Is volume displaced by an item in water = volume of item * specific gravity of item?

michaelw

Or does that hold true for just one particular problem im working on :)?

(this formula is for objects that sink, not float.. if they float volume displaced = volume of item)

HallsofIvy

Your second statement is wrong- if an item floats then the water displaced has the same mass as the object, not the same volume. Since not all of the object is in the water, the water "doesn't know" its volume. If an object is completely submerged (does not float) the amount of water displaced is exactly equal to its volume. However, in order to sink to the bottom, it is only necessary that the object's specific weight be greater than one. Other than that, the object's specific weight does not come into the equation: the volume of water displaced is equal to the objects volume times 1.0, not its specific weight.

michaelw

ah whoops
so then if an object floats, the amount of water displaced is
volume of item * specific gravity of item?

and if it sinks, amount of water displaced = volume of item?

dextercioby

Nope,Archimedes' principle applies,no matter what is the configuration,solid + fluid.
The volume displaced in the fluid is simply the volume of the solid inside the fluid.

BTW,"amount" is highly ambiguous.Use either MASS or VOLUME.

Daniel.

michaelw

specific gravity is = fraction submerged = p(object)/p(water)
so then wouldnt volume displaced be fraction submerged * volume of item? (ie specific gravity of item * volume of item)

dextercioby

Nope,you got them all mixed up.

I don't like the term "specific gravity",physicists don't use this term.It's "mass volumic density".

The volume of fluid displaced is a fraction of the solid's volume.

Daniel.

michaelw

right, but p(object)/p(water) will be < 1 for an object that floats, so volume displaced will be a fraction of the objects total volume

OlderDan

Right. For a floating object, the ratio of the densities is the inverse of the ratio of the volumes.

I think your earlier statement was misinterpreted.