Apparent weight of a fully submersed body in fluid

The Archimedean force acting on a body fully submersed 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 submersed in the fluid is proportional to its weight in vacuum and also depends on the ratio of the fluid density and body density.

Notes:

1. Positive apparent weight means that the body is sinking, whereas negative apparent weight means that the body is floating to the surface.

Conditions:

1. The body is completely submersed in the fluid.

Links:

1. Physics LibreTexts, derivable from here.

weight_in_fluid

Apparent weight of the body submersed 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:

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