
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