How is the density of a fluid determined?
Relative density
A pycnometer (from Greek: πυκνός (puknos) meaning "dense"), also called pyknometer or specific gravity bottle, is a device used to determine the density of a liquid. A pycnometer is usually made of glass, with a close-fitting ground glass stopper with a capillary tube through it, so that air bubbles may escape from the apparatus. This device enables a liquid's density to be measured accurately by reference to an appropriate working fluid, such as water or mercury, using an analytical balance.
Particle density (packed density)
The powder is placed inside a pycnometer of known volume, and weighed. The Pycnometer is then filled with a fluid of known density, in which the powder is not soluble. The volume of the powder is determined by the difference between the volume as shown by the pycnometer, and the volume of liquid added (i.e. the volume of air displaced). A similar method, which does not include pore volume, is to suspend a known mass of particles in molten wax of known density, allow any bubbles to escape, allow the wax to solidify, and then measure the volume and mass of the wax/particulate brick.
Mineral
Specific gravity numerically describes the density of a mineral. The dimensions of density are mass divided by volume with units: kg/m or g/cm. Specific gravity measures how much water a mineral sample displaces. Defined as the quotient of the mass of the sample and difference between the weight of the sample in air and its corresponding weight in water, specific gravity is a unitless ratio. Among most minerals, this property is not diagnostic. Rock forming minerals – typically silicates or occasionally carbonates – have a specific gravity of 2.5–3.5.
Friedmann equations
The density parameter, formula_35, is defined as the ratio of the actual (or observed) density formula_1 to the critical density formula_37 of the Friedmann universe. The relation between the actual density and the critical density determines the overall geometry of the universe; when they are equal, the geometry of the universe is flat (Euclidean).
In earlier models, which did not include a cosmological constant term, critical density was initially defined as the watershed point between an expanding and a contracting Universe.
Salinity
Salinity () is the saltiness or amount of salt dissolved in a body of water, called saline water (see also soil salinity). This is usually measured in formula_1 (note that this is technically dimensionless). Salinity is an important factor in determining many aspects of the chemistry
of natural waters and of biological processes within it, and is a thermodynamic state variable that, along with temperature and pressure, governs physical characteristics like the density and heat capacity of the water.
Density
Densities using the following metric units all have exactly the same numerical value, one thousandth of the value in (kg/m). Liquid water has a density of about 1 kg/dm, making any of these SI units numerically convenient to use as most solids and liquids have densities between 0.1 and 20 kg/dm.
Volume of fluid method
i.e., the volume of the fluids is constant. For each cell, properties such as density formula_14 are calculated by a volume fraction average of all fluids in the cell
Annular velocity
The other major variable is the rheology of the drilling fluid. Rheology is sometimes thought of as viscosity to the uninitiated, though improperly. Viscosity (sometimes thought of as its thickness) is a very basic measurement of the fluids resistance to change in movement or flow. The viscosity of a fluid can be measured with a Marsh Funnel. Rheology is the study of viscosity and requires more precise and complicated procedures and equipment for its determination. For drilling fluid applications a rheometer is used.
Total suspended solids
TSS of a water or wastewater sample is determined by pouring a carefully measured volume of water (typically one litre; but less if the particulate density is high, or as much as two or three litres for very clean water) through a pre-weighed filter of a specified pore size, then weighing the filter again after the drying process that removes all water on the filter. Filters for TSS measurements are typically composed of glass fibres. The gain in weight is a dry weight measure of the particulates present in the water sample expressed in units derived or calculated from the volume of water filtered (typically milligrams per litre or mg/L).
Galileo thermometer
Galileo discovered that the density of a liquid is a function of its temperature. This is the key to how the Galileo thermometer works: as the temperature of most liquids increases, their density decreases.
Settling
where "w" is the settling velocity, "ρ" is density (the subscripts "p" and "f" indicate particle and fluid respectively), "g" is the acceleration due to gravity, "r" is the radius of the particle and "μ" is the dynamic viscosity of the fluid.
Specific gravity
The density of water varies with temperature and pressure as does the density of the sample. So it is necessary to specify the temperatures and pressures at which the densities or weights were determined. It is nearly always the case that measurements are made at 1 nominal atmosphere (101.325 kPa ± variations from changing weather patterns). But as specific gravity usually refers to highly incompressible aqueous solutions or other incompressible substances (such as petroleum products), variations in density caused by pressure are usually neglected at least where apparent specific gravity is being measured. For true ("in vacuo") specific gravity calculations, air pressure must be considered (see below). Temperatures are specified by the notation ("T"/"T"), with "T" representing the temperature at which the sample's density was determined and "T" the temperature at which the reference (water) density is specified. For example, SG (20 °C/4 °C) would be understood to mean that the density of the sample was determined at 20 °C and of the water at 4 °C. Taking into account different sample and reference temperatures, we note that, while "SG" = (20 °C/20 °C), it is also the case that "SG" = = (20 °C/4 °C). Here, temperature is being specified using the current ITS-90 scale and the densities used here and in the rest of this article are based on that scale. On the previous IPTS-68 scale, the densities at 20 °C and 4 °C are and respectively, resulting in an SG (20 °C/4 °C) value for water of .
