$6597657$

$\frac{9}{12}$

$100\%$

Part $3$: Derivation, Analysis, and Problem$-$Solving Component

Problem $21.(23$ Points$)$ 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 $0\mathrm{.}5V_0,$ 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 plateras 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 vec$(V).$ Be sure and show which assumptions you're using to simplify the momentum and continuity equation.