We have flow through a $2-$D duct, as shown below. At the inlet, the

velocity profile is in the $x-$direction and parabolic, with $u(y)=4-4y^2.$ At the

outlet, the profile is in the $y-$direction and linear, with $v(x)=4-x.$ Select a

control mass consisting of all fluid in the duct.

a$.$ Sketch the location of the control mass at a time $t=0\mathrm{.}5$ seconds after this

instant.

b$.$ Sketch its location at $t=20$ seconds after this instant. Do you trust the

accuracy of the sketch?