ABC Tools

Buoyancy, Explained

After reading this you can predict whether a block floats, sinks or hovers in a given fluid, compute how much of it sits underwater, and reproduce the exact numbers the tank draws on screen.

What buoyancy is, and one example to fix it

Drop a sealed plastic block into water and it settles part-submerged, bobbing until it stops. It does not sink and it does not leap out. Something holds it at a precise depth. That something is the buoyant force, and Archimedes stated its size more than two thousand years ago: the upward push equals the weight of the fluid the object shoves aside.

Here is the hook. Take a block whose density is 0.6 grams per cubic centimeter and put it in fresh water at 1.0. It floats with exactly 60% of its volume below the surface. Now pour in salt until the water reaches brine at 1.2. The same block rises: only 50% now sits underwater, because 0.6 / 1.2 = 0.5. Nothing about the block changed. The fluid did the deciding.

The Buoyancy Tank lets you set the block's density and size and the fluid's density, then watch the block find its resting depth while the weight arrow and the buoyant-force arrow are drawn competing against each other.

When this model helps and when it misleads

Use the tank to build intuition for static equilibrium: a rigid, uniform block sitting still in a still liquid. It answers three questions cleanly. Does it float? How deep does it ride? What happens when the fluid changes? These are the questions Archimedes' principle was built to answer, and the tank answers them exactly.

Do not read the tank as a hydrodynamics engine. It ignores drag while sinking, surface tension, the meniscus that curls up at the block's edge, and the sloshing waves a real drop makes. It treats density as uniform, so it cannot model a ship whose steel hull encloses air. A real cargo ship floats because its average density, steel plus air plus cargo, stays below water's. The tank's block has one density throughout.

The tank models buoyant equilibrium, not the trip down to that equilibrium. In a real fluid a dense block accelerates, hits terminal velocity against drag, then stops at the bottom. The tank shows you the start and the end, not a physically accurate fall time.

The formula and why it works

The buoyant force on a submerged volume is the weight of displaced fluid:

F_b = \rho_{\text{fluid}} \cdot g \cdot V_{\text{displaced}}

Here \rho_{\text{fluid}} is the fluid's density, g is gravitational acceleration (about 9.81\ \text{m/s}^2), and V_{\text{displaced}} is the volume of the block below the waterline. Gravity pulls the block down with its full weight:

W = \rho_{\text{block}} \cdot g \cdot V_{\text{block}}

where \rho_{\text{block}} is the block's density and V_{\text{block}} its total volume. A floating block is in balance, so set F_b = W. The g cancels from both sides. Divide through and you get the submerged fraction:

\frac{V_{\text{displaced}}}{V_{\text{block}}} = \frac{\rho_{\text{block}}}{\rho_{\text{fluid}}}

Read that as the rule the whole tank obeys. The fraction of a block that sits underwater equals the ratio of the two densities. If the block is less dense than the fluid, the ratio is below 1, so part of the block stays above the surface and it floats. If the block is denser, the ratio exceeds 1, which is impossible for a floating body: more than the whole block would need to be submerged, so it sinks and rests on the bottom. If the densities match exactly, the ratio is 1, the block is fully but only just submerged, and it hovers in neutral equilibrium at any depth.

Set the block density to 0.6 and fluid density to 1.0 and the submerged fraction is 0.6, so 60 percent of the block sits below the waterline. Raise fluid density to 1.2 and the fraction falls to 0.5. When block density meets or exceeds fluid density the fraction reaches 1 and the block sinks.

A worked example reproducing the demo

The demo button loads the defaults: a block of density 0.6 g/cm3, a cube of side 10 cm, dropped into fresh water at 1.0 g/cm3. Follow the numbers.

Floating a light block on water

  1. Block volume: a 10 cm cube gives V_{\text{block}} = 10^3 = 1000\ \text{cm}^3.
  2. Block mass: 0.6 \times 1000 = 600 grams. Its weight is 0.6\ \text{kg} \times 9.81 = 5.886\ \text{N}.
  3. Submerged fraction: 0.6 / 1.0 = 0.6, so 60% of the cube sits below the waterline.
  4. Displaced volume: 0.6 \times 1000 = 600\ \text{cm}^3. Sitting flat, the cube sinks 6 cm of its 10 cm height.
  5. Displaced water mass: 1.0 \times 600 = 600 grams. Its weight is 0.6\ \text{kg} \times 9.81 = 5.886\ \text{N}.
  6. Check the balance: buoyant force 5.886 N equals weight 5.886 N. The arrows in the tank are equal and opposite, so the block rests.

