Digital Density Meters – Measurement Principle

This section contains some information about the basic principles of density determinations with digital density meters. The information is divided in several chapters. Please click on the desired section in the menu.

What is Density

The density of a material is defined as its mass per volume.

The most common units for density are the SI unit kilogram per cubic meter (kg/m³) and the cgs unit gram per cubic centimeter (g/cm³).

The density depends on temperature. The tables below show the density of air and water in relation to the temperature:

Density of dry air at 1013.25 hPa

Density of pure water

What is Specific Gravity

For historical reasons the density is often expressed as specific gravity (SG) or relative density (SR) which is a dimensionless quantity as it is the ratio of two densities.

If the reference is not exactly stated it is normally assumed to be be water. As the density depends on temperature, the specific gravity depends on the temperatures to which the densities of the substance and the reference relate. The two temperatures are specified by the notation (Ts/Tr) with Ts representing the temperature at which the sample’s density has been determined and Tr the temperature at which the reference density is specified. Commonly used are for example SG(20°C/20°C) and SG(20°C/4°C).

The specific gravity was usually determined with so called Pycnometers. Pycnometers are flasks normally made of glass. The Pycnometer is weighed empty, full of a liquid with a known density (normally water) and full of the liquid whose specific gravity is to be determined. For the later two weighings the Pycnometer must be thermostatted precisely to the reference temperature.

The calculation of the specific gravity with the three masses is easy to perform:

m₀ = mass of the empty Pycnometer
m₁ = mass of the Pycnometer filled with water
m₂ = mass of the Pycnometer filled with the sample

If both weighings are performed at 20°C SG(20°C/20°C) is yielded. The actual volume of the Pycnometer has no influence on the result and the result does not depend on the calibration of the balance either. The only requirement is that the balance reads linearly with force. However it must be noted that a balance does not determine the exact masses required for the above calculation. This is due to the buoyancy effect of the air (Archimedes Principle). If we determine the specific gravity of air using the weights determined with the balance, the result would be 0 (which is of course not true).

When calculating the specific gravity by means of the formula given above using the weights displayed by the balance, the so called apparent specific gravity SG_A is yielded. In order to determine the true specific gravity SG_V, the weighings would have to be performed in vacuo (for this reason the subscript V is used). SG_V can be calculated based on SG_A.

The specific gravity is often measured to determine concentrations of substances in aqueous solutions: The specific gravity of the solution is determined and converted to a concentration with a table SG vs. concentration. It is extremely important to use the correct form of the specific gravity when using such tables!

How does a Digital Density Meter work?

Measuring principle

KEM manufactures digital density meters based on the oscillating U-tube technique: The sample to be measured is filled into a U-shaped tube which is induced to vibrate. The eigenfrequency of the oscillation of the U-tube is influenced by the mass and therefore by the density of the sample.

The animations below illustrate this measuring principle:

A ball attached to leaf spring which is mounted on a wall starts to oscillate when it is pressed down with a finger and released. The frequency of the oscillation depends on the weight of the ball: A heavier ball (blue) oscillates with a lower frequency than a lighter ball (orange). If both balls have exactly the same size, the frequency of oscillation depends thus on the density of material the ball is made of: The higher the density of the material, the lower the frequency of oscillation.

The same happens with the U-tube of the density meter: The higher the density of the sample inside the cell, the lower the oscillation frequency.  The animations below illustrate this: The cell filled with water (high density, blue) oscillates with a higher frequency than the cell filled with air (low density, grey).

The oscillation frequency of the U-tube filled with a sample can be expressed as follows:

⍴ = density of the sample in the cell
Vc= internal volume of the U-tube
m_c = mass of the empty U-tube
K = U-tube specific constant

With this calibration factor (F) it is then possible to calculate the density of any sample:

Viscosity error

In practice, the oscillation frequency of the U-tube does not only depend on the density of the sample but also on it’s viscosity: If the U-tube is filled with a highly viscous sample it’s oscillation is dampened due to the shear forces which occur in the liquid. The observed oscillation frequency is too low and the density value yielded too high. The picture below illustrates the magnitude of this error in relation to the viscosity of the sample.

