Estimate Air Speed Above Plane Wings: Bernouli Eqn

In summary, the weight of the plane can be estimated to be 81,000 N based on the given pressure difference and wing surface area. To estimate the air speed above the wings, you can use Bernoulli's equation and the given air speed below the wings. However, since 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, you can also use the given velocities to do a Bernoulli calculation. The density of still air at standard temperature and pressure can be looked up to complete the calculation.
  • #1
kbyws37
67
0
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?
 
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  • #2
kbyws37 said:
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.
 
  • #3



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!
 

Related to Estimate Air Speed Above Plane Wings: Bernouli Eqn

1. How does the Bernouli Equation apply to estimating air speed above plane wings?

The Bernouli Equation is a fundamental equation in fluid dynamics that relates the pressure, velocity, and height of a fluid at a given point. In the context of estimating air speed above plane wings, the Bernouli Equation is used to calculate the pressure difference between the top and bottom surfaces of the wing. This pressure difference creates lift, which is what keeps the plane in the air.

2. What factors affect the accuracy of estimating air speed using the Bernouli Equation?

There are several factors that can affect the accuracy of estimating air speed using the Bernouli Equation. These include the shape and size of the wing, air density, and the angle of attack (the angle at which the wing meets the oncoming air). Additionally, turbulent or uneven airflow over the wing can also impact the accuracy of the calculation.

3. Can the Bernouli Equation be used for all types of aircraft?

The Bernouli Equation can be used for most types of aircraft, including airplanes, helicopters, and gliders. However, it is important to note that the equation assumes certain conditions, such as steady airflow and a smooth wing surface. For some specialized aircraft, such as supersonic jets, other equations may be used to estimate air speed.

4. How does airspeed affect the performance of a plane?

Airspeed is a critical factor in the performance of a plane. As air speed increases, the lift generated by the wings also increases, allowing the plane to climb, turn, and maintain altitude. On the other hand, if the air speed is too low, the plane may not have enough lift to stay in the air, resulting in a stall. Therefore, accurate estimation of air speed is crucial for safe and efficient flight.

5. Are there any limitations to using the Bernouli Equation for estimating air speed?

While the Bernouli Equation is a useful tool for estimating air speed, it does have some limitations. One limitation is that it assumes incompressible flow, which means that the air is not compressed or expanded as it flows over the wing. This is not always the case, especially at high speeds. Additionally, the equation does not take into account other factors that may affect the lift of the wing, such as air viscosity and wing surface roughness.

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