Fluid Pressure & Buoyancy Simulator

The pressure at a certain depth in a fluid (hydrostatic pressure) is given by the weight of the fluid column above it.

Where:
P = Pressure at depth (Pa)
P₀ = Pressure at the surface (e.g., atmospheric pressure) (Pa)
ρ = Density of the fluid (kg/m³)
g = Acceleration due to gravity (9.81 m/s²)
h = Depth below the surface (m)
This is why the pressure reading in the simulator increases when you increase Depth or Fluid Density.

The buoyant force on a submerged or floating object is described by Archimedes' principle.

Where:
F_b = Buoyant force (N)
ρ_fluid = Density of the fluid (kg/m³)
V_displaced = Volume of fluid displaced by the object (m³)
An object floats if $F_b = Weight_{object}$, which occurs when $\rho_{object}\lt \rho_{fluid}$. It sinks if $\rho_{object}\gt \rho_{fluid}$. This is the core physics you test by changing object and fluid densities in the simulator.

Ship Design & Submarines: Engineers must calculate the exact volume of a ship's hull to ensure it displaces enough water (creating a buoyant force) to carry its massive weight. Submarines control their buoyancy by taking in or expelling water from ballast tanks, changing their overall density to dive or surface.

Hydraulic Systems (Pascal's Law): Car brakes, excavators, and factory presses use incompressible fluids to transmit force. A small force applied to a small-area piston creates a pressure that is transmitted to a large-area piston, multiplying the output force. This allows you to stop a heavy car with light pedal pressure.

Medical Devices & Blood Pressure: As noted in the FAQ, the historical standard unit for blood pressure is millimeters of mercury (mmHg). This comes from mercury column manometers, where the height of the dense mercury balances the pressure from the bloodstream. Modern digital devices still calibrate to this physical principle.

Hot Air Balloons & Buoyancy in Gases: The principle works for gases too! A hot air balloon floats because the heated air inside is less dense than the cooler surrounding air. The "buoyant force" from the displaced cooler air is greater than the weight of the balloon, basket, and passengers, causing it to rise.

There are several key points you should be mindful of when starting with this simulator. First, it's easy to forget the fundamental principle that "buoyancy is determined not by the object's material, but by the volume of fluid it displaces." For example, a 1-cubic-meter block of iron and a 1-cubic-meter block of polystyrene foam experience exactly the same buoyant force (approximately 9800 N). The difference lies in the balance between that buoyant force and the object's own weight (gravity). Iron sinks because it's heavier than the buoyant force, while polystyrene floats because it's lighter.

Next, please interpret the action of changing the "Object Density" in the simulator as changing only the weight while keeping the shape constant. In practice, buoyancy is adjusted by changing the volume (= the submerged volume of a ship's hull) without altering the weight. Also, note that setting the "Fluid Density" to an extremely high value will calculate unrealistically enormous buoyant forces. For instance, iron will float in mercury (density ~13,600 kg/m³), but such high-density fluids require special handling.

Finally, always keep in mind that this tool deals with "hydrostatic pressure." When flow is present (e.g., a ship underway or fluid moving inside a pipe), the pressure distribution becomes entirely different due to the influence of dynamic pressure and viscosity. Precisely because it's a simple tool, understanding its underlying assumptions is the first step toward applying the concepts.