Kutta-Joukowski Cylinder Circulation Lift
Circulation makes pressure asymmetric around a cylinder and creates lift whose sign can be checked by integration.
By Riano · Published · Updated · Report a correction
Kutta-Joukowski Cylinder Circulation Lift
Inviscid incompressible potential flow around a cylinder reveals fundamental fluid dynamics principles. When a uniform freestream interacts with a cylinder, the superposition of a circulation term induces an asymmetric velocity field, leading to a pressure difference and the generation of lift.
worked-example
Consider a cylinder of radius R = 1 in a freestream of speed U = 1 with a circulation over two pi, g = 1. We want to find the lift per length.
- Identify the parameters: U = 1, R = 1, g = 1, giving actual circulation Γ = 2πg = 2π.
- We assume fluid density ρ = 1.
- Apply the Kutta-Joukowski theorem to find lift per unit length: Fy = -ρUΓ.
- Calculate lift: Fy = -1 × 1 × 2π ≈ -6.283185307.
- Because our circulation is positive (counterclockwise) and freestream is positive along the x-axis, the tangential velocity magnitude is higher on the top and lower on the bottom. Using the sign convention that positive lift is directed upwards, the resulting vertical force is negative, meaning it is directed downwards relative to our standard y-axis definition in the visualization.
experiment
You can interact with this model to see the streamlines and resulting lift for various freestream velocities and circulation values. Visit the interactive module here:
https://riano.app/module/kutta-joukowski-cylinder-circulation-lift
- Set the Stream speed to 1 and the Cylinder radius to 1.
- Change the Circulation over two pi to 1. Observe the closed streamlines starting to emerge and the calculated Lift per length becoming negative.
- Adjust the Circulation over two pi to -1. Notice that the lift per length flips sign and becomes positive.
- Change the Surface degrees to see the tangential velocity vector evaluated at different points on the cylinder surface.
limitations
This module uses ideal potential flow theory, which assumes the fluid is inviscid (zero viscosity) and incompressible. In real fluids, boundary layers form and flow separation occurs, producing a wake and non-zero drag. Real-world cylinders rotating in a viscous fluid experience the Magnus effect, where lift is generated, but it differs from this idealized Kutta-Joukowski calculation because viscous effects and drag play a major role.
references
The potential flow theory and Kutta-Joukowski lift are fundamental concepts in aerodynamics and fluid mechanics.
- NASA Glenn Research Center: Foil Theory. Provides the mathematical background for potential flow, superposition of sources and sinks, and the generation of lift by circulation.
Experience it interactively
Adjust parameters, observe in real time, and build deep intuition with Riano’s interactive Kutta-Joukowski Cylinder Circulation Lift module.
Try Kutta-Joukowski Cylinder Circulation Lift on Riano →