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Archimedes's Principle

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

The net force on a submersed object equals the difference between the weight of the object and its buoyancy. The buoyancy equals the product of density of the liquid, the displacement volume and gravitational acceleration. Finally, the fraction of the body submerged equals the volume of water displaced divided by the volume of the object.

Formula

{QuantityVariable[Subscript["F", "net"], "Force"] == -QuantityVariable["B", "Force"] + Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable[Subscript["m", "b"], "Mass"], QuantityVariable["B", "Force"] == Quantity[1, "StandardAccelerationOfGravity"]*QuantityVariable["ρ", "MassDensity"]*QuantityVariable[Subscript["V", "f"], "Volume"], QuantityVariable["R", "Unitless"] == QuantityVariable[Subscript["V", "f"], "Volume"]/QuantityVariable[Subscript["V", "b"], "Volume"]}

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Archimedes's Principle"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Archimedes's Principle"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject["Archimedes's Principle"], {QuantityVariable[ \!\(\*SubscriptBox[\("F"\), \("net"\)]\),"Force"] -> None, QuantityVariable["B","Force"] -> None, QuantityVariable["R","Unitless"] -> None, QuantityVariable["\[Rho]","MassDensity"] -> Quantity[1, ("Grams")/("Centimeters")^3]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: -212

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