List of top Aerodynamics Questions on Lift and Circulation asked in GATE AE

Consider a finite wing of aspect ratio 10 with span effectiveness factor 0.95. Its airfoil section has a lift slope of 0.106 per degree and a zero-lift angle of attack of -1.5\(^{\circ}\). The lift coefficient of the wing at an angle of attack of 3.5\(^{\circ}\) is ________ (rounded off to 2 decimal places).
Which of the following motions is primarily associated with lateral stability of an aircraft?
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is __________ m\(^2\)/s (rounded off to two decimal places).
A lifting surface has a spanwise circulation distribution of \( \Gamma(\theta) = A \sin 3\theta \) (where \( A \neq 0 \)) over its span \( -\frac{b}{2} \leq y \leq \frac{b}{2} \), and \( y = -\frac{b}{2} \cos \theta \) is the spanwise coordinate. Furthermore, the downwash varies along the span as \( w(\theta) = V_\infty \left( \frac{3A \sin 3\theta}{\sin \theta} \right) \), where \( V_\infty \) is the freestream velocity. Which one of the following options represents the total lift \( L \) and induced drag \( D_i \)?

The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is __________ m\(^2\)/s (rounded off to two decimal places).

A general aviation airplane is gliding with a speed \( V_g \) at minimum glide angle. Which of the following statements is/are true?
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).
A lifting surface has a spanwise circulation distribution of \( \Gamma(\theta) = A \sin 3\theta \) (where \( A \neq 0 \)) over its span \( -\frac{b}{2} \leq y \leq \frac{b}{2} \), and \( y = -\frac{b}{2} \cos \theta \) is the spanwise coordinate. Furthermore, the downwash varies along the span as \( w(\theta) = V_\infty \left( \frac{3A \sin 3\theta}{\sin \theta} \right) \), where \( V_\infty \) is the freestream velocity. Which one of the following options represents the total lift \( L \) and induced drag \( D_i \)?
A lifting surface has a spanwise circulation distribution of \( \Gamma(\theta) = A \sin 3\theta \) (where \( A \neq 0 \)) over its span \( -\frac{b}{2} \leq y \leq \frac{b}{2} \), and \( y = -\frac{b}{2} \cos \theta \) is the spanwise coordinate. Furthermore, the downwash varies along the span as \( w(\theta) = V_\infty \left( \frac{3A \sin 3\theta}{\sin \theta} \right) \), where \( V_\infty \) is the freestream velocity. Which one of the following options represents the total lift \( L \) and induced drag \( D_i \)?
A general aviation airplane is gliding with a speed \( V_g \) at minimum glide angle. Which of the following statements is/are true?
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).
A lifting surface has a spanwise circulation distribution of \( \Gamma(\theta) = A \sin 3\theta \) (where \( A \neq 0 \)) over its span \( -\frac{b}{2} \leq y \leq \frac{b}{2} \), and \( y = -\frac{b}{2} \cos \theta \) is the spanwise coordinate. Furthermore, the downwash varies along the span as \( w(\theta) = V_\infty \left( \frac{3A \sin 3\theta}{\sin \theta} \right) \), where \( V_\infty \) is the freestream velocity. Which one of the following options represents the total lift \( L \) and induced drag \( D_i \)?
A general aviation airplane is gliding with a speed \( V_g \) at minimum glide angle. Which of the following statements is/are true?
The lift per unit span for a spinning circular cylinder in a potential flow is 6 N/m. The free-stream velocity is 30 m/s, and the density of air is 1.225 kg/m\(^3\). The circulation around the cylinder is \_\_\_\_ m\(^2\)/s (rounded off to two decimal places).
A general aviation airplane is gliding with a speed \( V_g \) at minimum glide angle. Which of the following statements is/are true?
An airplane of mass 1000 kg is in a steady level flight with a speed of 50 m/s. The wing has an elliptic planform with a span of 20 m and planform area 31.4 m$^2$. Assuming the density of air at that altitude to be 1 kg/m$^3$ and acceleration due to gravity to be 10 m/s$^2$, the induced drag on the wing is ............ N (rounded off to 1 decimal place).
A two–dimensional potential–flow solution for flow past an airfoil has the streamline pattern shown. Which additional condition is required to satisfy the Kutta condition? \begin{center} \includegraphics[width=0.5\textwidth]{03.jpeg} \end{center}