Pressure

Definition

Pressure is force per unit area:

P = F / A

Units:

• Pascal (Pa) — SI unit, equal to 1 N/m². Very small in everyday terms.
• Atmosphere (atm) — 101,325 Pa, average sea-level atmospheric pressure.
• Bar — 100,000 Pa (about 1 atm).
• Pound per square inch (psi) — common in US; 1 atm ≈ 14.7 psi.
• Torr / mmHg — 133.3 Pa each; used in medical/lab.

Hydrostatic pressure

In a static fluid, pressure increases with depth due to the weight of fluid above:

P(h) = P_surface + ρ·g·h

Depth in seawater	Pressure (gauge)	Total pressure
0 m (surface)	0	1 atm
10 m	1 atm (~10⁵ Pa)	2 atm
30 m (recreational scuba limit)	3 atm	4 atm
100 m	10 atm	11 atm
1,000 m (military submarine)	~100 atm	~101 atm
4,000 m (typical ocean)	~400 atm	~401 atm
10,924 m (Mariana Trench)	~1,071 atm	~1,072 atm

Atmospheric pressure

Atmospheric pressure decreases with altitude (less air above):

Altitude	Pressure	Notes
Sea level	101,325 Pa = 1 atm	Standard reference
Denver (1 mi up)	~83,000 Pa = 0.82 atm	~17% less air
Mt. Everest summit	~33,000 Pa = 0.33 atm	~1/3 of sea level
Cruise altitude (~10 km)	~26,500 Pa = 0.26 atm	Cabins pressurized to ~0.75 atm
50 km (stratosphere)	~78 Pa = 0.0008 atm	Very thin
100 km (Kármán line, "space")	0.03 Pa = 3×10⁻⁷ atm	Effectively vacuum

Roughly halves every 5.5 km (scale height of atmosphere).

Pascal's principle

Pressure applied to an enclosed incompressible fluid is transmitted equally throughout the fluid.

Consequence — hydraulic systems multiply force. Press a small piston (area A₁) with force F₁:

P = F₁ / A₁

This pressure acts on a larger piston (area A₂):

F₂ = P · A₂ = F₁ · (A₂/A₁)

Force multiplied by area ratio. Used in hydraulic jacks, car brakes, lifts.

Real-world pressures

System	Pressure
Vacuum (theoretical)	0 Pa
Light bulb (interior)	~10 Pa
Atmospheric (sea level)	101,325 Pa
Soda can (carbonated)	~3-4 atm
Bicycle tire	~7 atm gauge (~8 atm absolute)
Car tire	~2 atm gauge
Steam locomotive boiler	~15 atm
Scuba tank (full)	~200 atm
Industrial water cutting	~6,000 atm
Blood pressure (peak)	~16 kPa above atmospheric
Mariana Trench	~1,070 atm
Sun's core	~250 billion atm
Neutron star core	~10³⁴ Pa

JavaScript — pressure calculations

// Hydrostatic pressure
function hydrostaticPressure(depth, density = 1000, g = 9.81, surfaceP = 101325) {
  return surfaceP + density * g * depth;
}

console.log(`10 m water: ${hydrostaticPressure(10).toFixed(0)} Pa`);  // ~199,425 (~2 atm)
console.log(`Mariana Trench: ${hydrostaticPressure(10924, 1025).toExponential(2)} Pa`);
// ~1.1e8 Pa (~1100 atm)

// Atmospheric pressure at altitude (rough exponential)
function atmosphericPressure(altitude_m) {
  const P0 = 101325;
  const H = 8000;  // scale height
  return P0 * Math.exp(-altitude_m / H);
}

console.log(`Mt Everest (8848 m): ${(atmosphericPressure(8848) / 1000).toFixed(0)} kPa`);  // ~33

// Pascal's principle: hydraulic jack
function hydraulicForce(F_input, A_input, A_output) {
  // Pressure equal: F_in/A_in = F_out/A_out
  return F_input * A_output / A_input;
}

console.log(`Hand pumps 100 N on 1 cm² piston, lifts 100 cm² piston: ${hydraulicForce(100, 0.0001, 0.01).toFixed(0)} N`);
// 10,000 N — like lifting 1 ton with 10 kg force

// Force on a submerged surface
function forceOnSurface(area, depth, density = 1000) {
  // F = P_avg × A. Pressure varies linearly with depth, so use depth at centroid
  return density * 9.81 * depth * area;
}

console.log(`1 m² window at 5 m depth: ${forceOnSurface(1, 5).toFixed(0)} N`);  // ~49,000 N (5 tonnes)

// Pressure in scuba tank
function gasPressure(n_moles, V, T = 293) {
  // Ideal gas: PV = nRT
  const R = 8.314;
  return n_moles * R * T / V;
}

// 100 L tank, 100 moles of O2 at 20°C
console.log(`Scuba tank pressure: ${gasPressure(100, 0.1).toExponential(2)} Pa`);
// ~2.4e6 Pa = ~240 bar

// Blood pressure conversion
function mmHg_to_Pa(mmHg) { return mmHg * 133.322; }
console.log(`120/80 mm Hg: ${mmHg_to_Pa(120).toFixed(0)}/${mmHg_to_Pa(80).toFixed(0)} Pa`); // 16000/10666

Where pressure shows up

• Weather and meteorology. High/low pressure systems, air masses, pressure gradient force drives wind, hurricanes have low-pressure centers.
• Diving and submarines. Hydrostatic pressure determines depth limits; submarines need pressure hulls; decompression sickness physics.
• Aviation. Cabin pressurization, altimeters (measure altitude via pressure), pressure differential between inside and outside aircraft.
• Medicine. Blood pressure, respiratory pressure, intra-cranial pressure, eye pressure (glaucoma).
• Hydraulics. Excavators, car brakes, jacks, presses, control surfaces in aircraft.
• Pneumatics. Air-powered tools, pneumatic locks, vehicle suspension.
• Cooking. Pressure cookers (raise boiling point), vacuum sealing, sous-vide bath physics.

Common mistakes

• Confusing absolute and gauge pressure. Tire gauge reads gauge (relative to atmospheric). Engineering papers often use absolute. Be careful: 30 psi gauge = ~45 psi absolute.
• Forgetting that pressure depends on depth, not on container shape. Pressure at depth h depends ONLY on h (and ρ, g). A wide pool and a narrow tube of same depth have same hydrostatic pressure (Stevin's law).
• Confusing pressure with force. Pressure is force PER unit area. A small force on a small area can produce large pressure (knife edge); a large force on a large area can produce low pressure (snowshoes).
• Misapplying Pascal's principle to compressible fluids. Pascal's works for incompressible fluids (oil, water). For compressible (air, gas), pressure changes need volume changes; energy and mass-flow analysis is more complex.
• Pressure unit confusion. Pa, kPa, MPa, bar, atm, psi, torr, mmHg, mb — many units. Always double-check conversions.
• Treating "vacuum" as below 0 Pa. 0 Pa is absolute vacuum; you can't go lower. Some engineers use "negative pressure" colloquially for "below atmospheric" — it's still positive absolute.