A long cylinder of radius R_1 is displaced along its axis with a c | Filo

Class 11

Physics

Mechanics

Mechanical Properties of Fluids

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150

A long cylinder of radius is displaced along its axis with a constant velocity inside a stationary co-axial cylinder of radius . The space between the cylinders is filled with viscous liquid. The velocity of the liquid as a function of the distance from the axis of the cylinders is .

What will be ?

1. r
Solution: Let us consider a coaxial cylinder of radius and thickness , then force of friction or viscous force on this elemental layer,

.

This force must be constant from layer to layer so that steady motion may be possible.

or, ........................(1)

Integrating,

or, .......................(2)

Putting , we get

...................(3)

From (2) / (3) we get,

Therefore,

Note: The force is supplied by the agency which tries to carry the inner cylinder with velocity .
598
150

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