Density logging
Assuming that the measured bulk density (formula_1) only depends on matrix density (formula_8) and fluid density (formula_9), and that these values are known along the wellbore, porosity (formula_10) can be inferred by the formula
Specific properties
Specific properties of a substance are derived from other intrinsic and extrinsic properties (or intensive and extensive properties) of that substance. For example, the density of steel (a specific and intrinsic property) can be derived from measurements of the mass of a steel bar (an extrinsic property) divided by the volume of the bar (another extrinsic property). Similarly, the specific gravity of a liquid is derived from the density of the liquid divided by the density of water (two intrinsic properties).
Litre
It is now known that the density of water also depends on the isotopic ratios of the oxygen and hydrogen atoms in a particular sample. Modern measurements of Vienna Standard Mean Ocean Water, which is pure distilled water with an isotopic composition representative of the average of the world’s oceans, show it has a density of at its point of maximum density (3.984 °C) under one standard atmosphere (760 Torr, 101.325 kPa) of pressure.
Mass flow meter
where "K" is the temperature dependent stiffness of the tube, "K" a shape-dependent factor, "d" the width, "τ" the time lag, "ω" the vibration frequency and "I" the inertia of the tube. As the inertia of the tube depend on its contents, knowledge of the fluid density is needed for the calculation of an accurate mass flow rate.
Viscosity
where formula_58 is the Boltzmann constant, formula_59 the molecular mass, and formula_60 a numerical constant on the order of formula_61. The quantity formula_62, the mean free path, measures the average distance a molecule travels between collisions. Even without "a priori" knowledge of formula_60, this expression has interesting implications. In particular, since formula_62 is typically inversely proportional to density and increases with temperature, formula_10 itself should increase with temperature and be "independent" of density at fixed temperature. In fact, both of these predictions persist in more sophisticated treatments, and accurately describe experimental observations. Note that this behavior runs counter to common intuition regarding liquids, for which viscosity typically "decreases" with temperature.
Relative density
Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity usually means relative density with respect to water. The term "relative density" is often preferred in scientific usage. It is defined as a ratio of density of particular substance with that of water.
Geophysical fluid dynamics
The density of air is mainly determined by temperature and water vapor content, the density of sea water by temperature and salinity, and the density of lake water by temperature. Where stratification occurs, there may be thin layers in which temperature or some other property changes more rapidly with height or depth than the surrounding fluid. Depending on the main sources of buoyancy, this layer may be called a pycnocline (density), thermocline (temperature), halocline (salinity), or chemocline (chemistry, including oxygenation).
Density
In general, density can be changed by changing either the pressure or the temperature. Increasing the pressure always increases the density of a material. Increasing the temperature generally decreases the density, but there are notable exceptions to this generalization. For example, the density of water increases between its melting point at 0 °C and 4 °C; similar behavior is observed in silicon at low temperatures.
Density
The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume. In most materials, heating the bottom of a fluid results in convection of the heat from the bottom to the top, due to the decrease in the density of the heated fluid. This causes it to rise relative to more dense unheated material.
Body fat percentage
With a well engineered weighing system, body density can be determined with great accuracy by completely submerging a person in water and calculating the volume of the displaced water from the weight of the displaced water. A correction is made for the buoyancy of air in the lungs and other gases in the body spaces. If there were no errors whatsoever in measuring body density, the uncertainty in fat estimation would be about ± 3.8% of the body weight, primarily because of normal variability in body constituents.
Relative density
The relative density of a liquid can be measured using a hydrometer. This consists of a bulb attached to a stalk of constant cross-sectional area, as shown in the adjacent diagram.
Oscillating U-tube
The oscillating U-tube is a technique to determine the density of liquids and gases based on an electronic measurement of the frequency of oscillation, from which the density value is calculated. This measuring principle is based on the Mass-Spring Model.
Gladstone–Dale relation
The Gladstone–Dale relation (J. H. Gladstone and T. P. Dale, 1864) is a mathematical relation used for optical analysis of liquids, the determination of composition from optical measurements. It can also be used to calculate the density of a liquid for use in fluid dynamics (e.g., flow visualization; Merzkirch 1987). The relation has also been used to calculate refractive index of glass and minerals in optical mineralogy (Mandarino 2007).
Ubbelohde viscometer
with ρ the density of the liquid, g the Standard gravity and H the average head of the liquid. In this way the viscosity of a fluid can be determined.
Relative density
Another practical method uses three measurements. The sample is weighed dry. Then a container filled to the brim with water is weighed, and weighed again with the sample immersed, after the displaced water has overflowed and been removed. Subtracting the last reading from the sum of the first two readings gives the weight of the displaced water. The relative density result is the dry sample weight divided by that of the displaced water. This method works with scales that can't easily accommodate a suspended sample, and also allows for measurement of samples that are less dense than water.
Vapour density
In many web sources, particularly in relation to safety considerations at commercial and industrial facilities in the U.S., vapour density is defined with respect to air, not hydrogen. Air is given a vapour density of one. For this use, air has a molecular weight of 28.97 atomic mass units, and all other gas and vapour molecular weights are divided by this number to derive their vapour density. For example, acetone has a vapour density of 2 in relation to air. That means acetone vapour is twice as heavy as air. This can be seen by dividing the molecular weight of Acetone, 58.1 by that of air, 28.97, which equals 2.