The graph illustrates that the measuring error caused by the sample’s viscosity is always less than 0.001 g/cm³.

• Digital density meters which offer only a 3 place accuracy like the DA-100 and the DA-130 density meters from KEM do thus not require any correction of this error.
• For samples with a viscosity below 10 mPa·s the shear forces do not cause any measurable error.

The digital density meters DA-640, DA-645 and DA-650 from KEM feature an automatic correction of the error caused by the samples viscosities. In order to evaluate the cell specific data required to correct this error, several measurements of viscous density standards must be performed with each instrument in our production plant. Many applications as for example alcohol content determinations in spirits do not require any correction of the viscosity error and it does not make sense for the corresponding customers to pay for the extra work required to evaluate the cell specific data required for the correction of the viscosity error. For this reason, KEM offers the three models mentioned above as well without automatic correction of the viscosity error at a considerably lower price (DA-640B, DA-645B and DA-650B).

In order to ensure traceability to recognized national standards of the results yielded with a digital density meter, system performance checks should be performed with certified density standard material. If the samples measured require a correction of the measuring error caused by their viscosity, viscous density standard material should be used for these system performance checks. For this reason, KEM offers certified standard reference material with different viscosities (see section ‘Accessories’ of the corresponding instruments).

Temperature control

Highly accurate density measurements require a highly accurate temperature control of the measuring cell. KEM’s laboratory density meters are equipped with a solid state thermostat a so called Peltier element for this purpose. Peltier elements create a heat flux between the junction of two different materials, they transfer heat from one side of the device to the other side against the temperature gradient (from cold to hot) with the consumption of electrical energy. Peltier elements are compact, have no moving parts and can be used for heating and cooling. When used for cooling, Peltier elements are only 5-10 % as efficient compared to vapor-compression devices used in normal refrigerators. Due to their low efficiency they thus have a relatively high power consumption.

In order to minimize energy consumption, the DA-640, DA-645 and DA-650 density meters from KEM

• are equipped with strong fans to cool the hot side of the Peltier elements. In order to prevent the accumulation of fine dust on the surface of the cooling fins (which would reduce the cooling efficiency), the density meters are equipped with a fine dust filter, which is easily accessible from outside (see picture below).
• feature a freely programmable time switch which allows to automatically deactivate the thermostat when the instrument is not in use.

To measure and control the temperature inside the cell, KEM’s density meters are equipped with several NTC temperature sensors. NTC temperature sensors offer one important advantage compared to Pt100 and Pt1000 temperature sensors: Under ideal conditions, good quality Pt100 and Pt1000 sensors have a drift of approximately 0.005 °C per year. To ensure a temperature measurement accuracy of 0.02 °C density meters equipped with this type of temperature sensors must be checked and readjusted if required every 5 years at least. NTC temperature sensors have a drift of less than 0.002 °C per year only. To ensure a temperature measurement accuracy of 0.02 °C KEM density meters must thus be checked every 10 – 15 years only. NTC temperature sensors show – contrary to Pt100 and Pt100 sensors – a non linear dependence between resistance and temperature. For this reason, KEM’s certified temperature sensors come with a so called thermistor table which is stored in the density meter and serves to accurately convert the measured resistance to a temperature by Lagrange Interpolation.

Sometimes is not possible to ensure a 100% homogeneous temperature distribution in the measuring cell as there is always a (small) heat flow from the outside. If a density meter is used in environments with high temperature fluctuations this non stable heat flow can cause measurement errors. To avoid such errors KEM’s density meters are equipped with a reference temperature sensor which enables the instrument to automatically correct errors caused by fluctuations of the ambient temperature.