Question

Find the pressure difference on an airplane wing if air flows over the upper surface with a speed of 115 m/s. If the area of the wing is 32m^2, what is the upward force exerted on the wing?

No idea how to approach this as we dont have the air speed below the wing.

Answer 1

please check your question again .. air speed below the wing should be given

if it is 105m/s given than this is the solution.

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 = 115 m/s

v(bot) = velocity of air on bottom of wing = 105 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)*[(115m/s)^2 - (105m/s)^2]

= 1.1 x 10^6 Pa

= 1,100 kPa

So the difference in pressure between top and bottom is 1100 kPa.


b) We use the fundamental definition of pressure:

Pressure = Force / Area = F / A


A = area = 32 m^2

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

F = P*A = (1.1x10^6 Pa) * (32 m^2)

= 3.52 x 10^7 Newtons

= 35200 kN

The force on the wing is 35,200 kN.