3.4 Pressure, Buoyancy & Barometers

Pressure, Buoyancy & Barometers

Pressure links force and area in solids and fluids and is central to hydraulics, fuel systems, pneumatics, and the atmosphere that instruments measure. This section covers p = F/A, hydrostatic pressure, Archimedes’ buoyancy, and barometers, always with SI units and aviation context.

Pressure = Force / Area

Pressure is the normal force acting per unit area:

p = F / A

SI unit: pascal (Pa) = 1 N/m². Larger practical units include kilopascal (kPa), megapascal (MPa), and the non-SI but common bar (1 bar = 10⁵ Pa ≈ atmospheric order) and psi in some manuals (convert carefully for exams that expect SI).

The same force on a smaller area produces higher pressure. That is why a sharp rivet set concentrates force, why tyre contact patches matter for runway loading, and why a hydraulic actuator piston area multiplies force: F = p × A.

Worked example — hydraulic jack. System pressure is 10 MPa (10 × 10⁶ Pa). Piston area is 20 cm² = 20 × 10⁻⁴ m² = 0.002 m².

F = p A = (10 × 10⁶) × 0.002 = 20 000 N

Halving the area halves the force at the same pressure; doubling pressure doubles force on the same piston — the essence of hydraulic mechanical advantage when a small input piston drives a large output piston (Pascal’s principle).

Fluid Pressure and Depth

In a static incompressible fluid (good model for liquid fuel or hydraulic oil at rest), pressure increases with depth:

p = p₀ + ρ g h

where p₀ is pressure at the free surface, ρ is density (kg/m³), g ≈ 9.81 m/s², and h is depth (m). Gauge pressure at depth h below a free surface open to atmosphere is simply ρ g h if p₀ is atmospheric and you report gauge values.

Worked example. Density of water ≈ 1000 kg/m³. At h = 5 m:

p_gauge = 1000 × 9.81 × 5 ≈ 49 050 Pa ≈ 49 kPa

Pressure in a static fluid acts equally in all directions at a point and is perpendicular to any solid surface. That is why tank walls and fuel cells need structural support against outward pressure, and why a hole in a pressurised line sprays fluid normal to the opening.

Absolute, Gauge, and Differential Pressure

• Absolute pressure — measured from a perfect vacuum (used in some engine and scientific contexts).
• Gauge pressure — measured relative to local atmospheric pressure (most hydraulic gauges, tyre gauges).
• Differential pressure — difference between two points (pitot minus static for airspeed; cabin delta-P for pressurisation).

Standard sea-level atmospheric pressure is approximately 101.325 kPa (1013.25 hPa / mbar), often rounded to 101.3 kPa or 14.7 psi. Altimeters are calibrated against a standard atmosphere model; setting QNH/QFE adjusts the reference so indicated altitude matches the chosen datum.

Pascal’s Principle (Hydraulics Preview)

Pascal’s principle: pressure applied to an enclosed incompressible fluid is transmitted undiminished throughout the fluid. A force F₁ on area A₁ creates p = F₁/A₁; the same p on area A₂ yields F₂ = p A₂ = F₁ (A₂/A₁). Aircraft hydraulic systems use this to move heavy landing gear, flaps, and flight controls with modest pump pressure and appropriately sized actuators. Leaks reduce available pressure and force; air in the system is compressible and destroys the “incompressible” assumption, causing spongy response.

Archimedes’ Principle and Buoyancy

Archimedes’ principle: a body wholly or partially immersed in a fluid experiences an upward buoyant force equal to the weight of fluid displaced.

F_b = ρ_fluid × V_displaced × g

• If F_b > weight of the body → net upward force (object rises / floats higher).
• If F_b < weight → object sinks.
• If F_b = weight → neutral buoyancy (floats at constant depth).

For floating, the submerged volume adjusts until weight of displaced fluid equals body weight. Average density of the floating object equals density of the fluid times the submerged fraction.

Worked example. A sealed equipment case of volume 0.02 m³ and mass 8 kg is submerged in fresh water (ρ = 1000 kg/m³).

Weight = 8 × 9.81 = 78.5 N
Buoyant force if fully submerged = 1000 × 0.02 × 9.81 = 196.2 N
Net force upward ≈ 117.7 N — the case would accelerate upward if released (it floats).

Aviation links: buoyancy of fuel in tanks affects gauging and structural loads; helium or hot air buoyancy is the flight principle of balloons and airships; seaplane hulls and floats displace water to support weight on the surface. Density altitude (atmosphere) is a related idea for aerodynamics but uses air density, not liquid buoyancy — keep the concepts separate.

Barometers and Atmospheric Pressure Measurement

A barometer measures atmospheric pressure.

Mercury barometer

A glass tube closed at one end is filled with mercury and inverted into a mercury reservoir. The mercury column falls until the weight of the column balances atmospheric pressure on the reservoir surface. At standard conditions the column height is about 760 mm of mercury (mmHg). Pressure follows p = ρ g h with ρ_mercury ≈ 13 600 kg/m³:

p ≈ 13 600 × 9.81 × 0.760 ≈ 101 300 Pa

Mercury barometers are laboratory references; they are fragile and toxic for aircraft use but explain the definition of historical pressure units (mmHg, torr).

Aneroid barometer

An aneroid uses a sealed, partially evacuated flexible capsule (aneroid cell). External atmospheric pressure compresses the capsule; a mechanical linkage amplifies the deflection to a needle or digital transducer. Aircraft altimeters and barometric pressure sensors are refined aneroid (or solid-state) devices. The altimeter converts static pressure into altitude using the standard atmosphere relationship; the airspeed system uses pitot and static pressures as a differential measurement.

Fortin and Kew patterns (awareness)

Laboratory mercury barometers may include vernier scales and temperature corrections (mercury and scale expand with temperature). For Module 2, know that column height ∝ atmospheric pressure for a mercury instrument and that aneroid deflection is the practical aviation method.

Integrated Aviation Picture

Formula Recap

• p = F/A
• Hydrostatic: p = ρ g h (gauge, from free surface)
• Buoyancy: F_b = weight of fluid displaced = ρ V g
• Mercury barometer: atmospheric p = ρ_Hg g h_column

Use pascals and metres in calculations; convert cm² and mm carefully. Distinguish absolute, gauge, and differential readings whenever an instrument is named.