## Related questions with answers

A rotating viscometer consists of two concentric cylinders - an inner cylinder of radius $R_i$ rotating at angular velocity (rotation rate) $\omega_r$, and a stationary outer cylinder of inside radius $R_o$. In the tiny gap between the two cylinders is the fluid of viscosity $\mu$. The length of the cylinders is $L . L$ is large such that end effects are negligible (we can treat this as a two-dimensional problem). Torque (T) is required to rotate the inner cylinder at constant speed. (a) Showing all of your work and algebra, generate an approximate expression for $\mathrm{T}$ as a function of the other variables. (b) Explain why your solution is only an approximation. In particular, do you expect the velocity profile in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radius $R_o$ were to increase, all else staying the same)?

Solution

VerifiedThe visual representation of the problem is needed to see how the viscosity effect is trying to rotate the cylinder in the opposite direction.

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