Confusion about Bernoulli's Equation & Airplane Wing

[snowcrystal42]

Hi,
I'm a little confused about the theory behind this problem related to fluids/Bernoulli's equation:

"An airplane wing is designed so that the speed of the air across the top of the wing is 251 m/s when the speed of the air below the wing is 225 m/s. The density of the air is 1.29 kg/m³. What is the lifting force on a wing of area 24.0 m²?"

Are the heights in this problem necessarily equal (is the height difference necessarily negligible)? The answer key has them equal (meaning that the ρgh terms drop out of the equation so you can easily solve for the difference in pressures and multiply by the area to give the lifting force), but can you necessarily tell that the heights are equal from the information stated in the problem? Just wondering if I missed something or if I was supposed to assume so for the problem.

Thanks!

 

[TSny]

Good question. The top and bottom surfaces are at different heights. But the effect of the height difference is negligible.

Compare ##\frac{1}{2}\rho(v_2^2 - v_1^2)## with ##\rho g \Delta h## for a reasonable value of ##\Delta h##.

 

[CWatters]

Are the heights in this problem necessarily equal (is the height difference necessarily negligible)?

Not sure you can solve it without making that reasonable assumption. Compare the thickness of a typical wing with the height it is flying at.