Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Archimedes' Law

Sponsored Links

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, lb f )

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

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

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

Sponsored Links

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.

Sponsored Links

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.