Fluid dynamic gauge
A fluid dynamic gauge (FDG) is a measurement technique used to study the behaviour of soft deposit layers in a liquid environment. It employs fluid mechanics to determine the thickness of the layer, and can also be used to obtain a measure of its strength. It was inspired by the technique of pneumatic gauging, which relies on a flow of air rather than the process liquid. Fluid dynamic gauging can be conducted as an in-line measuring technique, but is more commonly used as a research tool.
Heavy liquid
A heavy liquid is a solution or liquid chemical substance with a high density and a relatively low viscosity. Heavy liquids are often used for determination of density in mineralogy, for density gradient centrifugation and for separating mixtures.
Methanol (data page)
Here is a similar formula from the 67th edition of the CRC handbook. Note that the form of this formula as given is a fit to the Clausius–Clapeyron equation, which is a good theoretical starting point for calculating saturation vapor pressures:
Data obtained from "Lange's Handbook of Chemistry", 10th ed. and "CRC Handbook of Chemistry and Physics" 44th ed. The annotation, "d a"°C/"b"°C, indicates density of solution at temperature "a" divided by density of pure water at temperature "b" known as specific gravity. When temperature "b" is 4 °C, density of water is 0.999972 g/mL.Except where noted otherwise, data relate to standard ambient temperature and pressure.
Solvent
Often, specific gravity is cited in place of density. Specific gravity is defined as the density of the solvent divided by the density of water at the same temperature. As such, specific gravity is a unitless value. It readily communicates whether a water-insoluble solvent will float (SG < 1.0) or sink (SG > 1.0) when mixed with water.
Body composition
In a research laboratory setting, the overall density of the body (Db) is calculated from its mass and volume (Db = mass/volume). The mass of the body is found by simply weighing a person on a scale. The volume of the body is most easily and accurately determined by completely immersing a person in water and calculating the volume of water from the weight of water that is displaced (via "underwater weighing"). The proportions of water, protein and mineral in the body are found by various chemical and radiometric tests. The densities of water, fat, protein and mineral are either measured or estimated. The equation is then rearranged to solve for the proportion of fat (f) from the other quantities.
Gas
Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as compressibility. Like pressure and temperature, density is a state variable of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is "inversely" proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.
Liquid
The speed of sound in a fluid is given by
formula_4 where "K" is the bulk modulus of the fluid, and "ρ" the density. To give a typical value, in fresh water "c"=1497 m/s at 25 °C.
Hydraulic roughness
Hydraulic roughness is the measure of the amount of frictional resistance water experiences when passing over land and channel features.
One roughness coefficient is "Manning's n-value". Manning’s n is used extensively around the world to predict the degree of roughness in channels. Flow velocity is strongly dependent on the resistance to flow. An increase in this n value will cause a decrease in the velocity of water flowing across a surface.
Relative density
The application of simple physical principles allows the relative density of the unknown liquid to be calculated from the change in displacement. (In practice the stalk of the hydrometer is pre-marked with graduations to facilitate this measurement.)
Sir George Stokes, 1st Baronet
His work is the basis of the falling sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes's law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameter is normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes.
Pressure measurement
In most liquid-column measurements, the result of the measurement is the height "h", expressed typically in mm, cm, or inches. The "h" is also known as the pressure head. When expressed as a pressure head, pressure is specified in units of length and the measurement fluid must be specified. When accuracy is critical, the temperature of the measurement fluid must likewise be specified, because liquid density is a function of temperature. So, for example, pressure head might be written "742.2 mm" or "4.2 in at 59 °F" for measurements taken with mercury or water as the manometric fluid respectively. The word "gauge" or "vacuum" may be added to such a measurement to distinguish between a pressure above or below the atmospheric pressure. Both mm of mercury and inches of water are common pressure heads, which can be converted to S.I. units of pressure using unit conversion and the above formulas.
Particle density (packed density)
Another method based on buoyancy is to measure the weight of the sample in air, and also in a liquid of known density.
API gravity
With the formula presented in the previous section, the API gravity can be readily calculated. When converting oil density to specific gravity using the above definition, it is important to use the correct density of water, according to the standard conditions used when the measurement was made. The official density of water at 60 °F according to the 2008 edition of ASTM D1250 is 999.016 kg/m. The 1980 value is 999.012 kg/m. In some cases the standard conditions may be 15 °C (59 °F) and not 60 °F (15.56 °C), in which case a different value for the water density would be appropriate ("see" standard conditions for temperature and pressure).
Flotation of flexible objects
Consider two plates of infinite width, thickness formula_2, and length formula_3 that are connected by a torsional spring with spring constant per unit width formula_4. Furthermore, let formula_5 be the angle between a plate and the horizontal, and formula_6 the from where the meniscus meets the plate to the horizontal. The distance from the undisturbed water line to the plate's outer edge is formula_7. The density of water is formula_8, the density of air is considered negligible, and the plate density, formula_9, shall be varied. All systems naturally assume a configuration that minimizes total energy. Thus, the goal of this analysis is to identify the configurations (i.e., values of formula_7 and formula_5) that result in a stable equilibrium for a given value of formula_9.
