P15_048 - 48. The lift force follows from the pressure...

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Unformatted text preview: 48. The lift force follows from the pressure difference (large pressure on the bottom surface than on the top) and the fact that the pressure difference is related to force through the relation ∆p = F/A where we are asked to use L for F . From Bernoulli’s equation, we have pu − pt = 1212 ρv − ρvu + ρg ∆z 2t 2 where ∆z is the thickness of the wing. The last term makes a negligible contribution (we will return to this point in a moment) and can be ignored. We then have ∆p = 1 2 2 ρ vt − vu 2 =⇒ L = 1 2 2 ρA vt − vu 2 as desired. The contribution of the “potential” term would have been ρgA∆z which we can estimate as follows: let ρ ≈ 1 kg/m3 , A ≈ 100 m2 , and ∆z ≈ 1 m. Then ρgA∆z ≈ 1000 N which perhaps corresponds to the weight of a couple of adults, and is at least an order of magnitude less than the weight of an airplane with wings (the size of which are as estimated above) and equipment and crew. ...
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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