Circulation theory of lift is assumed for a thin symmetric airfoil at an angle of attack $\alpha$. Free stream velocity is $U$.
A second identical airfoil is placed behind the first one at a distance of $c / 2$ from the trailing edge of the first. The second airfoil has an unknown circulation $\Gamma_{2}$ placed at its quarter chord. The normal velocity becomes zero at the same chord-wise locations of the respective airfoils as in the previous question. The values of $\Gamma_{1}$ and $\Gamma_{2}$ are respectively
(A) $\frac{4}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(B) $\frac{2}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(C) $\frac{2}{3} \pi c U \alpha, \frac{1}{3} \pi c U \alpha$
(D) $\frac{4}{3} \pi c U \alpha, \frac{4}{3} \pi c U \alpha$
Circulation theory of lift is assumed for a thin symmetric airfoil at an angle of attack $\alpha$. Free stream velocity is $U$.
A second identical airfoil is placed behind the first one at a distance of $c / 2$ from the trailing edge of the first. The second airfoil has an unknown circulation $\Gamma_{2}$ placed at its quarter chord. The normal velocity becomes zero at the same chord-wise locations of the respective airfoils as in the previous question. The values of $\Gamma_{1}$ and $\Gamma_{2}$ are respectively
(A) $\frac{4}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(B) $\frac{2}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(C) $\frac{2}{3} \pi c U \alpha, \frac{1}{3} \pi c U \alpha$
(D) $\frac{4}{3} \pi c U \alpha, \frac{4}{3} \pi c U \alpha$
(A) $\frac{4}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(B) $\frac{2}{3} \pi c U \alpha, \frac{2}{3} \pi c U \alpha$
(C) $\frac{2}{3} \pi c U \alpha, \frac{1}{3} \pi c U \alpha$
(D) $\frac{4}{3} \pi c U \alpha, \frac{4}{3} \pi c U \alpha$