Beer measurement
The most common method measuring the density of a liquid is with a hydrometer; hydrometers can be calibrated with a number of scales. A common scale is that of specific gravity (SG); that is to say the density of a liquid relative to the density of pure water (at a standard temperature). Specific gravity can also be measured by a pycnometer or oscillating U-tube electronic meter. Water has a SG of 1.000, absolute alcohol has a SG of 0.789. Other density scales are discussed below.
Force density
The force density at a point in a fluid, divided by the density, is the acceleration of the fluid at that point.
Fluid dynamics
Mathematically, incompressibility is expressed by saying that the density ρ of a fluid parcel does not change as it moves in the flow field, i.e.,
where "D"/"Dt" is the material derivative, which is the sum of local and convective derivatives. This additional constraint simplifies the governing equations, especially in the case when the fluid has a uniform density.
Reynolds number
For a sphere in a fluid, the characteristic length-scale is the diameter of the sphere and the characteristic velocity is that of the sphere relative to the fluid some distance away from the sphere, such that the motion of the sphere does not disturb that reference parcel of fluid. The density and viscosity are those belonging to the fluid. Note that purely laminar flow only exists up to = 10 under this definition.
DM3 density meter
The DM3 weighs media (slurry) as it travels through a metered section of pipe using a patented, high resolution load cell. Using linear, direct sensing of mass per unit volume, measurement system within a reinforced rubber tube. This in-line section of pipe calculates % dry solids, wet density and wet or dry mass flow units. When coupled with compatible volumetric flow meters and processing units, this system gives a true value for density and mass flow. The DM3 is a bi-directional unit which allows media to flow continuously through either ends. "C" Clamps located within the DM3 allows the flow tube to withhold high levels of pressure encountered. The flow tube was designed to focus on the highest amount of accuracy, resolution, and least amount of weight without compromising mechanical stability and reliability. Because of the sensitivity of measurement provided by DM3, each unit must be programmed and calibrated to accommodate the variation in Earth's gravitational force.
Turbidite
Density-based flow, however, occurs when liquefaction of sediment during transport causes a change to the density of the fluid. This is usually achieved by highly turbulent liquids which have a suspended load of fine grained particles forming a slurry. In this case, larger fragments of rock can be transported at water velocities too low to otherwise do so because of the lower density contrast (that is, the water plus sediment has a higher density than the water and is therefore closer to the density of the rock).
Acoustic metamaterial
The mass density (or just "density") of a material is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm). In all three classic states of matter—gas, liquid, or solid—the density varies with a change in temperature or pressure, and gases are the most susceptible to those changes. The spectrum of densities is wide-ranging: from 10 g/cm for neutron stars, 1.00 g/cm for water to 1.2×10 g/cm for air. Also relevant here are area density which is mass over a (two-dimensional) area, linear density - mass over a one-dimensional line, and relative density, which is a density divided by the density of a reference material, such as water.
Humidity
Absolute humidity is the mass of the water vapor formula_1, divided by the volume of the air and water vapor mixture formula_2, which can be expressed as:
Relative density
Relative density is more easily and perhaps more accurately measured without measuring volume. Using a spring scale, the sample is weighed first in air and then in water. Relative density (with respect to water) can then be calculated using the following formula:
Porosity
The porosity of a rock, or sedimentary layer, is an important consideration when attempting to evaluate the potential volume of water or hydrocarbons it may contain. Sedimentary porosity is a complicated function of many factors, including but not limited to: rate of burial, depth of burial, the nature of the connate fluids, the nature of overlying sediments (which may impede fluid expulsion). One commonly used relationship between porosity and depth is given by the Athy (1930) equation:
Relative density
If the flask is weighed empty, full of water, and full of a liquid whose relative density is desired, the relative density of the liquid can easily be calculated. The particle density of a powder, to which the usual method of weighing cannot be applied, can also be determined with a pycnometer. The powder is added to the pycnometer, which is then weighed, giving the weight of the powder sample. The pycnometer is then filled with a liquid of known density, in which the powder is completely insoluble. The weight of the displaced liquid can then be determined, and hence the relative density of the powder.
Viscosity models for mixtures
where exponential function is written both as formula_243 and as formula_244. The molar volume of the reference fluid methane, which is used to calculate the mass density in the viscosity formulas above, is calculated at a reduced temperature that is proportional to the reduced temperature of the mixture. Due to the high critical temperatures of heavier hydrocarbon molecules, the reduced temperature of heavier reservoir oils (i.e. mixtures) can give a transferred reduced methane temperature that is in the neighborhood of the freezing temperature of methane. This is illustrated using two fairly heavy hydrocarbon molecules, in the table below.The selected temperatures are a typical oil or gas reservoir temperature, the reference temperature of the International Standard Metric Conditions for Natural Gas (and similar fluids) and the freezing temperature of methane (formula_245).
