Question

Consider a circulation distribution over a finite wing given by the equation below.
\[ \Gamma(y) = \begin{cases} \Gamma_0 \left(1 - \frac{2y}{b}\right) & \text{if } 0 \leq y \leq \frac{b}{2}, \\ \Gamma_0 \left(1 + \frac{2y}{b}\right) & \text{if } -\frac{b}{2} \leq y \leq 0, \end{cases} \] The wingspan \( b \) is 10 m, the maximum circulation \( \Gamma_0 \) is 20 m\(^2\)/s, density of air is 1.2 kg/m\(^3\), and the free stream speed is 80 m/s.
The lift over the wing is _________ N (rounded off to the nearest integer).

Hint:

The lift generated by a wing can be calculated using the Kutta-Joukowski theorem by multiplying the circulation, air density, free stream velocity, and wing span.

Answer 1

Correct Answer: 9500

The lift per unit span is given by the Kutta-Joukowski theorem: \[ L = \rho U \Gamma_0 b, \] where \(\rho = 1.2 \, \text{kg/m}^3\), \( U = 80 \, \text{m/s} \), and \( \Gamma_0 = 20 \, \text{m}^2/\text{s} \). Substituting the given values: \[ L = 1.2 \times 80 \times 20 \times 10 = 19200 \, \text{N}. \] Thus, the lift over the wing is approximately \( 19200 \, \text{N} \).