# Displacement (fluid)

In fluid mechanics, **displacement** occurs when an object is largely immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, and from this, the volume of the immersed object can be deduced (the volume of the immersed object will be exactly equal to the volume of the displaced fluid).

An object that sinks displaces an amount of fluid equal to the object's volume. Thus buoyancy is expressed through Archimedes' principle, which states that the weight of the object is reduced by its volume multiplied by the density of the fluid. If the weight of the object is less than this displaced quantity, the object floats; if more, it sinks. The amount of fluid displaced is directly related (via Archimedes' principle) to its volume.

In the case of an object that sinks (is totally submerged), the volume of the object is displaced. In the case of an object that floats, the amount of fluid displaced will be equal in **weight** to the displacing object.

Archimedes' principle, a physical law of buoyancy, states that any body completely or partially submerged in a fluid (gas or liquid) at rest is acted upon by an upward, or buoyant, force the magnitude of which is equal to the weight of the fluid displaced by the body. The volume of displaced fluid is equivalent to the volume of an object fully immersed in a fluid or to that fraction of the volume below the surface of an object partially submerged in a liquid. The weight of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. The buoyant force on a body floating in a liquid or gas is also equivalent in magnitude to the weight of the floating object and is opposite in direction; the object neither rises nor sinks. If the weight of an object is less than that of the displaced fluid, the object rises, as in the case of a block of wood that is released beneath the surface of water or a helium-filled balloon that is let loose in the air. An object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced. In fact, in some accurate weighing, a correction must be made in order to compensate for the buoyancy effect of the surrounding air. The buoyant force, which always opposes gravity, is nevertheless caused by buoyancy. Fluid pressure increases with depth because of the (gravitational) weight of the fluid above. This increasing pressure applies a force on a submerged object that increases with depth. The result is buoyancy.[1]

## Applications of displacement

This method can be used to measure the volume of a solid object, even if its form is not regular. Several methods of such measuring exist. In one case the increase of liquid level is registered as the object is immersed in the liquid (usually water). In the second case, the object is immersed into a vessel full of liquid (called an overflow can), causing it to overflow. Then the spilled liquid is collected and its volume measured. In the third case, the object is suspended under the surface of the liquid and the increase of weight of the vessel is measured. The increase in weight is equal to the amount of liquid displaced by the object, which is the same as the volume of the suspended object times the density of the liquid.[2]

The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.[3] The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, *m* = *ρV*. The fluid displaced has a weight *W* = *mg*, where *g* is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as *W* = *ρVg*.

The weight of an object or substance can be measured by floating a sufficiently buoyant receptacle in the cylinder and noting the water level. After placing the object or substance in the receptacle, the difference in weight of the water level volumes will equal the weight of the object.

## See also

## References

- "Archimedes' principle - physics". Retrieved July 27, 2017.
- Hughes, Stephen W. (2005). "Archimedes revisited: a faster, better, cheaper method of accurately measuring the volume of small objects".
*Physics Education*.**40**(5): 468–474. Bibcode:2005PhyEd..40..468H. CiteSeerX 10.1.1.426.6138. doi:10.1088/0031-9120/40/5/008. - "What is buoyant force?".