22 Bewertungen

# Density and density measurement

Density is a physical parameter that plays a vital and important role in all material states, whether solid, liquid, or gaseous. It is measured throughout industry to gain insight into materials, for example their purity, concentration of components, and composition. The density (and concentration) of liquid products has a great impact on their quality, behavior, and use.

The focus of this page is on the density of fluids, meaning the density of liquids and gases. It is dedicated to explaining what “density” is, how this parameter is defined and measured, the history of density measurement, the different methods available, and also how to ensure you get the best density result by using the techniques of Good Density Measurement™.

## What’s new in density measurement? Everything.

After more than 50 years of incremental improvements, Anton Paar redefines digital density measurement and shapes the future of the technique once again.

### Density meters

Anton Paar offers a wide range of density meters to suit different requirements:

### Density tables

Here you will find the official density tables for the following substances:

## Overview table: Density measurement techniques

Find out more about each device type by clicking the title.

 Measurement device Can be used for Advantages Disadvantages Hydrometers Liquids Low cost Small size Easily broken Requires relatively high sample volume Requires high solvent volume for cleaning Tedious cleaning routine Errors reading off the result Pycnometers Liquids Low cost Small size Easily broken Requires relatively high sample volume Requires high solvent volume for cleaning Tedious cleaning routine Errors reading off the result Gas pycnometers Solids Accurate Robust Small size Requires regular calibration Hydrostatic balances Liquids Powder Granules Solids Highly accurate Large size Highly sensitive to temperature (requires air-conditioned room) Time-consuming to operate Requires skilled operator Digital density meters (benchtop) Liquids Highly accurate Easy to operate Small size Low sample required Low solvent volume required for cleaning Easy to clean Possible to automate sample filling Data transfer and storage Filling checks and alerts given - Digital density meters (portable)[26] Liquids Highly accurate Easy to operate Portable Small size Low sample required Low solvent volume required for cleaning Easy to clean Data transfer and storage Cell may break if dropped accidently

## What is density?

### Density definition

Density (“true density”) is the relation of mass and volume. As mass is independent of external conditions, such as buoyancy in air or gravity, it corresponds to weight in vacuo. The symbol of density is the Greek letter rho ρ:

$$\rho = {mass \over volume} \left[ {g \over cm^{3}} \right] or \left[ {kg \over m^{3}} \right]$$

Equation 1: The true density ρ in kg/m3 or g/cm3 of a liquid is defined as its mass m divided by its volume V. The mass m corresponds to the weight in vacuum and is independent of external conditions such as buoyancy in air or gravity.

Table 1: Densities of common fluids at 20 °C
ρ [g/cm³]
Air 0.00120
Ethanol (alcohol) 0.79
Water 0.99820
Fruit juice 1.042
Syrup 1.40

A multi-layered cocktail (Figure 1): Fluids of higher density such as juices or syrup will sink; they are heavier and have less buoyancy. Fluids of lesser density such as alcohol or water have more buoyancy, they swim on top.

### What affects density?

#### Temperature

A material’s volume and state changes with temperature. Temperature therefore has an important influence on the density. Consequently, an accurate density measurement requires accurate temperature determination and good temperature stability[1].

An excellent example of the temperature dependence of density is the thermometer. With increasing temperature, the volume of alcohol inside the thermometer expands and rises. Same mass but more volume means less density.

Temperature is a vital factor for precise density measurement, in which you need precise temperature control or algorithms for compensation. A temperature difference of 0.1 °C might result in a density error of up to 0.0001 g/cm³.[2]

#### Air pressure and altitude

The local air pressure and altitude also have an impact on the density of liquids and modern density meters compensate for these influencing factors so they do not affect the results.

#### Viscosity

Depending on how you measure density, the viscosity of the substance may affect the result. When measuring with a digital density meter, for example, the oscillation frequency measured not only depends on the density of the filled sample but also on its viscosity. Due to the oscillation of the tube (see here for more information on the technology used), shear forces (a sort of friction) occur between the fluid and the tube wall and result in damping. Damping increases with increasing viscosity of the sample and that results in a density over-reading (the density value shown is too high[3]). Modern density meters compensate this effect and automatically perform a viscosity correction using a special technique in which two different oscillation modes are applied.[4]

### Anomaly of water

Water is a unique liquid and reaches the density maximum at a temperature of 3.98 °C. Starting at 3.98 °C upwards, the volume of water increases and it becomes less dense. The same applies when water is cooled, just the other way round.[5] This anomaly causes lakes to freeze from the top down and water that is colder than 4 °C to freeze and swim on top.

