February 17, 2020, 07:19:20 PM
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Topic: Flow of fluid between parallel plates, upper if fixed and lower moves at speed v  (Read 1722 times)

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Offline Kiwimarie

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Consider the flow of an incompressible Newtonian fluid between parallel plates of length L and width W as shown in the figure below. The upper plate is fixed (z=b) and the lower plate (at z=0) is moving with a speed v in the positive y-direction. There is no pressure gradient so the fluid moves as a result of the lower plate.
Write down the postulates of this system and perform a shell momentum balance.
Using this balance, obtain expressions for a) shear stress distribution, b) velocity distribution and c) volumetric flow rate.

Offline Borek

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Offline Enthalpy

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Welcome, Kiwimarie!

This question is possibly the very first in your course about fluid mechanics, a direct application of what you've learnt.

The only advice I'm willing to give is: do not stick to 3D calculus, which is rarely useful and makes everything complicated or impossible. Here the situation is 1D. Write the forces on a volume element, deduce the rest.

Also: the flow is probably laminar in this problem (we don't see any drawing here). It is sometimes the case in real life, but not so often. So, do not generalize.

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