Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown below

Q. Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, 2 m apart as shown below. The bottom plate is fixed and the upper plate moves to the right with a constant velocity of 3 m/s. With the assumptions of Newtonian fluid, steady, and fully developed laminar flow with zero pressure gradient in all directions, the momentum equations simplify to

If the dynamic viscosity of the lower fluid, 𝜇₂, is twice that of the upper fluid, 𝜇₁, then the velocity at the interface (round off to two decimal places) is ____m/s.

Ans: 0.98 – 1.02

Sol:

Newton’s law states that