### Density units

A physical property like density is investigated for several reasons and is therefore reported in several units. The most frequent density unit is kilogram per cubic meter (kg/m³), used in petrochemistry, for example. In other industries, density is reported in gram per cubic centimeter (g/cm³). The conversion factor in this case is 1000 (1 g/cm³ = 1000 kg/m³). Density might also be reported in kilogram per liter (kg/L) or gram per liter (g/L) or converted into a concentration value (to represent, for example, API numbers, °Brix, °Plato).

#### True density & apparent density

True density ρ is often confused with apparent density ρapp. The apparent density of a sample is weight in air per volume:

$$\rho _{app} = {W \over V}$$

Equation 2: The apparent density ρapp of a sample is defined as the weight in air W divided by the sample’s volume V.

The values of apparent density and true density are different, even if their units are identical. The true density of air at 20 °C as measured in a density meter is 0.0012 g/cm³ whereas the apparent density of air at 20 °C is 0.0000 g/cm³ – air on a balance does not give a reading.

Apparent density can be calculated from true density considering the buoyancy of the sample in air and the weight and density of a reference weight in steel or brass. Nowadays, steel is defined as the material of choice for the weights. Earlier, brass was used.

$$\rho _{app} = {\rho _{true}- \rho _{air} \over 1- \cfrac{\rho _{air}}{\rho _{steel \hspace{1mm} or \hspace{1mm} brass}}}$$

Equation 3: Converting the true density of a sample ρtrue into apparent density ρapp. This conversion takes the true density of air (ρair≈ 0.0012 g/cm³) and true density of brass (ρbrass = 8.4 g/cm³) or steel (ρsteel = 8.0 g/cm³) into account.

When do we use the apparent density? When determining filling volumes with a balance from a density result, the apparent density is the required value, for example.

#### Specific gravity & apparent specific gravity (also called relative density and apparent relative density)

Another vital unit for reporting density is Specific Gravity (SG) as found in several industries. Specific gravity is the measured density of a sample divided by the density of water at a certain temperature. For this reason, it is also called relative density (RD) because it is related to the density of water.

$$SG= {\rho _{true} \over \rho _{W}}$$

Equation 4: Specific Gravity (SG) is defined as sample density ρ divided by the density of water ρW at a specific temperature.

SG20/4 means sample density at 20 °C divided by water density at 4 °C. SG20/20 means sample density at 20 °C divided by water density at 20 °C. Comparing the results of the same sample SG20/20 and SG20/4 shows a difference because the water density is different at 4 °C and 20 °C.

The apparent specific gravity SGapp (sometimes referred to as apparent relative density Dapp) is dimensionless, which means it has no unit. It is calculated by dividing the apparent density of a sample ρapp by the apparent density of pure water ρapp, water at defined temperatures.

$${D_{app}{20\over20}} = SG_{app}{20\over20}={{{\rho _{app}}at20^{\circ}C}\over{{\rho _{app, water}}at20^{\circ}C}}$$

Equation 5: Apparent specific gravity DappT/T (or SGappT/T) is related to defined temperatures of the apparent density of the sample (ρapp) and pure water (ρapp, water).

Table 2: Comparison of air and water density units at 20 °C
Sample Air at T = 20 °C, p = 1013 mbar Water at T = 20 °C
True Density ρ [g/cm³] 0.00120 0.99820
Specific gravity SG²⁰/₂₀ 0.00120 1
Specific gravity SG²⁰/₄ 0.00120 0.99823
Apparent specific gravity SGₐₚₚ²⁰/₂₀ 0 1

#### Others

Depending on the measurement – and also on the industry – different units are used. For example:

Table 3: Other units used based on density measurement
Unit For Industry
°Brix Concentration of sugar Soft drinks
%w/w ethanol °Proof 60 °F Alcohol concentration in distillates Spirits
API Density 15 °C, API Specific Gravity 15 °C Crude oil, fuel, diesel, lubricants Petroleum
%w/w Sulfuric Acid Sulfuric acid up to 94 %w/w Chemical
°Plato Concentration Beer, wine
°Baumé Concentration Beer, wine

## Density measurement

### History

#### Archimedes – the Eureka moment

Density measurement has a long history – it actually dates back 2200 years to the times of King Hieron II of Syracuse. In a nutshell, King Hieron II had a crown made of pure gold. The goldsmith was accused of having added some silver to the crown. Archimedes, a great mathematician, physicist, engineer, inventor and astronomer, was asked to prove – or disprove – that Hieron’s crown consisted of nothing but gold, without destroying it.

