Problem $2$ As air $($treated as incompressible$)$ flows steadily over a flat plate, frictional

effect on the surface tend to form a boundary layer in which the streamwise velocity

profile changes from that of being uniform to one that is parabolic, defined by

$u=[1000y-83\mathrm{.}33**{10}^3{y}^2]\frac{m}{s},$ where y is in meters, and If the plate is

$0\mathrm{.}2$ m wide $($into the paper$),$ and this change of the velocity occurs within the distance of

$0\mathrm{.}5$ m $,$ use control volume analysis to determine $($use standard air density$)$

$($a$)$ The mass flow rate through sections $AB,CD$

$($b$)$ The mass flow rate through the lateral surface AC;

$($c$)$ The viscous drag on this portion of the plate $($assuming the pressure is

everywhere the same and the shear stress on AC is negligible$).$ Note: the fluid

"leaking from AC$"$ has a horizontal velocity of $3\frac{m}{s}$