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 t

Question

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.) (a) At takeoff the aircraft travels at 63.0 m/s, so that the air speed relative to the bottom of the wing is 63.0 m/s. Given the sea level density of air to be 1.29 kg/m3, how fast (in m/s) must it move over the upper surface to create the ideal lift

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Sigridomena 4 years 2021-07-20T06:27:34+00:00 1 Answers 38 views 0

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    2021-07-20T06:29:31+00:00

    Answer:

        v₂ = 63.62 m / s

    Explanation:

    For this exercise in fluid mechanics we will use Bernoulli’s equation

             P₁ + ρ g v₁² +  ρ g y₁ = P₂ +  ρ g v₂² +  ρ g y₂

    where the subscript 1 refers to the inside of the wing and the subscript 2 to the top of the wing.

    We will assume that the distance between the two parts is small, so y₁ = y₂

            P₁-P₂ =  ρ g (v₂² – v₁²)

    pressure is defined by

            P = F / A

    we substitute

            ΔF / A =  ρ g (v₂² – v₁²)

             v₂² = \frac{\Delta F}{A \ \rho  \ g} + v_1^2

    suppose that the area of ​​the wing is A = 1 m²

    we substitute

             v₂² = \frac{1000}{1 \ 1.29 \ 9.8} + 63^2

             v₂² = 79.10 + 3969

             v₂ = √4048.1

             v₂ = 63.62 m / s

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