Question

What is the lift (in newtons) due to Bernoulli's principle on a wing of area 86 m^2 if the air passes over the top and bottom surfaces at speeds of 340 m/s and 290 m/s respectively?

Answer 1

Answer on Question #64283, Physics / Mechanics | Relativity

What is the lift (in newtons) due to Bernoulli's principle on a wing of area $86\mathrm{m}^2$ if the air passes over the top and bottom surfaces at speeds of $340~\mathrm{m / s}$ and $290~\mathrm{m / s}$ respectively?

Solution:

$$P _ {b} + \frac {1}{2} \rho v _ {b} ^ {2} = P _ {t} + \frac {1}{2} \rho v _ {t} ^ {2}$$ $$P _ {b} - P _ {t} = \frac {1}{2} \rho v _ {t} ^ {2} - + \frac {1}{2} \rho v _ {b} ^ {2}$$ $$P _ {b} - P _ {t} = \frac {1}{2} \times 1.00 \times 10 ^ {3} \mathrm{kgm} ^ {-3} \times (340 \mathrm{m/s}) ^ {2} - + \frac {1}{2} \times 1.00 \times 10 ^ {3} \mathrm{kgm} ^ {-3} \times (290 \mathrm{m/s}) ^ {2}$$ $$P _ {b} - P _ {t} = 1.58 \times 10 ^ {7} \mathrm{N/m^2}$$ $$F _ {\text{lift}} = 1.58 \times 10 ^ {7} \mathrm{N/m^2} \times 86 \mathrm{m^2} = 1.36 \times 10 ^ {9} \mathrm{N}$$

Answer: $1.36 \times 10^{9} \mathrm{N}$

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