fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...

, displacement occurs when an object is largely immersed in a

fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...

, 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 immersed in a liquid displaces an amount of fluid equal to the object's volume. Thus,

buoyancy Buoyancy (), or upthrust, is the force exerted by a fluid opposing the weight of a partially or fully immersed object (which may be also be a parcel of fluid). In a column of fluid, pressure increases with depth as a result of the weight of t ...

is expressed through

Archimedes' principle Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. Archimedes' principle is a law of physics fun ...

, which states that the

weight In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. Some sta ...

of the object is reduced by its volume multiplied by the

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

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 ''weight'' of fluid displaced will be equal to the weight of the displacing object.

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 Overflow may refer to: Computing and telecommunications *Integer overflow, a condition that occurs when an integer calculation produces a result that is greater than what a given register can store or represent * Buffer overflow, a situation where ...

), 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. The concept of

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. 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, . The fluid displaced has a weight , where is acceleration due to gravity. Therefore, the weight of the displaced fluid can be expressed as . 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.

References

{{Authority control Physical quantities Fluid mechanics Volume

Applications of displacement

See also

References