Pressure difference accross airplane wings?

Question

An airplane flies on a level path. There is a pressure difference of 510 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 100 m2. The air moves below the wings at a speed of 80.3 m/s. Estimate (a) the weight of the plane and (b) the air speed above the wings.

Answer 1

Don't listen to the previous answer. Planes fly in great part because of Bernoulli's equation. It also allows sailboat to use the wind to point INTO the wind. If Gene was right, no sailboat would ever be capable of doing so.
Newton's third law is used only when the flaps are open at take-off and landing to increase the lift, but at the cost of much increased drag (which then is not important since speed is slow).
Of course saying, like this problem presupposes, that Bernoulli's equation is the sole answer is probably an oversimplification, but this is the case in 99.9% of physics problems where one is supposed to ignore friction and all sort of pesky problems. Then again, this is not the engineering board, it is the physic's board. So here goes:

510Pa = 510 N/m^2
The surface of each wing is 100 m^2 so total surface is 200m^2
So total lift is 200 m^2 x 510N/m^2 = 102 000 N

a) the weight of the plane is 102 000 N
b) Bernoulli's equation is

p + 1/2 ρ V² + ρgh = constant

we can assume h to be equal for the bottom and top surface of the wings so we get

p1 + 1/2ρV1² = p2 + 1/2ρV2²
(p1 - p2)+1/2ρV1² = 1/2ρV2²
2*(p1 - p2)/ρ+V1² = V2²
V2 = sqrt(2*(p1 - p2)/ρ+V1²)

You don't specify ρ which is air density so I will assume sea level, 20 degree celsius dry air = 1.2kg/m³

V2 = sqrt(2*510kg.m/s²/m²/1.2kg/m³ + (80.3m/s)²)
V2 = 85.4m/s

Answer 2

alright, so if the plane is not moving up or down, then the forces acting on the plane have to balance. Pressure is just a force divided by an area, so if you want to find the total force, you multiply by the area.

Now, on the top of the wing, there is 510Pa less than on the bottom. if you convert this value to Newtons by multiplying by the area of the wing surfaces (2 wings), you get 510N/m^2 * 200m^2 = 102000 N.

So there is 102kN more force acting on the bottom of the plane than on the top. If you were to balance all the forces, then you would see the pressure on the top of the plane added to the weight of the plane is equal to the pressure on the bottom. So the difference in pressure is the weight of the plane. The plane weighs 102kN. If you have to find it in kg, then divide by 9.81 to get 10397 kg.

To find the speed, you have to know Bernoulli's law, which basically states that the pressure + 1/2 (density)V^2 is equal throughout.

So if you use Bernoulli's law:
Pt + 1/2 d Vt^2 = Pb + 1/2 d Vb^2
1/2 d (Vt^2 - Vb^2) = Pb - Pt = 510
(Vt^2 - 80.3^2) = 510 * 2 / d

I will use density of air at sea level = 1.226 kg/m^3

So then Vt^2 = 831.97 + 80.3^2
Vt = 85.32 m/s


Hope that helped

Answer 3

rigidity distinction facilitates help weight. rigidity = rigidity distinction x area = mg so m = PA/g = 525 x 112/9.8 around 5000 kg Use Bernoulli's theorem P +rhogh + a million.2rho v^2 is persevering with P+525+a million/2rho80^2 = P +a million/2rhov^2 resolve for v rho is density of air in kg/m^3 rho is around a million.290 kg/m^3 i think of. you could have been given the fee, because of fact it relies upon on top and temperature

Answer 4

Aha -- the old bad science supposition that planes fly because of a differential pressure between the top and bottom of the wing, Have your teacher read this and he/she will see that the answer for this problem is wrong no matter what. A plane gets lift because of Newton's third law. The wing forces air down off the trailing edge creating the lift.

http://home.comcast.net/~clipper-108/lift.htm