# 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) $\frac{8 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$

3537

(C) $\frac{4 \pi \alpha c}{V_{\infty}\left(4-\pi^{2} \alpha^{2}\right)}$

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Air enters an aircraft engine at a velocity of $180 \mathrm{~m} / \mathrm{s}$ with a flow rate of $94 \mathrm{~kg} / \mathrm{s}$. The engine combustor requires $9.2 \mathrm{~kg} / \mathrm{s}$ of air to burn $1 \mathrm{~kg} / \mathrm{s}$ of fuel. The velocity of gas exiting from the engine is $640 \mathrm{~m} / \mathrm{s}$. The momentum thrust (in $N$ ) developed by the engine is
(A) 43241
(B) 45594
(C) 47940
(D) 49779