Understanding Lift Force and the Bernoulli Equation in Small Aircraft

In summary: P1-P2=1/2ρ(v22-v12) You have P1-P2=(1/2)ρ(v22-v12) .Do the subscripts, 1 & 2 refer to the bottom surface of the wing and the top surface of the wing respectively?How much lift force is needed? What part of the plane generates the lift? How are force, area, and pressure all related?Going with the idealized assumptions about lift for this problem, you can assume the pressure below the wing is some ambient pressure P1 (for pressure below), and above the wing it's P2. The the difference in pressure
  • #1
Donna14
27
0

Homework Statement


See attachment

Homework Equations



Maybe lift force = ClρAv2

A=area
Cl= lift coefficient= 0.3
ρ= air density
V=air speed but don't know which one it represents... Under or below wing or average?

And the bernoulli equation seems to be needed as well...

The Attempt at a Solution



To keep the plane just in the air the lift force must be equal to the gravitational force I guess. But I'm not sure how to continue from there...
 

Attachments

  • image.jpg
    image.jpg
    36.1 KB · Views: 399
Physics news on Phys.org
  • #2
Donna14 said:
V=air speed but don't know which one it represents... Under or below wing or average?
...
I think the diagram shows that explicitly.

Donna14 said:
And the bernoulli equation seems to be needed as well...
...
Yes, can you try and apply it here?
 
  • #3
But I am stuck on how to continue... Can you please help me a bit?
 
  • #4
Why don't you start by stating Bernoulli's equation and maybe try and substitute some values into it?
 
Last edited:
  • #5
P1-p2=1/2ρ(v22-v12)

But I don't know the pressure and I don't understand what to do with drag and lift force?
And do I have to use the given engine power?

Sorry this is completely new to me...
 
Last edited:
  • #6
Donna14 said:
P1-P2=1/2ρ(v22-v12)

But I don't know the pressure and I don't understand what to do with drag and lift force?
And do I have to use the given engine power?

Sorry this is completely new to me...
Forget that equation for lift force. I assume there are more parts to this problem, which you didn't show us. Some of the given information may be needed for those -- or may just be extra information.


You have P1-P2=(1/2)ρ(v22-v12) .

Do the subscripts, 1 & 2 refer to the bottom surface of the wing and the top surface of the wing respectively?

How much lift force is needed?

What part of the plane generates the lift?

How are force, area, and pressure all related?
 
  • #7
Going with the idealized assumptions about lift for this problem, you can assume the pressure below the wing is some ambient pressure P1 (for pressure below), and above the wing it's P2. The the difference in pressure (P1 - P2) times the wing area will equal the weight of the aircraft.
 
  • Like
Likes 1 person
  • #8
But P x A= force isn't it? So you say (Pbelow-Pabove)xA=mass? Or mg? And I haven't got any other info about P...

I have substituted (Pbelow-Pabove) for mg/A and my result seems to be correct now. But I am not sure why I can say that the difference of P is this...
 
Last edited:
  • #9
Maybe show your work explicitly but the difference in air pressure is what generates lift.
 

Related to Understanding Lift Force and the Bernoulli Equation in Small Aircraft

1. What is the Bernoulli principle and how does it apply to small aircraft?

The Bernoulli principle states that as the speed of a fluid (such as air) increases, its pressure decreases. This principle applies to small aircraft because as the air flows over the wings, it increases in speed, creating a lower pressure area above the wing and a higher pressure area below the wing. This pressure difference creates lift, which allows the aircraft to fly.

2. How does the shape of an aircraft's wings affect the application of the Bernoulli principle?

The shape of an aircraft's wings, specifically the curvature and angle of the wing, affects how the Bernoulli principle is applied. A curved or cambered wing creates a longer path for the air to travel over the top surface, resulting in a lower pressure and more lift. The angle of the wing, also known as the angle of attack, affects the speed and direction of the air flowing over the wing, further influencing the application of the Bernoulli principle.

3. Can the Bernoulli principle be used to explain the lift of all flying objects?

No, the Bernoulli principle is only one factor in the lift of flying objects. Other factors such as the angle of attack, air density, and weight also play a role in determining lift. Additionally, some flying objects, such as helicopters and rockets, use different principles to generate lift.

4. How does airspeed affect the application of the Bernoulli principle on a small aircraft?

The Bernoulli principle is directly related to airspeed. As the airspeed of the aircraft increases, the pressure difference between the top and bottom of the wing also increases, resulting in more lift. However, there is a maximum airspeed at which the principle can be applied before the air becomes too turbulent and the wing stalls, causing a decrease in lift.

5. Are there any limitations to the Bernoulli principle in the context of small aircraft?

While the Bernoulli principle is an important factor in the lift of small aircraft, it is not the only principle at play. As mentioned before, other factors such as air density and weight also affect lift. Additionally, the Bernoulli principle is more applicable to steady, subsonic flight and may not accurately explain lift in supersonic or highly maneuverable aircraft. It is also important to note that the Bernoulli principle does not explain the lift of inverted flight, as the air is flowing over the bottom of the wing instead of the top.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
957
  • Classical Physics
Replies
30
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
4K
Replies
13
Views
157
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
4K
Back
Top