Fluid Pressure & Buoyancy Calculator

Fluid Pressure Guide

What do I need to know about Pressure in Fluids?

Gauge pressure: P = ρgh. ρ = fluid density (kg/m³), g = 9.81 m/s², h = depth (m). Absolute pressure = P_gauge + P_atm = ρgh + 101,325 Pa. Pressure depends only on depth and fluid density — not on the shape of the container or the surface area. Example: at 10m depth in fresh water (ρ=1000). P = 1000 × 9.81 × 10 = 98,100 Pa = 98.1 kPa. Absolute: 98.1 + 101.3 = 199.4 kPa ≈ 2 atm. Every 10m in water ≈ 1 atm additional pressure. Scuba diving at 30m: approximately 4 atm absolute. Atmospheric pressure at the surface already adds a full atmosphere before any water depth is even considered, which is why total absolute pressure underwater rises faster than people intuitively expect.

What's the key thing to understand about Archimedes Principle?

Buoyancy force = weight of fluid displaced. F_b = ρ_fluid × g × V_submerged. Where V_submerged = volume of the object that is underwater. Example: 0.01 m³ object in seawater (ρ=1025). F_b = 1025 × 9.81 × 0.01 = 100.6 N. If the object weighs less than 100.6N (mass < 10.25kg): it floats. If heavier: it sinks. If exactly 100.6N: neutrally buoyant (submarine hovering). Ships float because the hull shape displaces a large volume of water — even though steel is denser than water, the total average density of the hull's shape, including the air inside, is less than water, which is what allows it to float.

What do I need to know about Floating and Sinking?

Object floats if: ρ_object < ρ_fluid. Object sinks if: ρ_object > ρ_fluid. Neutrally buoyant if: ρ_object = ρ_fluid. When floating: the object displaces its own weight of fluid. Fraction submerged = ρ_object / ρ_fluid. Ice in water: ρ_ice = 917 kg/m³. Fraction submerged = 917/1000 = 0.917. 91.7% of ice is below water — only 8.3% above the surface. Iceberg fraction: 917/1025 = 89.5% submerged in seawater. Human body: average density approximately 985 kg/m³ — just denser than fresh water (sinks), but close enough to neutral buoyancy that swimming requires little effort to stay afloat.

What's the key thing to understand about Pascal's Law and Hydraulics?

Pascal's Law: a pressure change in an enclosed fluid is transmitted equally to all parts of the fluid. Hydraulic systems: small force applied over small area = large force over large area. F_out/F_in = A_out/A_in. Car hydraulic brakes: small pedal force × small master cylinder area = large force at large brake caliper area. Hydraulic jack: input cylinder 2cm², output 100cm². 1N input → 50N output. A car jack lifting a 1-tonne car (about 9,810N of weight) with roughly 20N of input force needs an area ratio of approximately 490:1 (9,810 ÷ 20). Hydraulic systems can therefore multiply force dramatically using nothing but fluid pressure and a difference in piston area — no motors or gears required.

What do I need to know about Hydrostatic Pressure at Depth?

Pressure within a static fluid increases linearly with depth according to P = P₀ + ρgh, where P₀ is the pressure at the surface (usually atmospheric), ρ is fluid density, g is gravitational acceleration, and h is depth. This is why ears pop diving in a swimming pool after just a few metres, and why submarines and deep-sea equipment must be engineered to withstand pressures that climb by roughly one atmosphere for every 10 metres of seawater depth — at the bottom of the Mariana Trench (about 11 km down), pressure reaches over 1,000 times atmospheric pressure at sea level.

What's the difference between Gauge and Absolute Pressure?

Absolute pressure is measured relative to a perfect vacuum (zero pressure), while gauge pressure is measured relative to the surrounding atmosphere: P_absolute = P_gauge + P_atmospheric. Most practical pressure gauges — tyre gauges, blood pressure cuffs, scuba dive computers — read gauge pressure, because they're zeroed against the atmosphere around them before use. A car tyre reading '32 psi' is actually at about 32 + 14.7 = 46.7 psi absolute; engineers must be careful to specify which convention a given pressure value uses, since mixing the two is a common source of calculation errors.

What should I know about Atmospheric Pressure and Altitude?

