Flow of two adjacent immiscible fluids Consider the flow of two immiscible Newtonian liquids in a rectangular channel as shown in Figure $2.$ The respective properties of the liquids are $,,,.$ A pressure difference drives the flow from left to right. The flow is isothermal and one$-$directional. Assume that W and L are much greater than b$.$ Beginning with fundamental equations, derive a model to describe the flow at steady state in this system. Proceed as follows: a$.$ Obtain simplified GDEs clearly indicating the reason for canceling terms. b$.$ Specify appropriate boundary conditions. c$.$ Obtain the shear stress and velocity profiles. d$.$ Plot qualitatively the velocity profiles and the shear stress profiles in both types of graphs: conventional and embedded in the geometry. Plot the profile for the case when $\backslash$Iota $<mtext\; id="EditorElement\_16615941"></mtext><mi\; id="EditorElement\_16615942"></mi><mi\; id="EditorElement\_16615943">\backslash </mi>$Iota $\backslash$Iota $.$ e$.$ Write an expression for the average velocity of each liquid. You may leave these two expressions in terms of double line integrals without doing the integration. f$.$ Write expressions for the drag force exerted by each liquid on their respective wall. You may leave these two expressions in terms of double line integrals without doing the integration. This problem is $$solved$$ in the textbook $($In the $2$nd ed$.-$ Example $2\mathrm{.}5$ Flow of two adjacent immiscible fluids$).$ It might be of some help to see it