Consider the following situation. A constant density $,$ constant viscosity $$ fluid is contained between two parallel plates located at x $=0$ and x $=$ L$.$ The left plate is moving with constant speed V$0$ and the right plate is moving with a constant speed of $0\mathrm{.}5$V$0,$ as shown in the figure below. The flow field is $($i$)$ steady, $($ii$)$ planar$/$columnar$,$ and $($iii$)$ fully$-$developed in the y$-$direction with $($iv$)$ gravity pointing in the negative y$-$direction. The flow is due to the motion of the left plate as well as a pressure gradient that is applied in the y direction. Use these assumptions together with the proper boundary conditions to find an expression for the velocity profile V$.$ Be sure and show which assumptions you$$re using to simplify the momentum and continuity equation.