Solving Hard Viscosity Q Homework: Find Couple on Disk

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Homework Help Overview

The problem involves two coaxial disks with a specified radius and distance apart, rotating in a gas at standard temperature and pressure. The task is to determine the couple required to keep one disk stationary while the other rotates.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the concept of viscous shearing stress and questions why only the second term in their equation contributes to this stress. They express confusion regarding the limits of integration and the implications of ln(0).

Discussion Status

The discussion appears to be in an early stage, with the original poster seeking clarification on specific aspects of the problem. There has been no consensus or resolution, and participants have not yet provided substantial guidance or alternative approaches.

Contextual Notes

The original poster notes a potential issue with integrating from 0 to 0.001, highlighting a concern about the mathematical implications of ln(0). This suggests a need for further exploration of the mathematical setup and assumptions involved in the problem.

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Homework Statement



Two plane disks, each of radius 5cm, are mounted coaxially with their adjacent surfaces 1mm apart. They are in a chamber containing gas at STP (viscostiy of gas = 2.1 x 10^-5 Ns/m^2) and are free to rotate about the common acis. One of them rotates with angular velocity of 10 rad/s. Find the couple which must be exerted to keep the other stationary.


Homework Equations





The Attempt at a Solution



So letting the bottom plate be where r=0, top plate is at r=0.001

then i say du/dr = w + rdw/dr

textbook says that only the second term contributes to viscous shearing stress...Why is this?

so assuming that to be true,

F = pi (0.05)^2 n r dw/dr where n is the viscosity..

we can then integrate...but isn't the integral dr from 0 to 0.001? and don't we have a lnr between those limits..and ln 0 is a problem?

Help Please :S!
 
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