$3.($a$)$ Sand grains in a desert, having nominal diameter $\backslash ($ D $\backslash ),$ re often lifted by the wind and transported over large distances. Using dimensional analysis and by mking suitable assumptions which are to be clearly stated, estimate the critical $($or minimal$)$ wind velorty needed to lift the sand grains from the ground.

$($b$)$ Consider flow of two immiscible fluids with dynamic vicosities $\backslash (\backslash$mu$\_\{\backslash$text $\{$I $\}\}\backslash )$ and $\backslash (\backslash$mu$\_\{2\}\backslash )$ between two stationary parallel flat plates separated by distance $2$ H similar to plae Poiseuille flow. The flow is caused by a negative pressure gradient imposed between inlet and outt. The lower and upper halves of the space are occupied by the two fluids having dynamic viscosities $\backslash (/4\backslash )$ and $\backslash (\backslash$mu$\_\{2\}\backslash )$ respectively. The densities of the two fluids are assumed to be equal and effects due to grvity are neglected. Assume the flow to be parallel, steady and laminar. Write the governing differenal equation$($s$)$ and boundary conditions of the system. You do NOT need to solve the equation$($s$).$