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The airways of the lung are coated with a thin liquid lining of highly viscous fluid (of viscosity μ and density p). The thickness of this liquid lining (h) is much less than the radius of these airways (R). In the larger airways, cilia on the airway wall beat up and down, "pumping" the fluid upward (toward the mouth) and opposing the pull of gravity. We can model this process by assuming that the velocity of the fluid at the airway wall (y = 0) is Vo, a given quantity (see the figure). Find the velocity profile V(y) of the fluid flow in the liquid lining and determine what the value Vo must be so that the net volume flow rate of this liquid is upward. You may ignore any effects of surface tension. airway wall TVo y=0 liquid y=h air

The airways of the lung are coated with a thin liquid lining of highly viscous fluid (of viscosity μ and density p). The thickness of this liquid lining (h) is much less than the radius of these airways (R). In the larger airways, cilia on the airway wall beat up and down, "pumping" the fluid upward (toward the mouth) and opposing the pull of gravity. We can model this process by assuming that the velocity of the fluid at the airway wall (y = 0) is Vo, a given quantity (see the figure). Find the velocity profile V(y) of the fluid flow in the liquid lining and determine what the value Vo must be so that the net volume flow rate of this liquid is upward. You may ignore any effects of surface tension. airway wall TVo y=0 liquid y=h air

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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The airways of the lung are coated with a thin liquid lining of highly viscous fluid (of viscosity μ and density p). The thickness of this liquid lining (h) is much less than the radius of these airways (R). In the larger airways, cilia on the airway wall beat up and down, "pumping" the fluid upward (toward the mouth) and opposing the pull of gravity. We can model this process by assuming that the velocity of the fluid at the airway wall (y = 0) is Vo, a given quantity (see the figure). Find the velocity profile V(y) of the fluid flow in the liquid lining and determine what the value Vo must be so that the net volume flow rate of this liquid is upward. You may ignore any effects of surface tension. airway wall Vo y=0 liquid y=h g air
Transcribed Image Text:The airways of the lung are coated with a thin liquid lining of highly viscous fluid (of viscosity μ and density p). The thickness of this liquid lining (h) is much less than the radius of these airways (R). In the larger airways, cilia on the airway wall beat up and down, "pumping" the fluid upward (toward the mouth) and opposing the pull of gravity. We can model this process by assuming that the velocity of the fluid at the airway wall (y = 0) is Vo, a given quantity (see the figure). Find the velocity profile V(y) of the fluid flow in the liquid lining and determine what the value Vo must be so that the net volume flow rate of this liquid is upward. You may ignore any effects of surface tension. airway wall Vo y=0 liquid y=h g air
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