The same hydrostatic principles that govern pressure in liquids also apply to the atmosphere, treating air as a (compressible) fluid with weight. Just as water pressure increases with depth below the surface, atmospheric pressure decreases with altitude above sea level, because there is progressively less air above pressing down. Unlike water, however, air is compressible and its density itself decreases with altitude, so atmospheric pressure does not fall linearly the way hydrostatic pressure does in an incompressible liquid; instead it falls off approximately exponentially, roughly halving every 5.5 kilometres of altitude in the lower atmosphere. Standard sea-level atmospheric pressure is defined as 101,325 Pa (1 atmosphere), falling to about 70,000 Pa atop a 3,000-metre mountain and to around 24,000 Pa (less than a quarter of sea-level pressure) at typical cruising altitude for commercial aircraft, around 10,000–11,000 metres. This is why aircraft cabins must be pressurised and why high-altitude climbers need supplemental oxygen: the fraction of oxygen in air stays roughly constant at about 21%, but the falling total pressure means each breath delivers far fewer oxygen molecules, even though the proportion of oxygen is unchanged.

Worked Example: Pressure at the Bottom of a Swimming Pool

A swimming pool is 3 m deep and filled with fresh water (density ρ = 1,000 kg/m³). The gauge pressure at the bottom — the pressure due to the water alone, not counting the atmosphere pressing down from above — is found with P = ρgh = 1,000 × 9.8 × 3 = 29,400 Pa, or about 29.4 kPa. To find the absolute pressure (what a diver's body actually experiences), add standard atmospheric pressure: P_abs = P_atm + ρgh = 101,325 + 29,400 = 130,725 Pa, or about 130.7 kPa — roughly 1.29 times normal atmospheric pressure. This is why ear discomfort becomes noticeable even at moderate pool depths: the pressure increase from just 3 m of water (29.4 kPa) is already more than a quarter of the entire weight of the atmosphere pressing down at sea level. Doubling the depth to 6 m would double the gauge pressure to 58.8 kPa, since pressure in a fluid increases linearly with depth, not with volume or surface area.

Table: Approximate Pressure at Various Ocean Depths

Because hydrostatic pressure increases linearly and predictably with depth in seawater (density ≈ 1,025 kg/m³, slightly denser than fresh water due to dissolved salt), it's possible to build a quick reference table for how pressure scales as a diver or submersible goes deeper.

Pressure in Connected Vessels and the Hydraulic Lift

Pascal's principle — that pressure applied anywhere in a confined, incompressible fluid is transmitted equally throughout — is the basis for hydraulic lifts, car brakes, and hydraulic jacks. If a small piston of area 5 cm² has a force of 50 N applied to it, the pressure generated is P = F/A = 50 / 0.0005 m² = 100,000 Pa. Because that pressure is the same everywhere in the connected fluid, a second, larger piston with area 250 cm² (0.025 m²) experiences the same pressure, producing an output force of F = P × A = 100,000 × 0.025 = 2,500 N — fifty times the input force, matching the fifty-fold difference in piston areas. This is mechanical advantage without violating energy conservation: the large piston moves a proportionally shorter distance than the small one travels, so the work in (force × distance) still equals the work out. It's the same principle behind a car's hydraulic brake system, where light pressure on a small brake pedal piston is multiplied into the much larger clamping force needed at each wheel's brake caliper.

Why Blood Pressure Is Measured in mmHg

Blood pressure readings (like '120/80') use millimetres of mercury for exactly the same physical reason a barometer does: mercury is dense enough that even modest, everyday pressures produce a small, easily readable column height, rather than the metres of water column the same pressure would need. A pressure of 120mmHg is equivalent to about 16 kPa, or roughly 1.63 metres of water — showing why water-based or Pascal-based units would be impractical for a wall-mounted or wrist-worn medical device, while a few centimetres of mercury movement is easy to read precisely. This is the same hydrostatic pressure principle used throughout this calculator: pressure from a column of fluid depends on the fluid's density, so a denser fluid (mercury, roughly 13.6 times denser than water) needs a proportionally shorter column to register the same pressure — which is exactly why mercury, not water, became the historical standard for both barometers and blood pressure cuffs.