Two large stationary parallel plates are separated by a gap of thickness h. Two layers of fluid of different dynamic viscosities ( u and 2u) fill the gap. A thin sheet of area A lies in the interface between the two fluid layers and is pulled to the right with constant velocity V.
What is the viscous force resisting the motion of this sheet if the fluid-fluid interface is at yi= h/2? Plot the variation of this force as the interface position yi varies from 0 to h.