A frequently quoted rule of thumb in aircraft design is that wings should produce about 1000 N of lift per square meter of wing. (The fact that a wing has a top and bottom surface does not double its area.) Part (a) At takeoff, an aircraft travels at 69 m/s, so that the air speed relative to the bottom of the wing is 69 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast must it move over the upper surface to create the ideal lift?

Respuesta :

Answer:

[tex]v_{f}=6311.38\frac{m}{s}[/tex]

Explanation:

a)

The ideal lift is the relation of the density of the fluid and the velocity so:

[tex]F_{lift}=\frac{1}{2}*p*A*(v_{f}^2-v_{o}^2)[/tex]

The density of the fluid is determinate as a

[tex]p=1.29\frac{kg}{m^{3} }[/tex]

The area in the situation give the information that the wings produce about 100N of lift per square meter of wings so

[tex]A=1 m^2[/tex]

The initial speed is

[tex]v_{o}=69 \frac{m}{s}[/tex]

Replacing

[tex]F_{lift}=\frac{1}{2}*1.29\frac{kg}{m^3}*1*m^2*(v_{f}^2-69^2\frac{m}{s})[/tex]

Resolve for vf

[tex]v_{f}^2=69^2\frac{m}{s}+\frac{2*1000N}{1.29\frac{kg}{m^3}*1m^2}[/tex]

[tex]v_{f}=6311.38\frac{m}{s}[/tex]