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2. An incompressible Newtonian liquid of viscosity μ and density p is placed in the gap between two concentric disks of radius R as shown in the figure below. The lower disk, located at z = 0, is stationary, while the upper disk, located at z=B, is rotated at angular velocity @. Assume that there is a steady state. LIQUID fow Jac 4 1 N R (a) What can you say about Vr, Vz and 2/20? Does the continuity equation reveal anything of value? (b) Show that the 0-component of the Navier-Stokes equation simplifies to: მ წ1 მ 0 = 1)+ 2200 Jz2 (c) It is suggested that ve can be written as a product of r with a function of z. In other words, Ve=r f(z) Show that this choice of the form of the velocity leads to d²f = 0 dz² (d) Integrate the above equation. This will involve two constants of integration. (e) What are the two boundary conditions on f? Note that, due to no slip, ve at z = B is oor. (f) Determine f(z) and, thus, obtain ve(r,z).

2. An incompressible Newtonian liquid of viscosity μ and density p is placed in the gap between two concentric disks of radius R as shown in the figure below. The lower disk, located at z = 0, is stationary, while the upper disk, located at z=B, is rotated at angular velocity @. Assume that there is a steady state. LIQUID fow Jac 4 1 N R (a) What can you say about Vr, Vz and 2/20? Does the continuity equation reveal anything of value? (b) Show that the 0-component of the Navier-Stokes equation simplifies to: მ წ1 მ 0 = 1)+ 2200 Jz2 (c) It is suggested that ve can be written as a product of r with a function of z. In other words, Ve=r f(z) Show that this choice of the form of the velocity leads to d²f = 0 dz² (d) Integrate the above equation. This will involve two constants of integration. (e) What are the two boundary conditions on f? Note that, due to no slip, ve at z = B is oor. (f) Determine f(z) and, thus, obtain ve(r,z).

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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2. An incompressible Newtonian liquid of viscosity μ and density p is placed in the gap between two concentric disks of radius R as shown in the figure below. The lower disk, located at z = 0, is stationary, while the upper disk, located at z=B, is rotated at angular velocity @. Assume that there is a steady state. LIQUID fow Jac 4 1 N R (a) What can you say about Vr, Vz and 2/20? Does the continuity equation reveal anything of value? (b) Show that the 0-component of the Navier-Stokes equation simplifies to: მ წ1 მ 0 = 1)+ 2200 Jz2 (c) It is suggested that ve can be written as a product of r with a function of z. In other words, Ve=r f(z) Show that this choice of the form of the velocity leads to d²f = 0 dz² (d) Integrate the above equation. This will involve two constants of integration. (e) What are the two boundary conditions on f? Note that, due to no slip, ve at z = B is oor. (f) Determine f(z) and, thus, obtain ve(r,z).
Transcribed Image Text:2. An incompressible Newtonian liquid of viscosity μ and density p is placed in the gap between two concentric disks of radius R as shown in the figure below. The lower disk, located at z = 0, is stationary, while the upper disk, located at z=B, is rotated at angular velocity @. Assume that there is a steady state. LIQUID fow Jac 4 1 N R (a) What can you say about Vr, Vz and 2/20? Does the continuity equation reveal anything of value? (b) Show that the 0-component of the Navier-Stokes equation simplifies to: მ წ1 მ 0 = 1)+ 2200 Jz2 (c) It is suggested that ve can be written as a product of r with a function of z. In other words, Ve=r f(z) Show that this choice of the form of the velocity leads to d²f = 0 dz² (d) Integrate the above equation. This will involve two constants of integration. (e) What are the two boundary conditions on f? Note that, due to no slip, ve at z = B is oor. (f) Determine f(z) and, thus, obtain ve(r,z).
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