A viscous fluid is contained between two long concentric cylinders. The geometry of the system is...

Question

A viscous fluid is contained between two long concentric cylinders. The geometry of the system is such that the flow between the cylinders is approximately the same as the laminar flow between two infinite parallel plates. (a) Determine an expression for the torque required to rotate the outer cylinder with an angular velocity ω. The inner cylinder is fixed. Express your answer in terms of the geometry of the system, the viscosity of the fluid, and the angular velocity. (b) For a small, rectangular element located at the fixed wall, determine an expression for the rate of angular deformation of this element. (See Video V6.3 and Fig. P6.10.)

Q

Robert · Accepted Answer

Draw the schematic diagram of the cylinder representing the flow of the fluid:
Draw the sectional view of the cylinder:
(a.)Consider a small element and integrate over the entire area to find the shear stress on the entire 
surface. 
 

Write the velocity relation between the gap.

A viscous fluid is contained between two long concentric cylinders. The geometry of the system is such that the flow between the cylinders is approximately the same as the laminar flow between two...

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