Submerged volume of floating body via density ratio¶
If a body is fully or partially submerged in a fluid, an Archimedes force starts acting on it from the fluid pushing it in the opposite direction of the gravity force.
The ratio of the body’s volume submerged in a fluid to its total volume depends on the ratio of the densities of the body and the fluid.
Conditions:
\(\rho \le \rho_\text{fl}\), so the body must be floating.
The body must be in static equilibrium.
Links:
- submerged_volume¶
Volume submerged in the fluid, which is equal to the volume of the displaced fluid.
- Symbol:
V_fl- Latex:
\(V_\text{fl}\)
- body_volume¶
Total volume of the body.
- Symbol:
V
- body_density¶
Density of the body.
- Symbol:
rho- Latex:
\(\rho\)
- fluid_density¶
Density of the fluid.
- Symbol:
rho_fl- Latex:
\(\rho_\text{fl}\)
- law¶
V_fl / V = rho / rho_fl- Latex:
- \[\frac{V_\text{fl}}{V} = \frac{\rho}{\rho_\text{fl}}\]