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82. Problem 18.37 (RHK) In the diagram a cross-section of the upper layers of the
Earth has been shown. The surface of the Earth is broken into several rigid
blocks, called plates that slide (slowly) over a slushy layer called
asthenosphere. Suppose that the speed of the rigid plate shown is
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,
and that the base of the asthenosphere does not move. We have to calculate the
sheer stress on the plate. The viscosity of the asthenosphere material is
We
may ignore the curvature of the Earth.
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Solution: Click For PDF Version We will use the definition of viscosity of a fluid for solving this problem. The ratio between stress and strain in a fluid is called the coefficient
of viscosity
That is
Velocity gradient of the asthenosphere is
Therefore, the stress on the base of the plate
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of the
fluid. For fluids stress is the shearing stress and strain is the velocity
gradient,
.
