Answered: Liquid: p, u R. Inner cylinder Outer…

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Liquid: p, u R. Inner cylinder Outer cylinder

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Question

A very small circular cylinder of radius R_i is rotating at angular velocity ?_i inside a much larger concentric cylinder of radius R_o that is rotating at angular velocity ?_o. A liquid of density ? and viscosity ? is confined between the two cylinders. Gravitational and end effects can be neglected (the flow is two-dimensional into the page). If ?_i = ?_o and a long time has passed, generate an expression for the tangential velocity profile, u_? as a function of (at most) r, ? ,R_i, R_o, ?,and ?, where ? = ?_i = ?_o. Also, calculate the torque exerted by the fluid on the inner cylinder and on the outer cylinder.

Liquid: p, u
R.
Inner cylinder
Outer cylinder

Definition Definition Rate of change of angular displacement. Angular velocity indicates how fast an object is rotating. It is a vector quantity and has both magnitude and direction. The magnitude of angular velocity is represented by the length of the vector and the direction of angular velocity is represented by the right-hand thumb rule. It is generally represented by ω.

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