# Joukowsky Equation

The Joukowsky equation is a mathematical equation that describes the relationship between the flow of a fluid around a circular cylinder and the resulting lift and drag forces acting on the cylinder. It is used extensively in the field of fluid dynamics and is particularly useful for predicting the performance of aircraft wings and other aerodynamic structures.

The Joukowsky equation can be written as follows:

Z = f(z) = z + a^2/z

where:

Z is the complex potential of the flow field z is the complex coordinate in the plane a is the radius of the circular cylinder

Here’s an example to illustrate how the Joukowsky equation can be used:

Suppose we have a circular cylinder of radius 1 meter immersed in a fluid with a velocity of 10 meters per second. We want to calculate the lift and drag forces acting on the cylinder.

Using the Joukowsky equation, we can first transform the flow field around the cylinder to a flow field around a flat plate with a rounded leading edge. This transformation allows us to use the well-known lift and drag coefficients for a flat plate to calculate the lift and drag forces on the cylinder.

Let’s assume that the angle of attack of the cylinder is 5 degrees, and the lift and drag coefficients for a flat plate at this angle of attack are 0.75 and 0.05, respectively.

Using these values, we can calculate the lift and drag forces on the cylinder as follows:

Lift = 0.75 * (0.5 * 1 * 10^2) = 37.5 N Drag = 0.05 * (0.5 * 1 * 10^2) = 2.5 N

So the lift force acting on the cylinder is 37.5 Newtons, and the drag force is 2.5 Newtons.