Density is a substance's mass per unit of volume. The symbol most often used for density is ρ, although the Latin letter D can also be used. Mathematically, density is defined as mass divided by volume:
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.
Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length and height (cubed) is interrelated with volume. The volume of a container is generally understood to be the capacity of the container; i.e., the amount of fluid that the container could hold, rather than the amount of space the container itself displaces. By metonymy, the term "volume" sometimes is used to refer to the corresponding region.
Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is preferred in SI, whereas the term "specific gravity" is gradually being abandoned.
A viscometer is an instrument used to measure the viscosity of a fluid. For liquids with viscosities which vary with flow conditions, an instrument called a rheometer is used. Thus, a rheometer can be considered as a special type of viscometer. Viscometers can measure only constant viscosity, that is, viscosity that does not change with flow conditions.
A hydrometer or lactometer is an instrument used for measuring density or relative density of liquids based on the concept of buoyancy. They are typically calibrated and graduated with one or more scales such as specific gravity.
Flow measurement is the quantification of bulk fluid movement. Flow can be measured using devices called flowmeters in various ways. The common types of flowmeters with industrial applications are listed below:
Buoyancy, or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the submerged volume of the object, i.e. the displaced fluid.
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 fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.
A Cartesian diver or Cartesian devil is a classic science experiment which demonstrates the principle of buoyancy and the ideal gas law. The first written description of this device is provided by Raffaello Magiotti, in his book Renitenza certissima dell'acqua alla compressione published in 1648. It is named after René Descartes as the toy is said to have been invented by him.
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body".
A submersible is an underwater vehicle which needs to be transported and supported by a larger watercraft or platform. This distinguishes submersibles from submarines, which are self-supporting and capable of prolonged independent operation at sea.
In relativistic physics, Supplee's paradox is a physical paradox that arises when considering the buoyant force exerted on a relativistic bullet immersed in a fluid subject to an ambient gravitational field. If a bullet has neutral buoyancy when it is at rest in a perfect fluid and then it is launched with a relativistic speed, observers at rest within the fluid would conclude that the bullet should sink, since its density will increase due to the length contraction effect. On the other hand, in the bullet's proper frame it is the moving fluid that becomes denser and hence the bullet would float. But the bullet cannot sink in one frame and float in another, so there is a paradox situation.
Eureka is an interjection used to celebrate a discovery or invention. It is a transliteration of an exclamation attributed to Ancient Greek mathematician and inventor Archimedes.
Neutral buoyancy occurs when an object's average density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink or rise. An object that has neutral buoyancy will neither sink nor rise.
In fluid mechanics, the Cheerios effect is a colloquial name for the phenomenon of floating objects appearing to either attract or repel one another. The example which gives the effect its name is the observation that pieces of breakfast cereal floating on the surface of a bowl will tend to clump together, or appear to stick to the side of the bowl.
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. Nevertheless, one object will always weigh more than another with less mass if both are subject to the same gravity.
Hydrostatic weighing, also referred to as underwater weighing, hydrostatic body composition analysis and hydrodensitometry, is a technique for measuring the density of a living person's body. It is a direct application of Archimedes' principle, that an object displaces its own volume of water.
On Floating Bodies is a work, originally in two books, by Archimedes, one of the most important mathematicians, physicists, and engineers of antiquity. Thought to have been written towards the end of Archimedes' life, On Floating Bodies I-II survives only partly in Greek and in a medieval Latin translation from the Greek. It is the first known work on hydrostatics, of which Archimedes is recognized as the founder.
Flotation of flexible objects is a phenomenon in which the bending of a flexible material allows an object to displace a greater amount of fluid than if it were completely rigid. This ability to displace more fluid translates directly into an ability to support greater loads, giving the flexible structure an advantage over a similarly rigid one. Inspiration to study the effects of elasticity are taken from nature, where plants, such as black pepper, and animals living at the water surface have evolved to take advantage of the load-bearing benefits elasticity imparts.
![Measurement of volume by displacement, (a) before and (b) after an object has been submerged. The amount by which the liquid rises in the cylinder ([?]V) is equal to the volume of the object. Displacement-measurement.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/b/b1/Displacement-measurement.svg/290px-Displacement-measurement.svg.png)