A rotating viscometer consists of two concentric cylinders –an inner cylinder of radius Rirotating at angular velocity (rotation
rate) ωi, and a stationary outer cylinder of inside radius Ro. In the tiny gap between the two cylinders is the fluid of viscosity μ. The length of the cylinders (into the page) 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 a 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 prole in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusR0 were to increase, all else staying the same)?
(b) Explain why your solution is only an approximation. In particular, do you expect the velocity prole in the gap to remain linear as the gap becomes larger and larger (i.e., if the outer radiusR0 were to increase, all else staying the same)?
1 answer:
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Answer:
The axial force is
Explanation:
From the question we are told that
The diameter of the shaft steel is
The length of the cylindrical bushing
The outer diameter of the cylindrical bushing is
The diametral interference is
The coefficient of friction is
The Young modulus of steel is
The diametral interference is mathematically represented as
Where is the pressure (stress) on the two object held together
So making the subject
Substituting values
Now he axial force required is
Where A is the area which is mathematically evaluated as
So
Substituting values