Viscosity models for mixtures
The dense fluid viscosity is thus defined as the viscosity in excess of the dilute gas viscosity. This technique is often used in developing mathematical models for both purely empirical correlations and models with a theoretical support. The dilute gas viscosity contribution becomes important when the zero density limit (i.e. zero pressure limit) is approached. It is also very common to scale the dense fluid viscosity by the critical viscosity, or by an estimate of the critical viscosity, which is a characteristic point far into the dense fluid region. The simplest model of the dense fluid viscosity is a (trunkated) power series of reduced mole density or pressure. 
Jossi et al. (1962) presented such a model based on reduced mole density, but its most widespread form is the version proposed by 
Lohrenz et al. (1964) which is displayed below.
Torque density
Torque density is a measure of the torque-carrying capability of a mechanical component. It is the ratio of torque capability to volume and is expressed in units of torque per volume. Torque density is a system property since it depends on the design of each element of the component being examined and their interconnection.
Köhler theory
where formula_2 is the droplet water vapor pressure, formula_3 is the corresponding saturation vapor pressure over a flat surface, formula_4 is the droplet surface tension, formula_5 is the density of pure water, formula_6 is the moles of solute, formula_7 is the molecular weight of water, and formula_8 is the cloud drop diameter.
Density of air
The vapor pressure of water may be calculated from the saturation vapor pressure and relative humidity. It is found by:
Relative density
If a substance's relative density is less than one then it is less dense than the reference; if greater than 1 then it is denser than the reference. If the relative density is exactly 1 then the densities are equal; that is, equal volumes of the two substances have the same mass. If the reference material is water then a substance with a relative density (or specific gravity) less than 1 will float in water. For example, an ice cube, with a relative density of about 0.91, will float. A substance with a relative density greater than 1 will sink.
Stokes' law
Stokes' law is the basis of the falling-sphere viscometer, in which the fluid is stationary in a vertical glass tube. A sphere of known size and density is allowed to descend through the liquid. If correctly selected, it reaches terminal velocity, which can be measured by the time it takes to pass two marks on the tube. Electronic sensing can be used for opaque fluids. Knowing the terminal velocity, the size and density of the sphere, and the density of the liquid, Stokes' law can be used to calculate the viscosity of the fluid. A series of steel ball bearings of different diameters are normally used in the classic experiment to improve the accuracy of the calculation. The school experiment uses glycerine or golden syrup as the fluid, and the technique is used industrially to check the viscosity of fluids used in processes. Several school experiments often involve varying the temperature and/or concentration of the substances used in order to demonstrate the effects this has on the viscosity. Industrial methods include many different oils, and polymer liquids such as solutions.
Density
In practice, the void fraction is not necessarily air, or even gaseous. In the case of sand, it could be water, which can be advantageous for measurement as the void fraction for sand saturated in water—once any air bubbles are thoroughly driven out—is potentially more consistent than dry sand measured with an air void.
Pressure
Because pressure is commonly measured by its ability to displace a column of liquid in a manometer, pressures are often expressed as a depth of a particular fluid (e.g., centimetres of water, millimetres of mercury or inches of mercury). The most common choices are mercury (Hg) and water; water is nontoxic and readily available, while mercury's high density allows a shorter column (and so a smaller manometer) to be used to measure a given pressure. The pressure exerted by a column of liquid of height "h" and density "ρ" is given by the hydrostatic pressure equation , where "g" is the gravitational acceleration. Fluid density and local gravity can vary from one reading to another depending on local factors, so the height of a fluid column does not define pressure precisely. When millimetres of mercury or inches of mercury are quoted today, these units are not based on a physical column of mercury; rather, they have been given precise definitions that can be expressed in terms of SI units. One millimetre of mercury is approximately equal to one torr. The water-based units still depend on the density of water, a measured, rather than defined, quantity. These "manometric units" are still encountered in many fields. Blood pressure is measured in millimetres of mercury in most of the world, and lung pressures in centimetres of water are still common.
Shallow water equations
where "u" is the velocity in the "x"-direction, "v" is the velocity in the "y"-direction, "w" is the velocity in the "z"-direction, "t" is time, "p" is the pressure, ρ is the density of water, ν is the kinematic viscosity, and "f" is the body force in the "x"-direction.
Barotropic fluid
The density of most liquids is nearly constant (isopycnic), so it can be stated that their densities vary only weakly with pressure and temperature. Water, which varies only a few percent with temperature and salinity, may be approximated as barotropic. In general, air is not barotropic, as it is a function of temperature and pressure; but, under certain circumstances, the barotropic assumption can be useful.
Reynolds number
The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention – for example radius and diameter are equally valid to describe spheres or circles, but one is chosen by convention. For aircraft or ships, the length or width can be used. For flow in a pipe, or for a sphere moving in a fluid, the internal diameter is generally used today. Other shapes such as rectangular pipes or non-spherical objects have an "equivalent diameter" defined. For fluids of variable density such as compressible gases or fluids of variable viscosity such as non-Newtonian fluids, special rules apply. The velocity may also be a matter of convention in some circumstances, notably stirred vessels.
Saltwater intrusion
The figure shows the Ghyben–Herzberg relation. In the equation, formula_1 the thickness of the freshwater zone above sea level is represented as formula_2 and that below sea level is represented as formula_3. The two thicknesses formula_2 and formula_3, are related by formula_6 and formula_7 where formula_6 is the density of freshwater and formula_9 is the density of saltwater. Freshwater has a density of about 1.000 grams per cubic centimeter (g/cm) at 20 °C, whereas that of seawater is about 1.025 g/cm. The equation can be simplified to formula_10.
