Question 4 (10+10=20 Point): A symmetric airfoil operates at a small angle of attack (alpha =2^circ ) in subsonic flow. The lift coefficient is given by C_(L)=2pi alpha (with a in radians ) - (a) Calculate the lift coefficient (C_(L)) (b) If the chord length is 1.5 m, wing span is 2 m and the airspeed is 30m/s,rho _(infty )=1.225kg/m^3 determine the lift force.

(a) To calculate the lift coefficient $(C_{L})$, we need to convert the angle of attack from degrees to radians. <br /><br />Given that the angle of attack is $2^{\circ}$, we can convert it to radians using the formula:<br /><br />$\alpha_{rad} = \alpha_{deg} \times \frac{\pi}{180}$<br /><br />Substituting the given value of $\alpha_{deg} = 2^{\circ}$, we get:<br /><br />$\alpha_{rad} = 2 \times \frac{\pi}{180} = \frac{\pi}{90}$<br /><br />Now, we can calculate the lift coefficient using the given formula:<br /><br />$C_{L} = 2\pi\alpha$<br /><br />Substituting the value of $\alpha_{rad}$, we get:<br /><br />$C_{L} = 2\pi \times \frac{\pi}{90} = \frac{2\pi^2}{90} \approx 0.21$<br /><br />Therefore, the lift coefficient $(C_{L})$ is approximately 0.21.<br /><br />(b) To determine the lift force, we can use the lift equation:<br /><br />$L = \frac{1}{2} \rho_{\infty} v^2 S C_{L}$<br /><br />Where:<br />- $L$ is the lift force<br />- $\rho_{\infty}$ is the air density<br />- $v$ is the airspeed<br />- $S$ is the wing area<br />- $C_{L}$ is the lift coefficient<br /><br />Given that the chord length is 1.5 m, wing span is 2 m, and the airspeed is 30 m/s, we can calculate the wing area $S$ as:<br /><br />$S = \frac{1}{2} c^2 \alpha$<br /><br />Substituting the given values, we get:<br /><br />$S = \frac{1}{2} \times (1.5)^2 \times \frac{\pi}{90} \approx 0.0419 \, m^2$<br /><br />Now, we can calculate the lift force using the lift equation:<br /><br />$L = \frac{1}{2} \times 1.225 \times (30)^2 \times 0.0419 \times 0.21 \approx 0.98 \, N$<br /><br />Therefore, the lift force is approximately 0.98 N.