GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

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
$\frac{{\mathit{d}}^2\mathit{u}}{\mathit{d}{\mathit{y}}^2}=0$
If the dynamic viscosity of the lower fluid, μ2, is twice that of the upper fluid, μ1, then thevelocity at the interface (round off to two decimal places) is _________ m/s.