Saturation vapor density
Saturation vapor density (SVD) is a concept closely tied with saturation vapor pressure (SVP). It can be used to calculate exact quantity of water vapor in the air from a relative humidity (RH = % local air humidity measured / local total air humidity possible ) Given an RH percentage, the density of water in the air is given by . Alternatively, RH can be found by . As relative humidity is a dimensionless quantity (often expressed in terms of a percentage), vapor density can be stated in units of grams or kilograms per cubic meter.
Mass flow meter
If the density changes too often for manual calibration to be sufficient, the coriolis flow meter can be adapted to measure the density as well. The natural vibration frequency of the flow tubes depends on the combined mass of the tube and the fluid contained in it. By setting the tube in motion and measuring the natural frequency, the mass of the fluid contained in the tube can be deduced. Dividing the mass on the known volume of the tube gives us the "density" of the fluid.
Gravitic density meter
A Gravitic density meter is a type of density meter used in multiple industries to measure the density of a slurry flowing through a pipe line. It consists of a flexible rubber hose that deflects when weight is flowing through the hose. A displacement measurement device, usually a high precision laser or load cell, is used to measure how much change has occurred in the system. 
By calculating the change of deflection of the hose, a gravitic density meter can be used to 
find the real time, continuous density.
Base conditions
The density of both gases and liquids depends on the pressure and temperature of the fluid. Thus volumes measured in cold conditions or in pressurised conditions will be lower than the same mass of fluid at warmer or depressurised conditions. This fact gives rise to the necessity of choosing a benchmark pressure and temperature in which all 'net' volumes will be expressed.
Daniel Bernoulli
where P is pressure, ρ is the density of the fluid and u is its velocity.
Fick's laws of diffusion
where is the fluid density (for example, in kg/m). Note that the density is outside the gradient operator.
Density ratio
The density ratio of a column of seawater is a measure of the relative contributions of temperature and salinity in determining the density gradient. At a density ratio of 1, temperature and salinity are said to be "compensated": their density signatures cancel, leaving a density gradient of zero. The formula for the density ratio, R, is:
Specific gravity
Specific gravity is the ratio of the density of a substance to the density of a reference substance; equivalently, it is the ratio of the mass of a substance to the mass of a reference substance for the same given volume. "Apparent" specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance for liquids is nearly always water at its densest (at ); for gases it is air at room temperature (). Nonetheless, the temperature and pressure must be specified for both the sample and the reference. Pressure is nearly always .
Viscosity models for mixtures
where formula_29 is the area of the moving plate and the stagnant plate, formula_30 is the spatial coordinate normal to the plates. In this experimental setup, value for the force formula_31 is first selected. Then a maximum velocity formula_32 is measured, and finally both values are entered in the equation to calculate viscosity. This gives one value for the viscosity of the selected fluid. If another value of the force is selected, another maximum velocity will be measured. This will result in another viscosity value if the fluid is a non-Newtonian fluid such as paint, but it will give the same viscosity value for a Newtonian fluid such as water, petroleum oil or gas. If another parameter like temperature, formula_33, is changed, and the experiment is repeated with the same force, a new value for viscosity will be the calculated, for both non-Newtonian and Newtonian fluids. The great majority of material properties varies as a function of temperature, and this goes for viscosity also. The viscosity is also a function of pressure and, of course, the material itself. For a fluid mixture, this means that the shear viscosity will also vary according to the fluid composition. To map the viscosity as a function of all these variables require a large sequence of experiments that generates an even larger set of numbers called measured data, observed data or observations. Prior to, or at the same time as, the experiments is a material property model (or short material model) proposed to describe or explain the observations. This mathematical model is called the constitutive equation for shear viscosity. It is usually an explicit function that contains some empirical parameters that is adjusted in order to match the observations as good as the mathematical function is capable to do.
Pressure
Liquid pressure also depends on the density of the liquid. If someone was submerged in a liquid more dense than water, the pressure would be correspondingly greater. thus we can say that the depth, density and liquid pressure are directly proportionate. The pressure due to a liquid in liquid columns of constant density or at a depth within a substance is represented by the following formula:
Liquid
Viscosity measures the resistance of a liquid which is being deformed by either shear stress or extensional stress. In other words, viscosity is the resistance of a liquid to flow.
Relative density
As the principal use of relative density measurements in industry is determination of the concentrations of substances in aqueous solutions and these are found in tables of RD vs concentration it is extremely important that the analyst enter the table with the correct form of relative density. For example, in the brewing industry, the Plato table, which lists sucrose concentration by mass against true RD, were originally (20 °C/4 °C) that is based on measurements of the density of sucrose solutions made at laboratory temperature (20 °C) but referenced to the density of water at 4 °C which is very close to the temperature at which water has its maximum density of "ρ"() equal to 0.999972 g/cm (or 62.43 lb·ft). The ASBC table in use today in North America, while it is derived from the original Plato table is for apparent relative density measurements at (20 °C/20 °C) on the IPTS-68 scale where the density of water is 0.9982071 g/cm. In the sugar, soft drink, honey, fruit juice and related industries sucrose concentration by mass is taken from this work which uses SG (17.5 °C/17.5 °C). As a final example, the British RD units are based on reference and sample temperatures of 60 °F and are thus (15.56 °C/15.56 °C).
