# The Pitot tube of an aircraft registers a pressure $p_{0}=54051 \mathrm{~N} / \mathrm{m}^{2} .$ The static pressure, density and the ratio of specific heats of the freestream are $p_{\infty}=45565 \mathrm{~N} / \mathrm{m}^{2}, \rho_{\infty}=0.6417 \mathrm{~kg} / \mathrm{m}^{3}$ and $\gamma=1.4,$ respectively. The indicated airspeed $(\mathrm{in} m / s)$ is (A) 157.6 (B) 162.6 (C) 172.0 (D) 182.3

## Question ID - 155731 :- The Pitot tube of an aircraft registers a pressure $p_{0}=54051 \mathrm{~N} / \mathrm{m}^{2} .$ The static pressure, density and the ratio of specific heats of the freestream are $p_{\infty}=45565 \mathrm{~N} / \mathrm{m}^{2}, \rho_{\infty}=0.6417 \mathrm{~kg} / \mathrm{m}^{3}$ and $\gamma=1.4,$ respectively. The indicated airspeed $(\mathrm{in} m / s)$ is (A) 157.6 (B) 162.6 (C) 172.0 (D) 182.3

3537

(A) 157.6

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