Solving Hard Viscosity Q Homework: Find Couple on Disk

In summary, the problem involves two plane disks with a radius of 5cm mounted coaxially with a 1mm gap between them. They are in a chamber with gas at STP and one disk is rotating at 10 rad/s. The question asks for the couple needed to keep the other disk stationary. The solution involves considering the viscous shearing stress and integrating with respect to distance.
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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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What is viscosity and why is it important in physics?

Viscosity is a measure of a fluid's resistance to flow. In physics, it is important because it affects the motion of objects through fluids, such as air or water. Viscosity also plays a crucial role in understanding fluid dynamics and heat transfer.

What is the "couple on disk" problem and why is it considered difficult?

The "couple on disk" problem is a classic physics problem that involves finding the torque required to rotate a disk in a fluid with a given viscosity. It is considered difficult because it requires the use of complex mathematical equations, such as the Navier-Stokes equation, to solve for the torque.

What are the steps for solving the "couple on disk" problem?

The steps for solving the "couple on disk" problem include determining the geometry and properties of the disk, calculating the fluid viscosity, setting up the equations of motion, and solving for the torque using mathematical techniques such as integration or numerical methods.

What are some common challenges when solving the "couple on disk" problem?

Some common challenges when solving the "couple on disk" problem include dealing with nonlinear equations, accurately determining the properties of the fluid and disk, and choosing the appropriate method for solving the equations.

How can the "couple on disk" problem be applied in real-world scenarios?

The "couple on disk" problem has applications in various fields, such as fluid mechanics, engineering, and geophysics. It can be used to understand the behavior of fluids in motion, design efficient propellers or turbines, and study the movement of sediment particles in water bodies.

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