A rotating viscometer consists of two concentriccylinders—an inner cylinder of radius Ri rotating at angularvelocity (rotation rate) vi, and a stationary outer cylinder ofinside radius Ro. In the tiny gap between the two cylindersis the fluid of viscosity m. 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 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 Ro were to increase, all else staying the same)?
A rotating viscometer consists of two concentric
cylinders—an inner cylinder of radius Ri rotating at angular
velocity (rotation rate) vi, and a stationary outer cylinder of
inside radius Ro. In the tiny gap between the two cylinders
is the fluid of viscosity m. 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 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 Ro were to increase, all else
staying the same)?
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