Q$3$: $($i$)$ Consider a modified form of pure Couette flow in which there are two immiscible fluids sandwiched between two infinitely long and wide, parallel flat plates as shown in the Figure. The flow is $2$D steady, fully developed, incompressible, parallel, and laminar. The top plate moves at velocity V to the right, and the bottom plate is stationary. Gravity acts in the $-$z direction and the flow is shear driven. The interface between the two fluids is horizontal $($ignoring surface tension effects$)$ with continuity in velocity, shear stress and pressure between the two fluids. The pressure at the bottom