What is a fluid?
A fluid is a substance that flows: liquids and gases. Its particles can move past each other, so a fluid takes the shape of its container. In this simulator the fluid is at rest, so we can use hydrostatics, the physics of fluids that are not moving.
Density
Density ρ = m / V (mass per unit volume) tells you how tightly mass is packed. It is measured in kg/m³. Fresh water has a density of about 1000 kg/m³ (1 kg per litre), sea water about 1025 kg/m³, vegetable oil about 920 kg/m³ and honey about 1420 kg/m³. For an object made of several materials, or with air inside, what matters is itsaverage density: its total mass divided by its total volume.
Pressure in a fluid
Pressure is force per unit area, p = F / A, measured in pascals (1 Pa = 1 N/m²). A fluid at rest pushes on every surface it touches, at right angles to that surface. The deeper you go, the more fluid lies above you, so the pressure rises:
p = p₀ + ρ g h
Here p₀ is the pressure at the surface (the atmosphere, about 101.3 kPa), ρ is the fluid’s density, g ≈ 9.81 m/s² and h is the depth below the surface. Pressure depends only on depth and density, not on the shape or width of the container, and at a given depth it pushes equally in all directions.
Gauge and absolute pressure
| Type | Formula | At 0.5 m in water |
|---|---|---|
| Absolute | p = p₀ + ρgh | ≈ 106.2 kPa |
| Gauge | p_g = ρgh | ≈ 4.9 kPa |
Absolute pressure is measured from a perfect vacuum. Gauge pressure is the extra pressure above the atmosphere, which is what a tyre gauge reads. Because the atmosphere pushes equally on all sides of a submerged object and on both sides of the tank walls, its effect cancels, so the arrows in the simulator show gauge pressure.
Where buoyancy comes from
The bottom of a submerged object is deeper than its top, so the fluid pushes harder on the bottom than on the top. The sideways pushes cancel out. What is left is a net upward force: the buoyant force, sometimes called upthrust. You can see this in the pressure arrows on the objects: longer at the bottom, shorter at the top.
Archimedes’ principle
Adding up all those pushes gives a remarkably simple result, first described by Archimedes over 2,200 years ago: the buoyant force equals the weight of the fluid displaced by the object.
B = ρfluid g Vdisplaced
Vdisplaced is the volume of the part of the object below the surface. A fully submerged 1 L object in water displaces 1 L of water, weighing 9.81 N, so B = 9.81 N, whether it is a cube, a sphere or a cylinder, and whether it is made of cork or of steel. The displaced fluid also raises the fluid level in the tank.
Float, sink or hover?
- ρ_object < ρ_fluid: it floats. It rises until it displaces its own weight of fluid. The fraction below the surface is ρ_object ÷ ρ_fluid.
- ρ_object > ρ_fluid: it sinks. Even fully submerged, B < W. On the bottom it feels lighter: its apparent weight is W − B.
- ρ_object = ρ_fluid: it is neutrally buoyant and stays at whatever depth it is placed.
A steel ship floats because its hull encloses a large volume of air, so its average density is less than water’s. The same object can float in one fluid and sink in another: an egg sinks in fresh water but floats in very salty water.
Real-world applications
- Ships and boats float by displacing their own weight of water; the waterline (Plimsoll) marks show how low they may safely ride.
- Submarines and fish change their average density with ballast tanks or a swim bladder to rise, sink or hover.
- Hot-air balloons float in the “fluid” of the atmosphere, because hot air is less dense than the cold air around it.
- Dams are thicker at the bottom, where the water pressure is greatest; divers must equalise the pressure in their ears as they descend.
- Hydrometers measure the density of liquids, such as the sugar content of juice or the charge of a battery, by how deep they float.
Common misconceptions
- “Heavy things sink and light things float.” What matters is density compared with the fluid, not weight.
- “The buoyant force always equals the object’s weight.” Only for a floating object; a sinking object has B < W.
- “Deeper objects feel more buoyant force.” Once fully submerged, B is the same at any depth, because the displaced volume does not change.
- “Pressure in a fluid only pushes down.” It pushes in all directions, at right angles to every surface.
- “Shape decides whether something floats.” Shape matters only because it changes how much water the object can displace (like a hollow hull).
What the model assumes
The fluid is at rest and incompressible, with the same density everywhere, so the simple hydrostatic law p = p₀ + ρgh applies; g = 9.81 m/s² and the atmosphere is 101.3 kPa. The objects are solid and uniform, move only up and down, and do not tip, so a cube stays upright. While settling they feel a simple drag that only affects how they move, not where they come to rest. Surface tension and the motion of the fluid itself are ignored. Objects in the tank are kept from overlapping by moving them sideways. The tank is 60 cm wide and 30 cm from front to back, which sets how much the level rises.
Key takeaways
- Pressure in a fluid at rest grows with depth: p = p₀ + ρgh; gauge pressure leaves out the atmosphere.
- The extra push on an object’s lower surface produces the buoyant force.
- Archimedes’ principle: B equals the weight of the fluid displaced, B = ρ_fluid g V_displaced.
- Objects float, sink or hover depending on their average density compared with the fluid’s.
- A floating object has ρ_object/ρ_fluid of its volume below the surface.