Weight in fluid via ratio of densities¶

The Archimedean force acting on a body immersed in a fluid is equal to the weight of the fluid displaced by the body. It can be derived that the weight of the body immersed in the fluid is proportional to its weight in vacuum and also depends on the ratio of the fluid density and body density.

Links:

Physics LibreTexts, derivable from here.

weight_in_fluid¶: Weight of the body immersed in the fluid. See force.

Symbol:: W_fl
Latex:: \(W_\text{fl}\)
Dimension:: force

weight_in_vacuum¶: Weight of the body in vacuum, i.e. its true weight. See force.

Symbol:: W_vac
Latex:: \(W_\text{vac}\)
Dimension:: force

fluid_density¶: density of the fluid.

Symbol:: rho_fl
Latex:: \(\rho_\text{fl}\)
Dimension:: mass/volume

body_density¶: density of the body.

Symbol:: rho_b
Latex:: \(\rho_\text{b}\)
Dimension:: mass/volume

law¶

W_fl = W_vac * (1 - rho_fl / rho_b)

Latex:: \[W_\text{fl} = W_\text{vac} \left(1 - \frac{\rho_\text{fl}}{\rho_\text{b}}\right)\]