Now switch the fluid to brine at 1.2 without touching the block. The submerged fraction becomes 0.6 / 1.2 = 0.5, so only 5 cm of the cube stays underwater and it rides higher. Switch to oil at 0.9 and the fraction rises to 0.6 / 0.9 \approx 0.667, about 6.67 cm submerged, so the same block sits deeper in oil than in water.

The same block sinks deeper in lighter fluids. Denser fluid lifts it higher, matching 0.6 divided by each fluid density.

Reading and interpreting what you see

Three quantities on screen carry the meaning: the waterline position, the submerged fraction, and the two force arrows.

When the arrows are equal length and cancel, the block is floating in equilibrium and the waterline cuts it at the density ratio. When the weight arrow is clearly longer than the buoyant arrow, the block is denser than the fluid: it cannot balance and it sinks to the floor. On the floor the tank floor supplies a third force, the normal force, that makes up the difference, so the block stops even though buoyancy alone never balanced its weight.

The curve below shows submerged depth against block density for a 10 cm cube in water. It rises linearly from 0 to 10 cm as density climbs from 0 to 1.0, then flattens: any density at or above 1.0 means fully submerged and sinking.

Depth grows in step with density until the block hits full submersion at density 1.0, the marked cliff where floating turns into sinking.

Common mistakes

The size of the block does not change whether it floats. Only density does. A tiny 0.6 cube and a huge 0.6 slab both float with 60% submerged. Size sets how much force is involved, not the fraction, because volume cancels in the ratio. People often assume big means sinks; the tank shows it does not.

Weight and mass get mixed up. The buoyant force compares fluid weight to block weight, and g appears on both sides, so it cancels. That is why the float rule depends only on the density ratio and not on gravity's strength. The same block would float at the same waterline on the Moon.

Real ships and swimmers are not uniform blocks. A steel hull floats because its shape traps air, dropping its average density below water's. Do not conclude from the tank that steel floats. A solid steel cube at density 7.8 sinks instantly here, and it should.

Related simulations

If the falling and settling motion interests you more than the equilibrium, try the Falling-Sand Playground, where water, oil and sand sort themselves by density pixel by pixel. To watch springy bodies deform instead of stay rigid, the Soft-Body Jelly drops wobbly blobs that squash on impact. For the fluid itself in motion, the Fluid Flow Simulator stirs dye through a real-time flow. And the Brownian Motion tool shows the molecular bombardment that, averaged over a whole face, produces the steady pressure buoyancy relies on.

Frequently asked questions

Why does 8 percent of an iceberg show above water?

Ice has density about 0.92 and seawater about 1.0 (fresh water gives the same rough ratio). The submerged fraction is 0.92 / 1.0 = 0.92, so 92% hides below and only 8% shows. Set a block to 0.92 on water in the tank and you reproduce exactly that.

Does a heavier block sink faster in this tank?

The tank shows equilibrium, not accurate fall speed. In reality a denser block reaches equilibrium (the floor) quicker because net downward force is larger, but drag, which the tank ignores, sets the real terminal speed. Treat the settling animation as illustrative, not measured.

Why do you float more easily in the Dead Sea?

Dead Sea water is brine near density 1.24, well above the human body's average of roughly 1.01. The submerged fraction drops to about 1.01 / 1.24 \approx 0.81, so about 19% of you rides above the surface instead of the sliver you get in fresh water. Raise the fluid density in the tank and watch a barely-sinking block start to float.

Can a block hover in the middle?

Yes, when block density equals fluid density exactly. Then the ratio is 1, the buoyant force matches weight at any depth, and the block sits in neutral equilibrium. In practice this balance is fragile: a tiny density mismatch sends it slowly to the top or bottom.

Does gravity strength change the waterline?

No. Since g multiplies both weight and buoyant force, it cancels in the float condition. The waterline depends only on the density ratio, so a block floats at the same fraction on Earth, the Moon or Mars.

Try it yourself in the tool

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