A rectangular control volume around an airfoil is shown in the figure below. The velocity profiles are measured at the ends of upstream $($surface #$1)$ and downstream $($surface #$2).$ The pressure is constant over the entire surface of the control volume. $(50$ points$)$

a$)$ If the surfaces #$3$ and #$4$ are straight lines, calculate the drag coefficient for the airfoil.

$u$

b$)$ If the surfaces #$3$ and #$4$ are streamlines, calculate the drag coefficient for the airfoil.

c$)$ Compare a and b results

Note: Each student has a different set of values for the vertical dimension, H$/$c and constants, A and B appearing in the outlet velocity profile. The set of parameters can be found in the table below.