Consider a NACA 0012 aerofoil of chord $c$ in a freestream with velocity $V_{\infty}$ at a non-zero positive angle of attack $\alpha$. The average time-of-flight for a particle to move from the leading edge to the trailing edge on the suction and pressure sides are $t_{1}$ and $t_{2}$, respectively. Thin aerofoil theory yields the velocity perturbation to the freestream as $V_{\infty} \frac{(1+\cos \theta) \alpha}{\sin \theta}$ on the suction side and as $-V_{\infty} \frac{(1+\cos \theta) \alpha}{\sin \theta}$ on the pressure side, where $\theta$ corresponds to the chordwise position,
$x=\frac{c}{2}(1-\cos \theta) .$ Then $t_{2}-t_{1}$ is
(A) $-\frac{8 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$
(B) 0
(C) $\frac{4 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$
(D) $\frac{8 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$

Question ID - 155732 :-

Consider a NACA 0012 aerofoil of chord $c$ in a freestream with velocity $V_{\infty}$ at a non-zero positive angle of attack $\alpha$. The average time-of-flight for a particle to move from the leading edge to the trailing edge on the suction and pressure sides are $t_{1}$ and $t_{2}$, respectively. Thin aerofoil theory yields the velocity perturbation to the freestream as $V_{\infty} \frac{(1+\cos \theta) \alpha}{\sin \theta}$ on the suction side and as $-V_{\infty} \frac{(1+\cos \theta) \alpha}{\sin \theta}$ on the pressure side, where $\theta$ corresponds to the chordwise position,
$x=\frac{c}{2}(1-\cos \theta) .$ Then $t_{2}-t_{1}$ is
(A) $-\frac{8 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$
(B) 0
(C) $\frac{4 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$
(D) $\frac{8 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$