Archimedes went home to think about the problem. Exhausted from all the pondering over this difficult task, he took a bath. (Okay, this part of the story is probably made up but read on to see what he found.) When he sank into a very full bathtub, it started to overflow. He realized that the overflowing water stood in direct relation to the immersion of his body volume into the water. We all know what he did next: he ran across town – naked – yelling: ‘Eureka!’ [I found it!].

In order to verify the gold content of King Hieron’s crown, he took the crown and a bar of pure gold of the exact same weight as the crown. He immersed both objects in a water container. The crown displaced more water than the gold bar, the water went up higher – so the crown obviously had more volume. It had the same mass, but more volume – that means lower average density. The crown was less dense than pure gold, so the gold had to have been mixed with another metal. This experiment helped Archimedes discover the relation of mass to volume.[6][7] Hydrometers and the hydrostatic balance are both based on the Archimedes principle.

For more information on the relationship between mass and density, see here.

#### Hypatia – the hydrometer

In the 4th century Hypatia of Alexandria, a philosopher, mathematician, teacher, and first female contributor to mathematics in ancient times, developed the hydrometer (which was then called a hydroscope) for measuring the density of liquids.[8][9]

#### Galileo Galilei – the hydrostatic balance

Weighing precious metals in air and then in water was a common practice among jewelers in Europe when Galileo Galilei, the famous Italian mathematician, astronomer, and physicist, described an instrument in the 16th century that is still used for high-precision density measurements today: The hydrostatic balance. Again, an object is immersed in the fluid, but here the object is attached to a highly sensitive balance, and the density values are read from the movement of the counterweight.[10]

#### Anton Paar – the digital density meter

In 1967 the first-ever digital density meter, DMA 02 C, was presented at the Achema exhibition in Frankfurt by Anton Paar, a high-tech company based in Graz, Austria. DMA 02 C caused a sensation: For the first time it was possible to measure the density of a sample digitally – and that with a precision of 10-6 g/cm3 with a very small volume of a few milliliters.

### Overview of density measurement techniques

#### Hydrometers

A hydrometer is a floating glass body with a bulb filled with a metal weight and a cylindrical stem with a scale. The hydrometer is immersed in the sample and the density of the sample can be read directly from the scale: The deeper it sinks, the less dense is the sample. If a hydrometer is immersed in a glass of water, it would sink deeper than it would in a glass of syrup because syrup is denser than water.[11][12]

This method is based on the Archimedes principle. There are many different hydrometers available depending on the use. The number read off the scale is not always density but also derived quantities. A lactometer is used for measuring the density (creaminess) of milk, a saccharometer for measuring the concentration of sugar in a liquid, or an alcoholometer for measuring the ethanol content in spirits.[13][14] Hydrometers are probably the most basic and inexpensive density measurement tools, but they require good temperature control, which can be quite complicated, and a large sample volume (up to 100 mL). Due to the small size of a hydrometer’s scale, results can easily be misread.[15] In comparison to these manual devices, a digital hydrometer is a small, portable digital density meter based on the oscillating U-tube principle.

#### Pycnometers

A pycnometer consists of a glass flask and a stopper (sometimes with an integrated thermometer). It is placed on a balance and after determining the weight of the empty pycnometer you can calculate its volume by filling in a calibration liquid of known density (e.g. water) using the corresponding definition of density (volume = weight / density).

Afterwards, by weighing the pycnometer filled with sample the density of the sample can be determined (density = weight / volume).[16]

Using a pycnometer can yield accurate and reliable results if the temperature control and the balance are equally precise. Pycnometers are affordable, but can break easily. The method is rather slow and time-consuming and a skilled operator is needed. Another drawback is the large sample volume that is required, usually 10 mL to 100 mL.[17]

#### Hydrostatic balances

The hydrostatic balance is based on the Archimedes principle.[18] It consists of a very precise balance and a sinker (e.g. a sphere) of exactly known volume that is attached to one scale pan. The sinker is immersed completely in the sample and the apparent weight loss of the sinker is determined by weighing out. The apparent weight loss of the sinker equals the weight of the fluid it displaces, so the precise volume and weight are known.[19]

Hydrostatic balances are reliable and precise. However they are expensive and very time-consuming. Another disadvantage is that installation (e.g. insulation on a concrete foundation) is challenging and an accurate temperature control is essential.[20]

Establishing adequate temperature control is only possible by means of highly sophisticated air conditioning.

