The regime of aerodynamics that applies to low-speed flow fields, typically below Mach number 0.3. This type of flow can be simply approximated as having constant density throughout the flow. Because of this simplification, the pressure-velocity relation established by Daniel Bernoulli plays a vital role in determination of lift and drag over an immersed body.
The term incompressible can be somewhat confusing, as it implies that the fluid can not be compressed. In reality, any fluid can be compressed, given enough energy. This energy can be seen in the form of pressure or as an effect of a gravitational, electric, or magnetic field. However, the equations governing compressible flow involve energy continuity and are much more complicated than those of a near-constant density fluid. As a standard, a near-constant density fluid is one in which the average density is no more than 5% greater or smaller than the standard atmospheric density for a given altitude.
The most famous equation of incompressible flow is Bernoulli's equation, which relates pressure, velocity, and height.
P + ρV2 + ρgH = constant
where P is pressure, ρ is density, and H is height above some reference point.
This equation states that as the velocity of a fluid increases, the pressure will decrease, provided the height remains constant. A good example of this is a perfume bottle. Squeezing the balloon creates a jet of air, with relatively high velocity, across the top of a tube, the other end of which is submerged in a bottle of liquid perfume. The low pressure of the jet pulls fluid upward from the bottle and the liquid is carried away by the jet.
Additionally, it states that the velocity will increase as the height decreases, provided the pressure remains constant. The simplest example of this is a barrel with a hole in the side. Since the pressure at the top of the barrel is the same as the pressure of the air just outside the hole, the velocity of the jet of liquid shooting out of the hole is defined by the height difference between the hole and the liquid surface in the barrel. Since the hole is below the liquid surface, the height at the hole is lower than at the surface.
Both of these examples ignore the changes of the height of the liquid surface for simplicity.