Estimate Air Speed Above Plane Wings: Bernouli Eqn

[kbyws37]

An airplane flies on a level path. There is a pressure difference of 540 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 150 m^2. The air moves below the wings at a speed of 81.0 m/s.
(a) Estimate the weight of the plane.
(b) Estimate the air speed above the wings.



I figured out (a) weight of plane.
(150 m^2)(540 Pa) = 81,000 N

I am having trouble figuring out the air speed.
I am guessing that I have to use Bernouli's equation b/c there are two different points (upper and lower surfaces).
When using Bernouli's equation, don't I need density ? How can I find density if no mass is given?

 

[OlderDan]

An airplane flies on a level path. There is a pressure difference of 540 Pa between the lower and upper surfaces of the wings. The area of each wing surface is about 150 m^2. The air moves below the wings at a speed of 81.0 m/s.
(a) Estimate the weight of the plane.
(b) Estimate the air speed above the wings.



I figured out (a) weight of plane.
(150 m^2)(540 Pa) = 81,000 N

I am having trouble figuring out the air speed.
I am guessing that I have to use Bernouli's equation b/c there are two different points (upper and lower surfaces).
When using Bernouli's equation, don't I need density ? How can I find density if no mass is given?

You can look up the density of still air at standard temperature and pressure.

You might want to look at this link

http://www.grc.nasa.gov/WWW/K-12/airplane/right2.html

and hit the next button at the bottom until you get to the end. The Bernoulli approach is not wrong, but the assumption that the air over the top of the wing arrives at the same time as the air going under the wing is not correct. Since you have velocities given above and below (which in fact are not nearly constant over the top surface, so take it to be an average and use it) you can do a Bernoulli calculation.

 

[kyle8921]

I would first like to commend you for your efforts in solving the problem and identifying the need to use Bernoulli's equation. You are correct in thinking that we need density to solve for air speed using Bernoulli's equation. However, we can use the ideal gas law to calculate the density of air at a given pressure and temperature.

To estimate the air speed above the wings, we can rearrange Bernoulli's equation to solve for velocity:

v = √(2ΔP/ρ)

Where v is the velocity, ΔP is the pressure difference, and ρ is the density of air.

Since we know the pressure difference (ΔP = 540 Pa) and the area of the wings (150 m^2), we can calculate the force acting on the wings:

F = ΔP * A = 540 Pa * 150 m^2 = 81,000 N

Using the weight of the plane (81,000 N) and the force acting on the wings, we can calculate the density of air:

ρ = F/m = 81,000 N / 9.8 m/s^2 = 8,265 kg/m^3

Now, we can plug in the values for pressure difference and density into the equation to solve for air speed:

v = √(2*540 Pa/8,265 kg/m^3) = 17.5 m/s

Therefore, the air speed above the wings is approximately 17.5 m/s.

I hope this helps and keep up the good work!