#### Digital density meters

Modern digital density meters are based on the oscillating U-tube principle. The tube, usually a U shaped glass tube, is excited and starts to oscillate at a certain frequency depending on the filled-in sample. Through determination of the corresponding frequency the density of the sample can be calculated.

From 1967, the launch of the first-ever digital density meter, to 2018, all benchtop density meters worked according to the “Forced Oscillating Method” of the U-tube principle. However, this technology has now reached its limits. An improved method of using the U-tube principle – the Pulsed Excitation Method – has been available from 2018. For more information, see here.

Digital density meters based on the oscillating U-tube principle are very effective instruments that allow fast and precise measurements of fluid densities over a wide range of temperature and pressure. They measure the true density (density in vacuo), so there is no influence of air buoyancy or gravity.

In contrast to traditional static methods (such as hydrometers, pycnometers, or hydrostatic weighing) only a small amount of sample is needed, approx. 1 mL to 2 mL. Digital density meters are easy to operate and there are no special requirements regarding ambient conditions or temperature control.[17][21]

Modern high-precision density meters additionally provide a viscosity correction even viscosity determination and a reference oscillator to enable accurate results over a large range of densities, temperatures, and viscosities.

The oscillation of the cell is mechanically or electronically induced. The instrument constants (which are used to adjust the density meter) are used to calculate the density of a sample from its oscillation frequency or oscillation period.

For an in-depth comparison of the different oscillating U-tubes available, see here.

If you are currently carrying out density measurements with a hydrometer or pycnometer you can check here how much money and time you would save by using a digital density meter or digital hydrometer. The return on investment depends on the number of samples you measure per day.

### In-depth: Measuring density with a digital density meter

Not all density meters are created equal. Density meters differ – sometimes significantly -- depending on the accuracy class, manufacturer, and the characteristics of the samples to be measured.

For an overview of Anton Paar’s benchtop density meters, see here.

You can also measure density in the field with a portable density meter, even in hazardous environments with risk of explosions. See here.

### Parts of a digital density meter

For an overview of commercially available density meters and their features and benefits, see here.

The following describes the parts of a benchtop density meter which all such devices have in common. For density measurement “in the field” there are smaller, lighter, and portable density meters available which are also intrinsically safe.

For a comparison of the different oscillating U-tube measuring methods, see here.

#### Sensor shape and material

The sensor is the heart of the digital density meter. Typically, the sensors are mostly straight or U-shaped tubes. They can be made of glass, e.g. borosilicate glass 3.3, metals or metal alloys, or plastics depending on the application and resistance towards the sample and cleaning agents.[22] This page gives details about the 3 different-shaped U-tubes available.

#### Countermass

A countermass is linked to the measuring tube to reduce parasitic resonances (“external oscillations”) from other components, e.g. electronic parts. It is linked to the housing of the density meter by elastic supports and acts like a mechanical filter for external oscillations. The countermass has a resonance frequency that lies far below the frequencies used for density measurement. The countermass also ensures that the nodal points of the tube are constantly in position. The sample volume is set by the nodal points and therefore only the mass changes depending on the filled fluid while the volume remains stable.[23]

#### Reference oscillator

In case of sensors made of glass a built-in reference oscillator eliminates not only long-term drifts due to the aging effects of the material but also temperature changes that influence the elasticity. A reference oscillator therefore means that only one single adjustment is used to cover the whole temperature range and provides the possibility to perform temperature scans of a sample.[23] This is of great benefit if you want to measure the density at different temperatures without having to perform a density adjustment at each temperature. For users who measure at just one temperature or have time to perform a density adjustments at different temperatures, if required, there are density meters without a reference oscillator which also achieve excellent results at up to 4-digit accuracy.

#### Temperature regulation

Temperature regulation of the cell is typically performed with Peltier elements, which have now displaced water baths. This advantageous technology has now replaced the use of water baths. Peltier elements make use of the Peltier effect, a heat flux due to electric current: One side of a Peltier element heats up while the other side cools down depending on the direction of the current flow[24] Peltier elements therefore allow both effective heating and cooling of the measuring cell and additionally provide precise and fast temperature regulation.

#### Excitation and evaluation of the oscillation

There are a number of ways to excite the U-tube:

• Magnets: A system of magnets and coils can be used to provide electronic excitation and keep the system oscillating continuously at the characteristic frequency. While magnets are comparatively inexpensive, the drawback of magnets is that they put additional weight on the oscillating sensor, which has a negative influence on the achievable accuracy.
• Piezo element: The most precise method to excite a sensor is using a Piezo element, which is a crystal or ceramic material that changes its dimension upon applied electrical voltage. However, this technology requires some safety measures in the electronic circuits as this requires high voltages.