Fluidized bed
Furthermore, an object with a higher density than the bed will sink, whereas an object with a lower density than the bed will float, thus the bed can be considered to exhibit the fluid behavior expected of Archimedes' principle. As the "density", (actually the solid volume fraction of the suspension), of the bed can be altered by changing the fluid fraction, objects with different densities comparative to the bed can, by altering either the fluid or solid fraction, be caused to sink or float.
Density
To determine volumetric mass density, one must first discount the volume of the void fraction. Sometimes this can be determined by geometrical reasoning. For the close-packing of equal spheres the non-void fraction can be at most about 74%. It can also be determined empirically. Some bulk materials, however, such as sand, have a "variable" void fraction which depends on how the material is agitated or poured. It might be loose or compact, with more or less air space depending on handling.
Relative density
"Vibrating Element Transducers": This type of instrument requires a vibrating element to be placed in contact with the fluid of interest. The resonant frequency of the element is measured and is related to the density of the fluid by a characterization that is dependent upon the design of the element. In modern laboratories precise measurements of relative density are made using oscillating U-tube meters. These are capable of measurement to 5 to 6 places beyond the decimal point and are used in the brewing, distilling, pharmaceutical, petroleum and other industries. The instruments measure the actual mass of fluid contained in a fixed volume at temperatures between 0 and 80 °C but as they are microprocessor based can calculate apparent or true relative density and contain tables relating these to the strengths of common acids, sugar solutions, etc. The vibrating fork immersion probe is another good example of this technology. This technology also includes many coriolis-type mass flow meters which are widely used in chemical and petroleum industry for high accuracy mass flow measurement and can be configured to also output density information based on the resonant frequency of the vibrating flow tubes.
Shallow water equations
Here "η" is the total fluid column height (instantaneous fluid depth as a function of "x", "y" and "t"), and the 2D vector ("u","v") is the fluid's horizontal flow velocity, averaged across the vertical column. Further "g" is acceleration due to gravity and ρ is the fluid density. The first equation is derived from mass conservation, the second two from momentum conservation.
Cavitation modelling
If the pressure is greater than vapor pressure, then the fluid is liquid, otherwise vapor. This means density of liquid water is considered as the density of fluid if the pressure is greater than vapor pressure and the density of water vapor is considered when pressure is less than vapor pressure of water at the ambient temperature.
Density
To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative density" or "specific gravity", i.e. the ratio of the density of the material to that of a standard material, usually water. Thus a relative density less than one means that the substance floats in water.
Lorentz force velocimetry
where formula_41 is the specific electrical conductivity equals to the ratio of the electrical conductivity formula_3 and the mass density of fluid formula_43. formula_44 is a calibration factor that depends on the geometry of the LOFOS system.
API gravity
API gravity is thus an inverse measure of a petroleum liquid's density relative to that of water (also known as specific gravity). It is used to compare densities of petroleum liquids. For example, if one petroleum liquid is less dense than another, it has a greater API gravity. Although API gravity is mathematically a dimensionless quantity (see the formula below), it is referred to as being in 'degrees'. API gravity is graduated in degrees on a hydrometer instrument. API gravity values of most petroleum liquids fall between 10 and 70 degrees.
In 1916, the U.S. National Bureau of Standards accepted the Baumé scale, which had been developed in France in 1768, as the U.S. standard for measuring the specific gravity of liquids less dense than water. Investigation by the U.S. National Academy of Sciences found major errors in salinity and temperature controls that had caused serious variations in published values. Hydrometers in the U.S. had been manufactured and distributed widely with a modulus of 141.5 instead of the Baumé scale modulus of 140. The scale was so firmly established that, by 1921, the remedy implemented by the American Petroleum Institute was to create the API gravity scale, recognizing the scale that was actually being used.
Boundary layer
The thickness of the velocity boundary layer is normally defined as the distance from the solid body to the point at which the viscous flow velocity is 99% of the freestream velocity (the surface velocity of an inviscid flow). Displacement thickness is an alternative definition stating that the boundary layer represents a deficit in mass flow compared to inviscid flow with slip at the wall. It is the distance by which the wall would have to be displaced in the inviscid case to give the same total mass flow as the viscous case. The no-slip condition requires the flow velocity at the surface of a solid object be zero and the fluid temperature be equal to the temperature of the surface. The flow velocity will then increase rapidly within the boundary layer, governed by the boundary layer equations, below.
