$(15$ points$)$An engineering is measuring the lift and drag on an airfoil section mounted in a two$-$dimensional wind tunnel. The wind tunnel is $0\mathrm{.}5$ m high and $0\mathrm{.}5$ m deep $($into the paper$).$ The upstream wind velocity is uniform at $10\frac{m}{s},$ and the downstream velocity is $12\frac{m}{s}$ and $8\frac{m}{s}$ as shown. The vertical component of velocity is zero at both stations. The test section is $1$ m long. The engineer measures the pressure distribution in the tunnel along the upper and lower walls and finds:

$p_u=100-10x-20x(1-x)(Pa$ gage $)$

$p_l=100-10x+20x(1-x)(Pa$ gage $)$

where $x$ is the distance in meters measured from the beginning of the test section. The gas density is homogeneous throughout and equal to $1\mathrm{.}2k\frac{g}{m^3}.$ The lift and drag are the vectors indicated on the figure. The forces acting the on the fluid are in the opposite direction to these vectors. Find the lift and drag forces acting on the airfoil.