Understanding how air flows around wings is fundamental to flying. The Oxford Aviation Academy manual reminds students that while these notes support EASA ATPL theory studies, they should be used alongside an approved training syllabus and do not replace hands‑on instruction.

Continuity of Flow

The continuity equation states that for an incompressible fluid such as air at low sub‑sonic speeds (Mach < 0.4), the mass flow through a streamtube remains constant. Mathematically this is expressed as A × V × ρ = constant. A narrower streamtube therefore results in higher velocity, while a wider tube reduces velocity.

By designing the wing so that the upper surface curves more than the lower surface, the streamlines are squeezed closer together on top. This reduces the local cross‑sectional area and increases velocity. The lower surface often has a flatter profile, increasing the area and reducing the velocity.

This animated graphic visualises streamlines speeding up as they pass through a constriction – a direct consequence of the continuity equation.

Bernoulli’s Theorem and Pressure

Bernoulli’s theorem links velocity to pressure. It states that along a streamline, the sum of static and dynamic pressures remains constant. When the air speeds up, dynamic pressure increases (proportional to V²) and static pressure must drop. Doubling the velocity therefore quadruples dynamic pressure and lowers static pressure by the same amount.

Generation of Lift

Lift arises because the pressure on the upper surface of the wing is lower than on the lower surface. According to Bernoulli’s theorem, faster flow over the top reduces static pressure, while slower flow underneath maintains higher pressure.

Streamlines illustrate the path of particles in the flow; they never cross. A bundle of streamlines forms a streamtube. If the streamtube narrows, velocity increases and pressure drops; if it widens, velocity decreases and pressure rises.

Compressibility Effects

For Mach numbers below about 0.4, air can be considered incompressible. At higher speeds approaching transonic flow, density changes significantly and shock waves form. The relationships in this chapter apply only to low sub‑sonic flight.

Key Takeaways

• The continuity equation ensures that mass flow (A × V × ρ) is constant.
• Reducing cross‑sectional area increases velocity; increasing area reduces velocity.
• Bernoulli’s theorem states that static pressure drops when velocity increases.
• Lift arises because velocity over the upper surface is greater than underneath.
• Streamlines and streamtubes visualise how flow accelerates and decelerates around a wing.
• Air behaves incompressibly below Mach 0.4; compressibility effects appear at higher speeds.

By mastering the continuity equation, Bernoulli’s theorem and the principles of lift, you’ll have a strong grasp of basic aerodynamic theory. This knowledge underpins more advanced topics such as drag, stalls and aircraft performance covered in later chapters.