GATE 2019 Mechanical Engineering Q45

Question

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
$\frac{d^2u}{dy^2} = 0$.
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.

Accepted Answer

0.98 to 1.02