Calculating lift using bernoulli's equation

In summary, the conversation discusses the use of Bernoulli's principle to calculate the lift on a wing based on the difference in pressure between the top and bottom surfaces. The equations used are P1 + 1/2rv1^2= P2 + 1/2 r v2^2 and F=P/A. The approach to solving the problem involves finding the difference in pressure and then using it to calculate the "Bernoulli force," which is responsible for a small percentage of total lift force on an airplane.
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Homework Statement



What is the lift (in Newtons) due to Bernoulli's principle on a wing of area...m^2 if the air passes over the top and bottom surfaces at speeds of ...m/sand ...m/s, respectively? I've given the values but I just want to know if I'm doing the problem right conceptually.

Homework Equations



P1 + 1/2rv1^2= P2 + 1/2 r v2^2
F=P/A

The Attempt at a Solution



Hello, can someone help me with the approach to this problem?
I tried solving for P2-P1 in Bernoulli's and then using that as P in F=P/A and solving for F. I realize that the pressure on the bottom has to be greater than the pressure on the top to create lift so that's why I did P2-P1.
 
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  • #2
Yes, you are going about solving the problem correctly. It doesn't really matter whether you subtract P2 from P1 or vise versa. You just need the difference in pressure to find the "bernoulli force" and then you just say "it's upward."

By the way, just do the problem as they ask you, and then let yourself know that the "Bernoulli force" is way over-hyped, and does not account for any more than 6% of total lift force on an airplane.
 
  • #3




Hello, your approach is correct. To calculate the lift on a wing using Bernoulli's equation, we need to first find the pressure difference between the top and bottom surfaces of the wing. This pressure difference is caused by the difference in air speeds over the top and bottom surfaces. As you correctly mentioned, the pressure on the bottom surface needs to be greater than the pressure on the top surface in order to create lift.

Once you have found the pressure difference, you can use the formula F = P/A to calculate the lift force. P represents the pressure difference and A is the area of the wing. This will give you the lift force in Newtons.

It is important to note that Bernoulli's equation is just one factor in determining lift on a wing. Other factors such as angle of attack, air density, and wing shape also play a role. But using Bernoulli's equation is a good starting point for understanding the basic principles of lift.

I hope this helps and good luck with your calculations!
 

1. How is Bernoulli's equation used to calculate lift?

Bernoulli's equation is a fundamental principle in fluid dynamics that relates the velocity of a fluid to its pressure and density. In the context of calculating lift, Bernoulli's equation is used to determine the difference in pressure between the top and bottom surfaces of an airfoil, which creates a net force in the upward direction.

2. What is the significance of the airfoil shape in calculating lift?

The shape of an airfoil is crucial in calculating lift because it determines the velocity and pressure distribution of the airflow around it. The curved upper surface of an airfoil creates a longer path for the air to travel, resulting in a lower pressure and higher velocity. This difference in pressure creates a net force in the upward direction, which is the lift force.

3. How does the angle of attack affect lift calculation using Bernoulli's equation?

The angle of attack refers to the angle between the airfoil and the direction of the oncoming airflow. As the angle of attack increases, the air must travel a greater distance over the curved upper surface of the airfoil, resulting in a larger difference in pressure and a higher lift force. However, if the angle of attack becomes too large, the airflow may separate from the surface of the airfoil, reducing lift and potentially causing a stall.

4. Are there any limitations to using Bernoulli's equation for calculating lift?

While Bernoulli's equation is a useful tool for understanding lift, it does have some limitations. For example, it assumes that the air is incompressible and inviscid, meaning it has no viscosity or resistance to flow. In reality, air is compressible and has some viscosity, so Bernoulli's equation is only an approximation of the actual lift forces at play.

5. Can Bernoulli's equation be used to calculate lift on objects other than airfoils?

Yes, Bernoulli's equation can be applied to any object in a fluid flow, not just airfoils. However, the shape and orientation of the object will determine the magnitude and direction of the lift force. For example, an airplane wing is designed specifically to create lift, while a flat plate may experience a lift force in a different direction depending on the angle of attack.

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