# Aerodynamic Lift/Kutta-Zhukovsky theorem

Nikitin
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)?

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

I believe my book used Kutta-Zhukovsky's theorem,
$$L = \Gamma \cdot \rho U_{\infty}$$
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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## Answers and Replies

2021 Award
What is the book's author, title, edition and page numbers.

Staff Emeritus
Homework Helper
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.

1 person
Nikitin
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?

Staff Emeritus
Homework Helper
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.

1 person
Nikitin
OK thanks