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A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius Ri rotating at angular velocity (rotation rate) wi and a stationary outer cylinder of inside radiusRO. In the tiny gap between the two cylinders is the fluid of viscosity p. The length of the cylinders (into the page in Fig. P2-89) isL. Lis large such that end effects are negligible (we can treat this as a two- dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed, (a) Showing all of your work and algebra, generate an approximate expression for T as a function of the other variables, (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusRO were to increase, all else staying the same)?

A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius Ri rotating at angular velocity (rotation rate) wi and a stationary outer cylinder of inside radiusRO. In the tiny gap between the two cylinders is the fluid of viscosity p. The length of the cylinders (into the page in Fig. P2-89) isL. Lis large such that end effects are negligible (we can treat this as a two- dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed, (a) Showing all of your work and algebra, generate an approximate expression for T as a function of the other variables, (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusRO were to increase, all else staying the same)?

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Find the velocity and shear stress equations..
A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius Ri rotating at angular velocity (rotation rate) wi and a stationary outer cylinder of inside radiusRO. In the tiny gap between the two cylinders is the fluid of viscosity µ. The length of the cylinders (into the page in Fig. P2-89) isL. L is large such that end effects are negligible (we can treat this as a two- dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed, (a) Showing all of your work and algebra, generate an approximate expression for T as a function of the other variables, (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusRO were to increase, all else staying the same)?
Transcribed Image Text:A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius Ri rotating at angular velocity (rotation rate) wi and a stationary outer cylinder of inside radiusRO. In the tiny gap between the two cylinders is the fluid of viscosity µ. The length of the cylinders (into the page in Fig. P2-89) isL. L is large such that end effects are negligible (we can treat this as a two- dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed, (a) Showing all of your work and algebra, generate an approximate expression for T as a function of the other variables, (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusRO were to increase, all else staying the same)?
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