Fundamentals of Aerodynamics: Atmosphere, Airflow, Bernoulli and Continuity, Two-Dimensional Flow
This domain tests whether you can turn the standard atmosphere and the conservation laws into numbers the aeroplane actually senses: density, dynamic pressure and the pressure field around a two-dimensional section. Expect ISA values, simple continuity and Bernoulli calculations, and conceptual items on streamline curvature and stagnation.
Standard atmosphere
- ISA sea level: 1013.25 hPa, 15 °C, density 1.225 kg/m³, speed of sound 661.5 kt (340.3 m/s).
- Troposphere lapse rate 1.98 °C per 1000 ft (6.5 °C/km) up to 11 km; the tropopause is 216.65 K (−56.5 °C) and the layer above is isothermal to 20 km.
- Pressure halves near 18,000 ft, density near 22,000 ft; for a fixed IAS, TAS grows with altitude.
- Dynamic pressure q = ½ρV²; EAS = TAS × √(ρ/ρ0).
Bernoulli and continuity
- Along a streamline in steady, incompressible, frictionless flow: p + ½ρV² + ρgh = constant. Static plus dynamic equals total pressure, and in the free stream total pressure is constant, so where local velocity rises, static pressure falls.
- Continuity: ρAV = constant, which for incompressible flow becomes AV = constant. Halving the area doubles the velocity and quadruples dynamic pressure.
Two-dimensional flow
- Section data assumes infinite span, so there are no tip vortices; CL and CD against alpha come from this idealisation.
- Streamline curvature: the convex upper surface forces the flow to curve, and the pressure gradient supplies the centripetal force, so pressure must fall towards the surface. Lift is the reaction to downward momentum given to the air, not to equal transit times.
- The stagnation point sits just below the leading edge at positive alpha; the Kutta condition holds the rear stagnation point at the trailing edge, fixing the circulation and hence the lift.
Worked example
A duct narrows from 0.20 m² to 0.10 m², upstream velocity 40 m/s, ρ = 1.225 kg/m³. Continuity gives V2 = 40 × 0.20/0.10 = 80 m/s. Then q1 = 0.5 × 1.225 × 1600 = 980 Pa and q2 = 0.5 × 1.225 × 6400 = 3920 Pa, so static pressure falls by 2940 Pa. Note that the drop follows from continuity plus Bernoulli, not from a separate suction effect.
Traps
- Confusing static and total pressure: the pitot tube senses total pressure, the static port senses static, and their difference is q.
- Using the simple Bernoulli form at high altitude or high Mach, where density changes along the streamline.
- Quoting equal transit times: it gives the wrong relative velocity and predicts no lift at zero incidence.
- Forgetting that the tropopause temperature is −56.5 °C, and that the speed of sound depends only on temperature.