AcademyFluids
Academy
Buoyancy
Level 1 - Physics topic page in Fluids.
Principle
Buoyancy is the net upward pressure force from the surrounding fluid.
Notation
\(F_B\)
buoyant force
\(\mathrm{N}\)
\(\rho_f\)
fluid density
\(\mathrm{kg\,m^{-3}}\)
\(V_{\mathrm{disp}}\)
displaced fluid volume
\(\mathrm{m^{3}}\)
\(p_{\mathrm{top}},p_{\mathrm{bottom}}\)
pressures at the top and bottom faces
\(\mathrm{Pa}\)
\(A\)
cross-sectional area
\(\mathrm{m^{2}}\)
\(h\)
vertical separation of top and bottom faces
\(\mathrm{m}\)
Method
Buoyancy comes from the pressure being larger on the lower face than on the upper face.
Pressure difference
\[p_{\mathrm{bottom}}-p_{\mathrm{top}}=\rho_fgh\]
Net upward force
\[F_B=(p_{\mathrm{bottom}}-p_{\mathrm{top}})A\]
Displaced volume
\[V_{\mathrm{disp}}=Ah\]
Buoyancy formula
\[F_B=\rho_f g V_{\mathrm{disp}}\]
The free-body diagram replaces the detailed pressure forces by one buoyant force acting upward on the body.
For a floating body, vertical equilibrium requires the buoyant force to equal the body's weight.
Rules
These are the compact buoyancy relations.
Buoyant force
\[F_B=\rho_f g V_{\mathrm{disp}}\]
Floating condition
\[F_B=W\]
Supported immersion
\[N+F_B=W\]
Examples
Question
A cube of side
\[0.10\,\mathrm{m}\]
is fully submerged in water. Find the buoyant force.Answer
The displaced volume is
\[V_{\mathrm{disp}}=(0.10)^3=1.0\times10^{-3}\,\mathrm{m^3}\]
so \[F_B=1000(9.8)(1.0\times10^{-3})=9.8\,\mathrm{N}\]
Checks
- Use the fluid density, not the object's density, in the buoyancy formula.
- Use displaced volume, not automatically the full object volume.
- Buoyant force points upward because pressure increases downward.
- A floating object has zero net vertical force, not zero forces.