Lift (force) - Description of Lift On An Airfoil - Bernoulli's Principle: Lift, Pressure, and Speed - Conservation of Mass

Conservation of Mass

If one takes the experimentally observed flow around an airfoil as a starting point, then lift can be explained in terms of pressures using Bernoulli's principle and conservation of mass.

Returning to the picture from the previous section, the flow approaching an airfoil can be divided into streamtubes, which are defined based on the area between two streamlines. By definition, fluid never crosses a streamline in a steady flow. Assuming that the air is incompressible, the rate of flow (e.g. liters or gallons per minute) must be constant within each streamtube since matter is not created or destroyed. If a streamtube becomes narrower, the flow speed must increase in the narrower region to maintain the constant flow rate. This idea is called "conservation of mass", and for incompressible flow mass is conserved within each streamtube.

The picture shows that the upper stream tubes constrict as they flow up and around the airfoil. Conservation of mass says that the flow speed must increase as the stream tube area decreases. Similarly, the lower stream tubes expand and the flow slows down.

From Bernoulli's principle, the pressure on the upper surface where the flow is moving faster is lower than the pressure on the lower surface where it is moving slower. The pressure difference thus creates a net aerodynamic force, pointing upward and downstream to the flow direction. The component of the force perpendicular to the free stream is lift; the component parallel to the freestream is drag. In conjunction with this force by the air on the airfoil, the airfoil imparts an equal-and-opposite force on the surrounding air that creates the downwash, in accordance with Newton's third law. Measuring the momentum transferred to the downwash is another way to determine the amount of lift on the airfoil.