3.1 Bernoulli's Principle, Venturi Effect & Lift Generation
Key Takeaways
- Bernoulli's Principle states that in a streamline flow of an ideal fluid, total energy remains constant, meaning an increase in fluid velocity results in a simultaneous decrease in static pressure.
- The Continuity Equation (Mass Flow Rate = \rho \cdot A \cdot V = \text{constant}) dictates that when subsonic airflow passes through a constricted passage like a Venturi tube, flow velocity must increase proportionally to the area reduction.
- Aerofoil upper camber forces air streamtubes to constrict, accelerating local flow speed and creating a localized sub-atmospheric static pressure zone (suction) on the upper surface.
- Aerodynamic lift is generated primarily by the static pressure differential between the lower high-pressure surface and upper low-pressure surface, augmented by Newton's Third Law downwash reaction.
- The aerodynamic resultant is the single net aerodynamic force on the aerofoil; it resolves into lift (perpendicular to relative airflow) and drag (parallel to it).
Fluid Dynamics & Bernoulli's Principle
Understanding how an aircraft generates lift requires a firm grasp of fluid dynamics, pressure relationships, and energy conservation. In aerodynamic theory under EASA Part-66 Module 08, air at subsonic speeds (typically below Mach 0.4) is treated as an ideal, incompressible, non-viscous fluid. This simplification allows maintenance engineers and aerodynamicists to apply classical physical laws to model airflow over lifting surfaces.
The Continuity Equation
The fundamental law governing steady fluid flow is the Continuity Equation, which enforces the conservation of mass. For a fluid moving through a closed tube or streamtube bounded by streamlines, the mass of air entering the tube per unit time must equal the mass of air exiting the tube per unit time.
Where:
- $\rho$ (rho) is the air density in kilograms per cubic metre ($\text{kg/m}^3$).
- $A$ is the cross-sectional area of the streamtube in square metres ($\text{m}^2$).
- $V$ is the airflow velocity in metres per second ($\text{m/s}$).
In subsonic flow where density $\rho$ remains practically constant, the equation simplifies to the volumetric continuity relationship:
This simple relationship proves that if a streamtube narrows ($A_2 < A_1$), the airflow velocity must increase proportionally ($V_2 > V_1$) to maintain a constant mass flow rate.
The Venturi Tube & Pressure Conservation
A Venturi tube is a classical physical demonstration device consisting of a converging duct, a narrow throat, and a diverging duct. Applying the continuity equation across a Venturi tube reveals the direct relationship between velocity and static pressure.
Total, Static, and Dynamic Pressure
According to Bernoulli's Principle (derived from the law of conservation of energy), the total pressure ($P_t$) within an ideal fluid stream remains constant along a streamline:
Where:
- $P_s$ is the static pressure, acting equally in all directions against any surface immersed in or parallel to the flow.
- $q = \frac{1}{2}\rho V^2$ is the dynamic pressure (kinetic energy per unit volume), acting solely in the direction of fluid motion.
| Location in Venturi | Cross-Sectional Area ($A$) | Airflow Velocity ($V$) | Dynamic Pressure ($q$) | Static Pressure ($P_s$) | Total Pressure ($P_t$) |
|---|---|---|---|---|---|
| Upstream Entrance | Large ($A_1$) | Low ($V_1$) | Low ($q_1$) | High ($P_{s1}$) | Constant ($P_t$) |
| Constricted Throat | Small ($A_2$) | High ($V_2$) | High ($q_2$) | Low ($P_{s2}$) | Constant ($P_t$) |
| Downstream Diffuser | Large ($A_3$) | Low ($V_3$) | Low ($q_3$) | High ($P_{s3}$) | Constant ($P_t$) |
When air enters the constricted throat ($A_2$), continuity forces velocity $V_2$ to rise. Because dynamic pressure $q$ increases as the square of velocity, $q_2$ increases sharply. To keep total pressure $P_t$ constant, static pressure $P_{s2}$ must drop below ambient atmospheric pressure. This localized drop in static pressure is known as the Venturi Effect or suction effect.
Thrust, Weight, and the Aerodynamic Resultant
In Module 08 force diagrams, the net aerodynamic force on the aerofoil is often shown as a single vector called the aerodynamic resultant (or total aerodynamic force). It is the vector sum of all pressure and shear forces, and it may be resolved into:
- Lift — component perpendicular to the relative airflow
- Drag — component parallel to the relative airflow
Together with thrust (propulsive force along the thrust line) and weight (acting through the centre of gravity), the aerodynamic resultant closes the force picture for steady flight. Exam questions may ask you to identify the aerodynamic resultant as the single force that is later split into lift and drag — not as a fifth independent force alongside lift and drag.
Lift Generation on an Aerofoil
An aircraft wing (aerofoil) acts as an half-Venturi tube moving through open air. The geometric shape of a typical cambered aerofoil creates a physical obstruction that divides incoming freestream airflow into upper and lower streamtubes.
Streamline Constriction and Pressure Distribution
- Upper Camber Effect: The curved upper surface of a cambered aerofoil restricts the cross-sectional area of upper streamtubes passing overhead. By continuity, the air must accelerate over the upper surface ($V_{\text{upper}} > V_{\infty}$). According to Bernoulli's principle, this acceleration increases upper dynamic pressure and reduces upper static pressure ($P_{\text{upper}} < P_{\infty}$), creating a distinct suction zone (sub-atmospheric static pressure).
