Different incompressible newtonian fluids

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Reference no: EM13254364

Two layers of different incompressible Newtonian fluids are contained between two flat plates separated by a distance D. Both layers are of the same thicnkess (D/2). The fluid in the top layer has a viscosity uii, and the fluid in the bottom layer has a viscosity ui. The bottom plate is kept stationary. To move the top plate with speed V in the horizontal direction, it is necessary (at steady state) to exert on the top plate a force F per unit plate area in the horizontal direction. An effective viscosity u* for the system is defined by

F = u*V/d

Derive a formula which expresses u* as a funcion of ui and uii only. Assume that

$\frac{\partial p}{\partial x}=o$

everywhere and that the flow is laminar

Reference no: EM13254364

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