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Buoyancy experiment calculator

Explore how a spherical object floats when its volume displaces one liquid or two stable layers.

Calculator

Sphere volume
0.0005236
Object density
1,100
Sphere mass
0.575959
Immersion height
0.05
Lower-liquid density
1,200
Volume in lower liquid
0.0002618
Volume in upper fluid
0.0002618
Lower-fluid buoyancy
3.08085
Upper-fluid buoyancy
2.56737

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How this calculator works

A spherical cap of height h occupies pi h^2(r-h/3). Each liquid supports the weight of the volume it displaces. At equilibrium the two buoyant forces add to the sphere weight. Setting upper-fluid density to zero gives a one-liquid experiment with negligible air buoyancy. Use measured solution densities; salt concentration alone needs a temperature-dependent density model. Surface tension, mixing and wall contact are excluded.

Formula

V = 4 pi r^3/3; V_lower = pi h^2(r-h/3); m = rho_lower V_lower + rho_upper(V-V_lower).

Worked example

A sphere with r = 0.05 m has volume 0.000523598776 m3. At an interface between 1000 and 1200 kg/m3 liquids, half-volume immersion supports mass 0.575958653 kg.

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Frequently asked questions

Can I use salt water?

Yes. Enter the measured density in kg/m3 or another offered density unit.

What if the object sinks?

If its density exceeds both fluid densities, there is no floating interface solution. The tool reports that condition.

Is a hollow ball allowed?

Yes, if it is rigid and sealed. Use its total mass and outside diameter.

Sources

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