A long cylinder of radius R_1 is displaced along its axis with a c | Filo
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Class 11



Mechanical Properties of Fluids

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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
Correct Answer: Option(a)
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)


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

Putting , we get


From (2) / (3) we get,


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