Force density
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid. Force density is represented by the symbol f 
, and given by the following equation, where "P" is the pressure:
Density
If the body is not homogeneous, then its density varies between different regions of the object. In that case the density around any given location is determined by calculating the density of a small volume around that location. In the limit of an infinitesimal volume the density of an inhomogeneous object at a point becomes: formula_2, where formula_3 is an elementary volume at position formula_4. The mass of the body then can be expressed as
Vertical pressure variation
Whether or not density and gravity can be reasonably approximated as constant depends on the level of accuracy needed, but also on the length scale of height difference, as gravity and density also decrease with higher elevation. For density in particular, the fluid in question is also relevant; seawater, for example, is considered an incompressible fluid; its density can vary with height, but much less significantly than that of air. Thus water's density can be more reasonably approximated as constant than that of air, and given the same height difference, the pressure differences in water are approximately equal at any height.
Relative density
"Buoyant Force Transducer": the buoyancy force produced by a float in a homogeneous liquid is equal to the weight of the liquid that is displaced by the float. Since buoyancy force is linear with respect to the density of the liquid within which the float is submerged, the measure of the buoyancy force yields a measure of the density of the liquid. One commercially available unit claims the instrument is capable of measuring relative density with an accuracy of ± 0.005 RD units. The submersible probe head contains a mathematically characterized spring-float system. When the head is immersed vertically in the liquid, the float moves vertically and the position of the float controls the position of a permanent magnet whose displacement is sensed by a concentric array of Hall-effect linear displacement sensors. The output signals of the sensors are mixed in a dedicated electronics module that provides a single output voltage whose magnitude is a direct linear measure of the quantity to be measured.
Relative density
Since the density of dry air at 101.325 kPa at 20 °C is 0.001205 g/cm and that of water is 0.998203 g/cm we see that the difference between true and apparent relative densities for a substance with relative density (20 °C/20 °C) of about 1.100 would be 0.000120. Where the relative density of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller.
Viscosity
In general, the viscosity of a system depends in detail on how the molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relations for the linear shear viscosity or the "transient time correlation function" expressions derived by Evans and Morriss in 1985. Although these expressions are each exact, calculating the viscosity of a dense fluid using these relations currently requires the use of molecular dynamics computer simulations. On the other hand, much more progress can be made for a dilute gas. Even elementary assumptions about how gas molecules move and interact lead to a basic understanding of the molecular origins of viscosity. More sophisticated treatments can be constructed by systematically coarse-graining the equations of motion of the gas molecules. An example of such a treatment is Chapman–Enskog theory, which derives expressions for the viscosity of a dilute gas from the Boltzmann equation.
Particle image velocimetry
In some cases the particles will, due to their higher density, not perfectly follow the motion of the fluid (gas/liquid). If experiments are done in water, for instance, it is easily possible to find very cheap particles (e.g. plastic powder with a diameter of ~60 µm) with the same density as water. If the density still does not fit, the density of the fluid can be tuned by increasing/ decreasing its temperature. This leads to slight changes in the Reynolds number, so the fluid velocity or the size of the experimental object has to be changed to account for this.
Density
The effect of pressure and temperature on the densities of liquids and solids is small. The compressibility for a typical liquid or solid is 10 bar (1 bar = 0.1 MPa) and a typical thermal expansivity is 10 K. This roughly translates into needing around ten thousand times atmospheric pressure to reduce the volume of a substance by one percent. (Although the pressures needed may be around a thousand times smaller for sandy soil and some clays.) A one percent expansion of volume typically requires a temperature increase on the order of thousands of degrees Celsius.
Flow conditions
In fluid measurement, the fluid's flow conditions (or flowing conditions) refer to quantities like temperature and static pressure of the metered substance. The flowing conditions are required data in order to calculate the density of the fluid at flowing conditions. The flowing density is in turn required in order to compensate the measured volume to quantity at base conditions.
Density meter
Many density meters can measure both the wet portion and the dry portion of a sample. The wet portion comprises the density from all liquids present in the sample. The dry solids comprise solely of the density of the solids present in the sample.
Soil mechanics
Density, Bulk Density, or Wet Density, formula_19, are different names for the density of the mixture, i.e., the total mass of air, water, solids divided by the total volume of air water and solids (the mass of air is assumed to be zero for practical purposes):
Fluid dynamics
All fluids are viscous, meaning that they exert some resistance to deformation: neighbouring parcels of fluid moving at different velocities exert viscous forces on each other. The velocity gradient is referred to as a strain rate; it has dimensions formula_14. Isaac Newton showed that for many familiar fluids such as water and air, the stress due to these viscous forces is linearly related to the strain rate. Such fluids are called Newtonian fluids. The coefficient of proportionality is called the fluid's viscosity; for Newtonian fluids, it is a fluid property that is independent of the strain rate.
Vertical pressure variation
When density and gravity are approximately constant (that is, for relatively small changes in height), simply multiplying height difference, gravity, and density will yield a good approximation of pressure difference. Where different fluids are layered on top of one another, the total pressure difference would be obtained by adding the two pressure differences; the first being from point 1 to the boundary, the second being from the boundary to point 2; which would just involve substituting the and values for each fluid and taking the sum of the results. If the density of the fluid varies with height, mathematical integration would be required.
Flow conditions
There are broad general methodologies used to calculate the density of a liquid at specific conditions. In order to discuss a specific methodology, one must choose a liquid that holds sufficient interest to warrant a calculation specific to it. EOS 87.3 is a density calculation for seawater; API chapter 11 specifies calculations pertaining to oil, fuels and natural gas liquids.