We consider a modified couette flow in which there are two immiscible fluids sandwiched between two infinite, parallel plates. the flow is steady, incompressible, parallel, and laminar. the top plate moves at velocity v to the right, and the bottom plate is fixed. gravity acts in the z-direction. there is no pressure gradient pushing the fluids through the channel. ignore surface tension effects and assume that the interface is horizontal. the pressure at the bottom z = 0 is equal to p0.
(a) list all the appropriate boundary conditions on both velocity and pressure. there are six required boundary conditions.
(b) solve for the velocity field. you will need to split up the solution into two portions, one for each fluid.
(c) solve for the pressure field. again, you will split up the solution.
(d) if fluid 1 be water and fluid 2 is engine oil, both at 20oc, for h1 = 3 mm, h2 = 8 mm and v = 5 m/s, plot u a