Engineering
Archimedes' Buoyancy Force, Apparent Immersed Weight & Iceberg Draft fraction
Calculate static buoyancy and a floating volume fraction, distinguishing neutral buoyancy and signed support force under full immersion.
Displaced volume and static force balance
Assume a rigid object of uniform average density in a static, uniform-density fluid, neglecting surface tension and other support. The floating volume fraction is object density divided by fluid density only when the object is no denser than the fluid. Equal densities give neutral buoyancy; denser objects have no unsupported floating equilibrium.
Full-immersion buoyancy uses the total displaced volume. A partially floating object displaces less volume, and its equilibrium buoyancy balances its weight. The full-immersion value below is therefore not the actual floating ice buoyancy.
Under full immersion, (rho_object-rho_fluid)*V*g is signed external support: positive requires upward support, negative requires downward restraint. It is not a crane capacity specification; motion, rigging, fluid forces and safety factors are omitted. Volume fraction is not generally a fraction of object height or draft.
| Buoyancy Input | Cell | Glacial Ice vs Steel Block | Marine Physics Output |
|---|---|---|---|
| Total Object Volume V | B2 = 0.40 m^3 | 400-liter block | Full-immersion displaced V |
| Object Density rho_obj | B3 = 920 kg/m^3 | Glacial ice (< 1,025) | Floats! (89.76% submerged) |
| Seawater Density & Gravity | B4 = 1,025, B5 = 9.81 | Max F_b = 1025 * 0.4 * 9.81 | 4,022.10 N full buoyancy |
| Steel Block (B3 = 7,850) | 7,850 > 1,025 -> Sinks | (7850 - 1025) * 0.4 * 9.81 | 26,781.30 N underwater crane load |
Floating volume fraction or no floating equilibrium
Do not clamp a sinking object’s density ratio to1 and call it equilibrium. Equal-density objects can be fully immersed with zero net force.
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",IF(B3>B4,"No floating equilibrium",ROUND(B3/B4,4)))Full-immersion buoyant force in newtons
For the given total volume, the full-immersion buoyant force is4022.10N. The supported steel example requires26781.30N upward under the stated static assumptions.
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",ROUND(B4 * B2 * B5, 2))Signed support force under full immersion
For fully immersed ice the result is-412.02N: a downward restraint is needed. Freely floating ice is only partly immersed.
=IF(OR(COUNT(B2:B5)<>4,MIN(B2:B5)<=0),"Invalid inputs",ROUND((B3-B4)*B2*B5,2))Try the example
Use the original values or change them to test your understanding.