Aerodynamic Lift/Kutta-Zhukovsky theorem

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In summary, the conversation discusses the formulas for lift and drag, which are expressed in terms of fluid density, velocity, and characteristic area. The concept of non-dimensionalization is mentioned, which allows for testing of scale models. The characteristic area is defined as the projected area normal to the flow for bluff bodies and the planform area for lifting surfaces. The velocity 'U' refers to the undisturbed fluid velocity.
  • #1
Nikitin
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Hello! My fluid dynamics book doesn't bother explaining this properly, so can somebody please give a short, intuitive (if possible...) explanation to the following 3 formulas concerning lift and drag? And are they only valid for circular, rotating cylinders (magnus effect)?

[tex] L = C_L \cdot \frac{1}{2} \rho U^2 \cdot A[/tex]
[tex] D = C_D \cdot \frac{1}{2} \rho U^2 \cdot A[/tex]
[tex] C_L = \pi a \omega / U_{\infty}[/tex]

I believe my book used Kutta-Zhukovsky's theorem,
[tex] L = \Gamma \cdot \rho U_{\infty} [/tex]
to get the first. The second one I am very confused about, because according to inviscid theory drag is non-existant.
 
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What is the book's author, title, edition and page numbers.
 
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The first two formulas for L and D are standard. The express the values of the actual lift and drag force in terms of the density of the fluid, the velocity of the fluid, and a characteristic area, usually the projected area of the body normal to the fluid flow. When testing various bodies to determine their lift and drag, the actual force values are non-dimensionalized to calculate the lift and drag coefficients, CL and CD, respectively. This is a useful concept, because it allows one to test scale models instead of full size objects. By scaling the fluid velocity using the Reynolds No., one can use the CL and CD values to predict the lift and drag force on a full size aircraft, for instance, using data obtained from a wind tunnel test on a small scale model aircraft.
 
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Thanks for the reply.

2 questions:

1) What exactly do you mean by "characteristic area"? What's the characteristic area of an aerofoil and, say, a sphere?
2) "U" is the velocity of the fluid parallel to the surface of the object, right?
 
  • #5
Nikitin said:
Thanks for the reply.

2 questions:

1) What exactly do you mean by "characteristic area"? What's the characteristic area of an aerofoil and, say, a sphere?
2) "U" is the velocity of the fluid parallel to the surface of the object, right?


1. For bluff bodies, like spheres or bodies of revolution, it usually means the projected area normal to the flow. For lifting surfaces, like plates or wings, the area is usually the planform area, or the area as viewed looking down on the plate or wing.

2. 'U' is the undisturbed fluid velocity.
 
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OK thanks
 

1. What is aerodynamic lift?

Aerodynamic lift is the force that is generated by the flow of air around an object, such as an airplane wing, that allows it to stay airborne. It is perpendicular to the direction of the airflow and is essential for flight.

2. How is aerodynamic lift created?

Aerodynamic lift is created by the difference in air pressure between the upper and lower surfaces of an object, such as an airplane wing. As air flows over the curved upper surface of the wing, it has to travel a greater distance, causing a decrease in pressure. This creates a pressure gradient, and the higher pressure underneath the wing pushes it up, generating lift.

3. What is the Kutta-Zhukovsky theorem?

The Kutta-Zhukovsky theorem is a fundamental principle in aerodynamics that explains the relationship between the shape of an object and the amount of lift it can generate. It states that the lift produced by an object is equal to the product of its circulation (the tendency of air to flow around the object) and the free-stream velocity of the fluid.

4. How does the Kutta-Zhukovsky theorem relate to the shape of an airplane wing?

The shape of an airplane wing is designed to take advantage of the Kutta-Zhukovsky theorem. By curving the upper surface of the wing, the air has to travel a greater distance, creating a pressure gradient and generating lift. This lift is then adjusted by changing the angle of the wing, allowing the airplane to control its altitude and direction.

5. What are some real-world applications of the Kutta-Zhukovsky theorem?

The Kutta-Zhukovsky theorem has numerous real-world applications, including airplane design, sailboat design, and wind turbine design. It is also used in the design of sports equipment, such as golf balls and tennis rackets, to optimize aerodynamics and improve performance. Understanding this theorem is crucial for creating efficient and effective flying and sailing machines.

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