A NACA $32014$ with a cusped trailing edge and a chord of $1$ m is placed in a flow with ${}_{}=1\mathrm{.}16k\frac{g}{m^3},P_{}=94$kPa, and $V_{}=46\frac{m}{s},$ at an angle of attack of $6.$ The flow leaves the trailing edge at a velocity magnitude of $0\mathrm{.}9$ V $.$

Compute the design lift coefficient $($i$.$e$.$ lift at zero angle of attack$)$ and the maximum camber location along the chord if the leading edge of the airfoll is placed at the origin. Give your answers to three significant digits.

Design lift coefficient $=$

Chordwise location of maximum camber $=$ m$.$

Compute the components of velocity at the trailing edge using the Kutta condition if the camber is defined as

$k_1=42\mathrm{.}15,r=0\mathrm{.}13,(\frac{x}{c})y_{c}xy{v}_x=,\frac{m}{s}.$

$v_y=,\frac{m}{s}.\frac{k_1}{6}((\frac{x}{c}{)}^3-3r(\frac{x}{c}{)}^2+r^2(3-r)(\frac{x}{c})),0\frac{x}{c}$

where $k_1=42\mathrm{.}15,r=0\mathrm{.}13,(\frac{x}{c})is$ the chordwise position $as$ a fraction $of$ chord, and $y_{c}is$ the camber expressed $as$ a fraction $of$ chord. Note that the velocity components are $in$ a reference frame with $x-$axis aligned with the freestream velocity vector and $y-$axis $is$ positive upwards. Give your answers $to$ three significant digits.

$v_x=,\frac{m}{s}.$

$v_y=,\frac{m}{s}.$