Buoyant Force (Archimedes' Principle)

Also known as archimedes principle

F_b = \rho V g

F_b =

ρ =

V =

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Constant used — built into this formula, no need to enter

g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

Learning zone

Archimedes' insight — allegedly shouted from the bath — is that the fluid pushing on a submerged body doesn't care what the body is made of, only what volume of fluid it shoved aside. Displace 1 m³ of water and you get 1000 × 1 × 9.80665 ≈ 9807 N of lift, about a tonne-force, whether the displacer is steel or styrofoam. A ship floats by settling until its displaced water weighs exactly as much as the ship; a submarine hovers by pumping ballast until the two match.

Buoyant Force (Archimedes' Principle)

F_b = \rho V g

Where

$F_b$ = Buoyant force
$\rho$ = Fluid density
$V$ = Displaced volume

Missing one of these? Work it out first, then come back

Buoyant force — Newton's Second Law, Stokes' Drag (F = 6πμrv)
Fluid density — Dynamic Pressure (q = ½ρv²), Pressure Head (h = P/ρg)
Displaced volume — Density, Ideal Gas Law