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# Archimedes' Law

Archimedes' principle states that:

"If a solid body floats or is submerged in a liquid - the liquid exerts an upward thrust force - a buoyant force - on the body equal to the gravitational force on the liquid displaced by the body."

The buoyant force can be expressed as

F B =  W

= V γ

= V ρ g                                     (1)

where

F B = buoyant force acting on submerged or floating body (N, lbf )

W = weight (gravity force) of displaced liquid (N, lbf )

V = volume of body below surface of liquid (m3, ft3 )

γ = ρ g = specific weight of fluid (weight per unit volume) (N/m3, lbf /ft3 )

ρ = density of fluid (kg/m3, slugs/ft3 )

g = acceleration of gravity (9.81 m/s2, 32.174 ft/s2)

.

### Example - Density of a Body that floats in Water

A floating body is 95% submerged in water with density 1000 kg/m 3.

For a floating body the buoyant force is equal to the weight of the water displaced by the body.

F B =  W

or

V b ρ b g = V w ρ w g

where

V b = volume body (m3 )

ρ b = density of body ( kg/m3 )

V w = volume of water (m3 )

ρ w = density of water ( kg/m3 )

The equation can be transformed to

ρ b = V w ρ w / V b

Since 95% of the body is submerged

0.95 V b = V w

and the density of the body can be calculated as

ρ b = 0.95 V b (1000 kg/m3 ) / V b

= 950 kg/m3

### Example - Buoyant force acting on a Brick submerged in Water

A standard brick with actual size 3 5/8 x 2 1/4 x 8 (inches) is submerged in water with density 1.940 slugs /ft3 . The volume of the brick can be calculated

V brick = (3 5/8 in) (2 1/4 in) (8 in)

= 65.25 in3

The buoyant force acting on the brick is equal to the weight of the water displaced by the brick and can be calculated as

F B =  (( 65.25 in3 ) / (1728 in/ft3 )) ( 1.940 slugs/ft3 ) ( 32.174 ft/s2)

= 2.36 lbf

The weight or the gravity force acting on the brick - common red brick has specific gravity 1.75 - can be calculated to

W B = (2.36 lbf ) 1.75

= 4.12 lbf

The resulting force acting on the brick can be calculated as

W (WB - FB) = (4.12 lbf ) - (2.36 lbf )

= 1.76 lbf

## Related Topics

### • Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

### Hydrostatic Force acting on Submerged Surface

Calculate the thrust force acting on a submerged surface.

### Hydrostatic Pressure vs. Depth

Depth and hydrostatic pressure.

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