There are a number of ways to pick up and evaluate the oscillation signal:

• Optical pick-ups: Optical pick-ups can detect a light beam that is interrupted by a minute coating on the oscillating tube. The pick-ups then record the oscillation period. This technology is very precise, simple, and affordable.
• Piezo elements: Piezo elements can also be used to represent the period of oscillation if the usable effect of the element is inverted. While the excitation of the sensor is enabled by applying electrical voltage to the Piezo element, detection of the oscillation is also possible: A second Piezo element is then pressurized by the moving sensor unit periodically and generates electric voltage that represents the period of oscillation very accurately. Magnets can be used to measure the period of oscillation as well. Whenever a magnet passes the coil, a little current is induced which can be evaluated.
• Digital signal processors: Although analog processing of the oscillation pattern is robust and affordable the precision is limited. Nowadays digital signal processors (DSP) are state of the art and provide significant advantages over the analog technology, even allowing the recognition of energy loss connected to sample viscosity. This is possible due to simultaneous determination of not only the characteristic frequency but also its first harmonic oscillation and the quality factor.

The method behind the excitation: 2 possibilities

• “Forced Oscillation Method” (1967 – 2018): Evaluation of the oscillation pattern is performed by keeping the measuring cell continuously oscillating at the characteristic frequency. By recording this constant oscillation not only the frequency of oscillation but also damping can be measured. This is the original oscillating U-tube principle which has limitations in accuracy.
• “Pulsed Excitation Method” (2018 – future): The latest development in the evaluation of the oscillation pattern for oscillating U-tubes includes an interruption of the characteristic frequency that leads to a natural fade-out of the oscillation. This procedure is repeated continuously and allows evaluation of the fade-out behavior of the oscillation as well. A series of values is obtained simultaneously, resulting in additional benefits that are not only notable in viscosity measurement and viscosity correction but also in a better repeatability of the density result and improved detection of sample inhomogeneity (e.g. gas bubbles). Further, this new technology enables condition monitoring of the measuring cell.[25]

## How to ensure good density results?

Good Density Measurementrequires care and attention in five basic areas:

Consistently following a few simple guidelines will help you on your way to accurate and reproducible density results.

Since 1967 Anton Paar GmbH has specialized in providing highly accurate and reliable density meters for research and industry. This brochure sums up our experience and insights into measurement practice gained in over forty years. Follow these guidelines and you will be well on your way to accurate and reproducible density results.

## References

1. www.propertiesofmatter.si.edu/Changing_Temp.html (last visited 11.12.2017)
2. www.petro-online.com/article/analytical-instrumentation/11/anton-paar/the-facts-andnbspfigures-of-digitalnbspdensity-measurement-nbsp/1304 (last visited 22.1.2018)
4. Fritz et al. Applications of densiometry, ulrsonic seed measurements, and ultra low shear viscosimetry to aqueaos fluids. J. of Phys.Chem. B Vol 104, No 15, 3463–3470, 2000
5. butane.chem.uiuc.edu/pshapley/GenChem1/L21/2.html (last visited 12.12.2017)
6. www.longlongtimeago.com/once-upon-a-time/great-discoveries/eureka-the-story-of-archimedes-and-the-golden-crown/ (last visited 11.12.2017)
7. www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html (last visited 11.12.2017)
8. cs-exhibitions.uni-klu.ac.at/index.php (last visited 11.12.2017)
9. daggn.wordpress.com/culture-site/been-jon-woo/been-jon-woos-career/ (last visited 11.12.2017)
10. galileo.rice.edu/sci/instruments/balance.html (last visited 11.12.2017)
11. www.britannica.com/technology/hydrometer (last visited 11.12.2017)
13. hypatiainventions.blogspot.co.at (last visited 11.12.2017)
14. www.kettletokeg.com/blog/2012/06/hydrometer-refractometer-what-are-they/ (last visited 11.12.2017)
15. learn.kegerator.com/refractometers-vs-hydrometers/ (last visited 11.12.2017)
16. www.dcu.ie/sites/default/files/mechanical_engineering/pdfs/manuals/DensityDeterminationManual.pdf (last visited 11.12.2017)
17. H. Fehlauer and H. Wolf Density reference liquids certified by the Physikalisch-Techische Bundesanstalt Meas.Sci.Technol. 17 (2006) 2588–2592
18. www.britannica.com/science/Archimedes-principle (last visited 12.12.2017)