PHAK Ch. 4 · study note

Bernoulli’s principle of differential pressure

In the Pilot’s Handbook of Aeronautical Knowledge, lift is introduced with Newton’s laws of motion and Bernoulli’s principle of differential pressure. This note is the PHAK pilot-level story—what you need for the knowledge test and clear mental models. For circulation, Kutta–Joukowski, and a fuller theory of lift, use the Lift Theory Lab.

The principle (one sentence)

As the velocity of a moving fluid (liquid or gas) increases, the pressure within the fluid decreases. (PHAK Ch. 4)

“Pressure” here means static pressure—the pressure you would feel if moving with the fluid. Speed up the flow, static pressure drops; slow it down, static pressure rises (along a streamline, under the idealizations Bernoulli assumes).

Diagram: slower flow has higher static pressure; faster flow has lower static pressure — **Figure 1.** Core idea: along a streamline, higher speed pairs with lower static pressure (idealized Bernoulli picture).

The venturi: Bernoulli in a tube

PHAK’s practical demonstration is the venturi tube: inlet → narrow throat → outlet (same diameter as the inlet).

Venturi tube diagram showing higher speed and lower pressure at the throat — **Figure 2.** Venturi: mass flow is conserved, so air speeds up in the constriction and static pressure falls—then recovers as the tube widens again. (Educational schematic inspired by the PHAK venturi discussion.)

Mass of air entering must equal mass leaving (continuity).
At the constriction, speed increases so the same mass can pass in the same time.
When speed increases, static pressure decreases.
Downstream of the throat, flow slows and pressure recovers.

Same physics shows up in a float carburetor venturi: low pressure at the throat helps meter fuel into the airstream (and contributes to carburetor icing when moist air cools in that low-pressure region).

Application to a wing

An airfoil is shaped so that, at a positive angle of attack (and/or with camber), air moving over the upper surface is forced to move faster than air along the lower surface. By Bernoulli, higher speed above → lower static pressure above the wing.

Cambered airfoil with faster upper streamlines, low pressure above, higher pressure below, and net lift — **Figure 3.** Wing section (schematic): faster upper flow (cyan) → suction on top; lower surface often at higher pressure (orange). Net force includes **lift**. PHAK: do not freeze a fixed “% from top vs bottom.”

That reduced pressure on top is a component of total lift. Under the wing, flow is often slower in places (especially as angle of attack rises), so pressure can be higher than free stream—another contribution to lift.

PHAK is careful: it is neither accurate nor useful to assign fixed percentages like “70% from the top, 30% from the bottom.” Those shares change with design and flight condition.

Airfoil vocabulary (from the same chapter)

Term	Meaning
Camber	Curvature of upper and lower surfaces (upper often more pronounced)
Chord line	Straight line from leading edge to trailing edge
Mean camber line	Line equidistant from upper and lower surfaces
Leading / trailing edge	Rounded front; tapered rear
Angle of attack (AOA)	Angle between chord line and relative wind
Center of pressure (CP)	Average location of the pressure distribution; moves with AOA

Bernoulli is not the whole story (PHAK says so)

Lift is more complex than a simple pressure difference alone.
Symmetrical airfoils (same upper and lower shape) still produce lift when flown at AOA—so “longer path on top” is not a complete explanation.
Newton’s third law also operates: the wing imparts downward momentum to the air (downwash); the reaction is an upward force on the wing.
PHAK: both Bernoulli’s principle and Newton’s laws are in operation whenever lift is generated.

Two panels: Bernoulli pressure picture and Newton downwash reaction picture of the same lift — **Figure 4.** Same physics, two bookkeeping systems: pressure field (Bernoulli) and momentum change / downwash (Newton). PHAK treats them as working together—not as rivals.

Newton side-by-side (same PHAK section family)

Law	Pilot-relevant picture
1st	Body at rest stays at rest / uniform motion until forces act
2nd	Force relates to mass and acceleration of the air (and airplane)
3rd	Action–reaction: prop pushes air back → air pushes airplane forward; wing pushes air down → air pushes wing up

Knowledge-test style takeaway

Faster flow over the curved upper surface → lower pressure on top of the wing (MIT 16.687 / PHAK-aligned practice framing). Keep the caveats above so you don’t oversell a cartoon.

Practice deeper

Open Lift Theory Lab → (interactive venturi, airfoil C_p, Newton, circulation / Kutta–Joukowski + myths)

Primary sources

FAA PHAK FAA-H-8083-25C Ch. 4 — Bernoulli’s Principle of Differential Pressure; airfoil design; low/high pressure; Newton’s laws
PHAK systems chapters — carburetor venturi (same principle)
MIT OCW 16.687 — lift / four forces practice emphasis

Figures on this page are original educational schematics (SVG), not scans of FAA handbook art.

← All notes · Density altitude · Home