Answered: Liquid: p, u. R. R Rotating inner…

Engineering

Civil Engineering

Liquid: p, u. R. R Rotating inner cylinder Stationary outer cylinder

Residential Construction Academy: House Wiring (MindTap Course List)

5th Edition

ISBN:9781337402415

Author:Gregory W Fletcher

Publisher:Gregory W Fletcher

Chapter4: Test And Measurement Instruments Used In Residential Wiring

Section: Chapter Questions

Problem 12RQ

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MATLAB

MATLAB software is a registered trademark, multi-model programming language, and numerical computing environmental system created by MathWorks. 'MATLAB' is the short-form of "Matrix Laboratory". The MATLAB software permits the utilization of matrix operations, graphical representation of data, execution of algorithms, development of user interface, and linking programs created in other languages. Even though MATLAB is developed mainly for numerical computing, there is an optional toolbox that uses a symbolic engine known as MuPAD giving access to all the symbolic computing abilities. In addition to this, a Simulink package delivers graphical multi-domain simulation and design that is model-based for embedded and dynamic systems. MATLAB users are spread worldwide across the world and use MATLAB extensively.

Question

A rotating viscometer consists of two concentric cylinders—an inner cylinder of radius Ri rotating at angular velocity (rotation rate) ?_i, and a stationary outer cylinder of inside radius R_o. In the tiny gap between the two cylinders is the fluid of viscosity ? . The length of the cylinders (into the page 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. (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 R_o were to increase, all else staying the same)?

Liquid: p, u.
R.
R
Rotating inner cylinder
Stationary outer cylinder

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