Problem $6.$ Two immiscible fluids are contained between two infinite parallel plates. The plates are separated by distance $\backslash (2$ h $\backslash ),$ and the two fluid layers are of equal thickness $\backslash ($ h $\backslash ).$ The dynamic viscosity of the upper layer $($fluid B $)$ is three times that of the lower layer $($fluid A$).$ Find the velocity at the interface if the lower plate is stationary and the upper plate moves at constant speed, $\backslash ($ U$=20\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Assume laminar flows, and that the pressure gradient in the direction of flow is zero.