A viscous fluid is contained in the space between concentric cylinders. The inne

Question

A viscous fluid is contained in the space between concentric cylinders. The inner wall is fixed and the outer wall rotates with a speed . Assume that the velocity distribution in the gap is linear. For a small rectangular element shown find the shear rate of the fluid in terms of the radii and speed of the cylinders.

A viscous fluid is contained in the space between concentric cylinders. The inner wall is fixed and the outer wall rotates with a speed ?. Assume that the velocity distribution in the gap is linear. For a small rectangular element shown find the shear rate of the fluid in terms of the radii and speed of the cylinders.

Explanation / Answer

Tangential velocity of the outer clinder = V = .r0

Velocity of inner cylinder = 0

du = V - 0 = .r0 - 0 = .r0

Now, dr = r0 - ri

For a small elemental of the fluid, applying Newtons Law of Viscosity:

shaer stress = = . du/dr, where =viscosity of fluid

   = x .r0 / (r0 - r1 )

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