$2-(20$ pts$)$ Two$-$dimensional, steady, low$-$speed flow passes over a symmetric airfoil. Velocity profiles are measured at the upstream $($surface $1)$ and downstream $($surface $3)$ locations of the rectangular control volume. The velocity profile at surface $3$ is measured as follows:

$u_x=U_{}(\frac{y}{}{)}^{\frac{1}{7}}$ for $y$

$u_x=U_{}$ for $y$

where, $=0\mathrm{.}04m$

a$)$ Calculate the mass flow rate passing through surface $4$ using the continuity equation.

b$)$ Calculate the drag force on the airfoil using the momentum and continuity equations. $($Note that surface $2($the lower boundary of the control volume$)$ is a line of symmetry$)$