Two incompressible viscous fluids of the same density p flow, one on top of the other, down an inclined plane making an angle a with the horizontal. Their viscosities are µ, and u2, the lower fluid is of depth h, and the upper fluid is of depth h2. Show that u, (9) = [(h, + h2)y –y"| 1 sin a so that the velocity of the lower fluid u;(y) is dependent on the depth hz, but not the viscosity, of the upper fluid. Why?

Structural Analysis
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Author:KASSIMALI, Aslam.
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Chapter2: Loads On Structures
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Two incompressible viscous fluids of the same density p flow, one on top of the
other, down an inclined plane making an angle a with the horizontal. Their
viscosities are u1 and µ2, the lower fluid is of depth h, and the upper fluid is of
depth h2. Show that
|g sin a
4, (9) = [ch, + hɔ)y - ]ª
v1
so that the velocity of the lower fluid u(y) is dependent on the depth h2, but not
the viscosity, of the upper fluid. Why?
Transcribed Image Text:Two incompressible viscous fluids of the same density p flow, one on top of the other, down an inclined plane making an angle a with the horizontal. Their viscosities are u1 and µ2, the lower fluid is of depth h, and the upper fluid is of depth h2. Show that |g sin a 4, (9) = [ch, + hɔ)y - ]ª v1 so that the velocity of the lower fluid u(y) is dependent on the depth h2, but not the viscosity, of the upper fluid. Why?
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