Buoyant Force (Archimedes)

F_{B} = γ V_{displaced}

The buoyant force equals the weight of the displaced fluid and acts upward through the centroid of the displaced volume. A floating body displaces its own weight. Fully submerged, V_displaced equals the body volume.

$F_{B}$ (N): Buoyant force
$γ$ (N/m³): Specific weight of the fluid
$V_{displaced}$ (m³): Displaced fluid volume

Step-by-step solved example

A 0.80 m³ object is fully submerged in freshwater (γ = 9.81 kN/m³). Buoyant force?

Archimedes: F_B equals the weight of displaced fluid.

1. Archimedes
F_B = γ V = 9.81 kN/m³ × 0.80 m³ = 7.85 kN.
$F_{B} = 7.85 kN$
2. Direction
The force is vertically upward through the centroid of the displaced water.

Answer: 7.85 kN upward

10 practice questions

0/10 correct

1.2.0 m³ fully submerged in freshwater. F_B =

2.Archimedes’ principle states that F_B equals

3.A floating body displaces

4.Static stability of a floating body needs the metacenter

5.SG = 0.60 cube of 1.0 m³ floating in water. V_sub =

6.Buoyancy in air compared with water is

7.Fully submerged, V_displaced equals

8.γ of seawater is about

9.Body weight 5 kN, F_B = 8 kN fully submerged. Net force is

10.A balloon’s buoyancy is mainly