Applications. A thin plate is separated from two fixed plates by two different v

Question

Applications. A thin plate is separated from two fixed plates by two different viscous liquids. as illustrated below. The thin plate id unequally between the two fluids. The contact area is A between the center plate and each fluid. Assume a linear velocity distribution in each fluid. Find the force F required to pull the plate at velocity V. Provide free-body diagram of the problem. Choose one coordinate system for the entire problem, and then determine the velocity distribution in each fluid by applying the appropriate boundary conditions.

Explanation / Answer

Assuming a linear velocity distribution on each side of the plate, we obtain the force required to pull the plate at velocity V as

F = 1A + 2A = (1V/h1 + 2V/h2 )*A

The formula is of course valid only for laminar (nonturbulent) steady viscous flow.

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