Shafts in Newtonian Fluids

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

$\frac{d^{2}u}{d{y}^2}=0$

If the dynamic viscosity of the lower fluid ${\mu }_2$, is twice that of the upper fluid ${\mu }_1,$ then the velocity at the interface (round off to two decimal places) is m/s.

1. 1