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.

Answer 1

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