Consider steady, incompressible, laminar flow of two Newtonian fluids sandwiched between two infinitely large parallel plates. The fluids have different densities, different viscosities, and they form a well-defined interface (i.e., they are immiscible). The lower plate is stationary whereas the upper plate moves to the right at constant velocity U. There is no applied pressure gradient pushing the fluid through the gap. The fluid is set into motion due to the movement of the upper plate. Determine the velocity at the interface in terms of U, µ1, and 42. moving plate U h Fluid 1 Fluid 2 fixed plate

Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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Consider steady, incompressible, laminar flow of two Newtonian fluids sandwiched between
two infinitely large parallel plates. The fluids have different densities, different viscosities, and
they form a well-defined interface (i.e., they are immiscible). The lower plate is stationary
whereas the upper plate moves to the right at constant velocity U. There is no applied pressure
gradient pushing the fluid through the gap. The fluid is set into motion due to the movement of
the upper plate.
Determine the velocity at the interface in terms of U, 41, and Hz.
moving plate
U
Fluid 1
Fluid 2
fixed plate
Transcribed Image Text:Consider steady, incompressible, laminar flow of two Newtonian fluids sandwiched between two infinitely large parallel plates. The fluids have different densities, different viscosities, and they form a well-defined interface (i.e., they are immiscible). The lower plate is stationary whereas the upper plate moves to the right at constant velocity U. There is no applied pressure gradient pushing the fluid through the gap. The fluid is set into motion due to the movement of the upper plate. Determine the velocity at the interface in terms of U, 41, and Hz. moving plate U Fluid 1 Fluid 2 fixed plate
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