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Archimedes' Law

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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)


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

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

V = volume of body below surface of liquid (m 3 , ft 3 )

γ = ρ g = specific weight of fluid (weight per unit volume) (N/m 3 , lb f /ft 3 )

ρ = density of fluid (kg/m 3 , slugs/ft 3 )

g = acceleration of gravity (9.81 m/s 2 , 32.174 ft/s 2 )

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


V b ρ b g = V w ρ w g


V b = volume body (m 3 )

ρ b = density of body ( kg/m 3 )

V w = volume of water (m 3 )

ρ w = density of water ( kg/m 3 )

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/m 3 ) / V b

= 950 kg/m 3

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 /ft 3 . The volume of the brick can be calculated

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

= 65.25 in 3

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 in 3 ) / (1728 in/ft 3 )) ( 1.940 slugs/ft 3 ) ( 32.174 ft/s 2 )

= 2.36 lb f

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 lb f ) 1.75

= 4.12 lb f

The resulting force acting on the brick can be calculated as

W (WB - FB) = (4.12 lb f ) - (2.36 lb f )

= 1.76 lb f

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Related Topics

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

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