A rotating viscometer consists of two concentric cylinders—a stationary inner cylinder of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) vo. In the tiny gap between the two cylinders is the fluid whose viscosity (m) is to be measured. The length of the cylinders is L. 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. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables.

A rotating viscometer consists of two concentric cylinders—a stationary inner cylinder of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) vo. In the tiny gap between the two cylinders is the fluid whose viscosity (m) is to be measured. The length of the cylinders is L. 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. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables.

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter11: Calibrating Instruments

Section: Chapter Questions

Problem 4RQ: Temperature-measuring instruments may be designed to measure the temperature of vapors, ________,...

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A rotating viscometer consists of two concentriccylinders—an inner cylinder of radius Ri rotating at angularvelocity (rotation rate) vi, and a stationary outer cylinder ofinside radius Ro. In the tiny gap between the two cylindersis the fluid of viscosity m. The length of the cylinders is L. 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 radius Ro were to increase, all else staying the same)?
For liquid viscosity measurement, it is desired to create a viscometer consisting of two 30 cm long concentric cylinders. The diameter of the inner cylinder is 20 cm and the diameter of the outer cylinder is 20.2 cm. Since a torque of 0.13 N cinsm is required to rotate the inner cylinder with an angular velocity of 40 rad / s, what will be the viscosity of the fluid in the viscometer in Pa⋅s? Take the value of as 3.
A rotating viscometer consists of two concentric cylinders—a stationary inner cyliner of radius Ri and an outer cylinder of inside radius Ro rotating at angular velocity (rotation rate) ?o. In the tiny gap between the two cylinders is the fluid whose viscosity (? ) is to be measured. The length of the cylinders in Fig is L. 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. Showing all your work and algebra, generate an approximate expression of T as a function of the other variables.
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