a.) Find the pressure difference on an airplane wing where air flows over the up

Question

a.) Find the pressure difference on an airplane wing where air flows over the upper surface with a speed of 120 m/s and along the bottom surface with a speed of 90 m/s.
_____ Pa

b.) If the area of the wing is 25 m2, what is the net upward force exerted on the wing?
____ N

(You may assume the density of air is fixed at 1.29 kg/m3 in this problem. Also, you may neglect the thickness of the wing-- though could you incorporate this too, if it was given?)

The answer is NOT a) 3.4x10^4 and b) 8.5 x 10^5. These were both incorrect.

Explanation / Answer

The solutions are:

P(top) = pressure on top of wing

P(bot) = pressure on bottom wing

d = density of air = 1000 kg/m^3

g = gravitational acceleration = 9.81m/s^2

h(top) = height of top of wing above ground

h(bot) = height of bottom of wing above ground

v(top) = velocity of air on top of wing = 120 m/s

v(bot) = velocity of air on bottom of wing = 90 m/s

a)

We use Bernoulli's Equation:


P(top) + d*g*h(top) + 1/2*d*v(top)^2 = P(bot) + d*g*h(bot) + 1/2*d*v(bot)^2


Question "a" asks us to find the pressure difference, P(diff), between the top and bottom of the wing:

P(diff) = P(top) - P(bot)

If we use Bernoulli's Equation we can solve for this:

P(top) - P(bot) = d*g*[h(top) - h(bot)] + 1/2*d*[v(top)^2 - v(bot)^2]

The key idea here is that since the wing is thin, h(top) - h(bot) = 0, and so the 1st term on the right side of the equation VANISHES. We are left with:

P(top) - P(bot) = 1/2*(1000kg/m^3)*[(120m/s)^2 - (90m/s)^2]

= 3.15 x 10^6 Pa



So the difference in pressure between top and bottom is 3.15 x 10^6 Pa .


b) We use the fundamental definition of pressure:

Pressure = Force / Area = F / A


A = area = 25 m^2

If we solve the above equation for force, we get:

F = P*A = (3.15 x 10^6 Pa ) * (25 m^2)

= 7.875*10^7 Newtons



The force on the wing is 7.875*10^7 Newtons

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