- Lower Surface Effect: The lower surface is flatter or less cambered. Air passing underneath undergoes minimal streamtube constriction or slight deceleration ($V_{\text{lower}} \le V_{\infty}$), causing static pressure to remain near or slightly above ambient static pressure ($P_{\text{lower}} \ge P_{\infty}$).
- Net Static Pressure Differential: Integrating static pressure around the entire aerofoil surface yields a net resultant force. Because static pressure on the lower surface is significantly higher than static pressure on the upper surface, the net pressure force acts upward and slightly backward. The upward component perpendicular to the freestream airflow is Lift.
Stagnation Point & Suction Peak
At the very leading edge of the aerofoil, a unique point exists called the stagnation point. At this exact point, incoming airflow divides: air above goes over the upper surface, and air below goes under the lower surface. Right at the stagnation point:
- Local airflow velocity drops to zero ($V = 0$).
- Dynamic pressure becomes zero ($q = 0$).
- Static pressure reaches its absolute maximum value, equal to the freestream total pressure ($P_s = P_t$).
Immediately downstream of the stagnation point on the upper surface, airflow accelerates rapidly toward the point of maximum thickness/camber, reaching maximum velocity and producing a sharp negative static pressure peak known as the suction peak. On average, approximately 70% to 75% of total aerodynamic lift produced by a subsonic aerofoil is generated by upper surface suction, while only 25% to 30% is produced by lower surface positive pressure push.
Thrust, Weight, and the Aerodynamic Resultant
In Module 08 force diagrams, the net aerodynamic force on the aerofoil is often shown as a single vector called the aerodynamic resultant (or total aerodynamic force). It is the vector sum of all pressure and shear forces, and it may be resolved into:
- Lift — component perpendicular to the relative airflow
- Drag — component parallel to the relative airflow
Together with thrust (propulsive force along the thrust line) and weight (acting through the centre of gravity), the aerodynamic resultant closes the force picture for steady flight. Exam questions may ask you to identify the aerodynamic resultant as the single force that is later split into lift and drag — not as a fifth independent force alongside lift and drag.
Circulation Theory & Newton's Third Law
While Bernoulli's principle explains lift through pressure differentials, two complementary theories complete the aerodynamic model required for EASA Part-66 examinations: Circulation Theory and Newtonian Downwash.
Circulation Theory & Kutta-Joukowski Theorem
Mathematical aerodynamics models lift using the concept of circulation ($\Gamma$, gamma). In fluid dynamics, circulation represents the line integral of fluid velocity around a closed curve surrounding the aerofoil. The Kutta-Joukowski Theorem establishes that lift per unit span ($L'$) is directly proportional to air density ($\rho$), freestream velocity ($V$), and circulation ($\Gamma$):
- When an aerofoil starts moving from rest, fluid viscosity causes a starting vortex to shed from the trailing edge.
- By Kelvin's Circulation Theorem (total circulation in an ideal fluid remains zero), an equal and opposite bound vortex is generated around the aerofoil profile.
- The clockwise bound vortex superimposes over the translational airflow, accelerating air over the upper surface (adding velocities) and decelerating air on the lower surface (subtracting velocities), directly producing the Bernoulli pressure distribution.
Newton's Third Law and Downwash
Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. As airflow passes over the upper camber and leaves the trailing edge at an angle, the wing imparts a net downward momentum to the air mass. This downward deflection is called downwash.
Where $\dot{m}$ is the mass flow rate of deflected air and $w$ is the vertical downwash velocity component. The force required to push thousands of kilograms of air downward per second generates an equal and opposite upward reaction force on the wing structure.
Synthesis for EASA Part-66 Engineers
EASA Part-66 Module 08 emphasizes that Bernoulli's Principle and Newton's Laws are not mutually exclusive competing theories, but rather two alternative ways of describing the exact same physical phenomenon:
- Bernoulli's perspective: Evaluates local static pressure fields acting directly on the upper and lower skins of the wing structure.
- Newton's perspective: Evaluates global momentum changes imparted to the surrounding fluid volume as a whole.
Both models yield identical numerical values for total aerodynamic lift.
Thrust, Weight, and the Aerodynamic Resultant
In Module 08 force diagrams, the net aerodynamic force on the aerofoil is often shown as a single vector called the aerodynamic resultant (or total aerodynamic force). It is the vector sum of all pressure and shear forces, and it may be resolved into:
- Lift — component perpendicular to the relative airflow
- Drag — component parallel to the relative airflow
Together with thrust (propulsive force along the thrust line) and weight (acting through the centre of gravity), the aerodynamic resultant closes the force picture for steady flight. Exam questions may ask you to identify the aerodynamic resultant as the single force that is later split into lift and drag — not as a fifth independent force alongside lift and drag.
According to Bernoulli's Principle in subsonic, incompressible airflow, what occurs to dynamic pressure and static pressure as air flows through the narrow throat of a Venturi tube?
At the leading-edge stagnation point of an aerofoil in steady flight, what is the value of local airflow velocity and static pressure relative to freestream conditions?
Which physical mechanism accounts for the downward deflection of air behind a lifting wing, fulfilling Newton's Third Law of Motion?