## Digital density measurement using the oscillating U-tube principle

The example of a tuning fork shows that by applying a mechanical impulse one can generate a sound with a characteristic pitch. This sound is the result of the oscillation created by deflecting the prongs of the tuning fork. A determining factor in the pitch of the note obtained, and thus of the oscillating frequency, is the mass of the tuning fork.

Digital density measurement puts this relationship to use by means of the U-tube oscillation principle. The extremely fine capillaries are made to oscillate by a piezoelectric or magnetic transducer with a characteristic frequency.

The resulting resonant frequency of the U-tube will depend on the mass of the filled sample. This frequency can be measured very accurately and used to calculate the density of the sample. The physical relationship of oscillation frequency (the reciprocal of the period of oscillation) to density is very simple and linear.

Accordingly, calibration is only possible with two standards as a rule – air and water.

## What is Density?

Density ρ is a characteristic property of materials and indicates the relationship of mass m to volume V. It is measured in g/cm³ or kg/m³. For high-precision measurements, the most significant influencing factor is the temperature of the sample. It is essential therefore that modern density meters are equipped with efficient temperature control of the measurement room.

## Relationship of density to temperature

Temperature [°C] | Ultra-pure Water [kg/m³] | Air [kg/m³] |
---|---|---|

4 | 999,972 | 1,270 |

20 | 998,203 | 1,205 |

60 | 983,191 | 1,060 |

Density measurement is often also used for determining the concentrations of mixtures of fluids. Strictly speaking, this applies to mixtures of two substances, also known as binary systems. Extensive concentration tables can be created in DS7800 for our customers to facilitate everyday measurements. However, digital density measurement can also be of significant benefit in analysing complex solutions such as beer or fruit juices.

## 3 measuring methods and the advantages of digital density measurement

#### Areometer

The areometer works on the principle of buoyancy as a function of mass. The glass float sinks into the liquid sample until its massdependent weight force and the buoyancy force are in equilibrium. The density that corresponds to the depth of immersion is shown on the scale inside the float column.

An areometer is inexpensive but difficult to read in case of highly viscous or dark samples and very fragile. It also requires a sample volume of at least 100 ml and the maximum accuracy of 0.001 g/cm³ demands a lengthy exact temperature control.

#### Pycnometer

The pycnometer – a glass flask whose inner volume can be very precisely determined and reproduced – is a device used for measuring the gravimetric density.

You first weigh the empty flask and then the one filled with the liquid sample. The density is then calculated from the measured weight of the sample.

A pycnometer can be used for a wide temperature and pressure range and is more accurate than an areometer. However, the measure ment takes several hours due to the elaborate weighing and requires skilled personnel.

#### U-Tube Oscillator

This method takes advantage of the fact that the oscillation frequency of a body is a function of its mass. A U-shaped capillary is filled with the liquid sample and piezoelectric or magnetic oscillations are induced. The mass and thus the density of the sample can be calculated from the resulting eigenfrequency of the U-tube oscillator.

Density meters using the oscillating U-tube method

allow for a highly accurate measurement at a controlled temperature and with easily reproducible results within minutes, require a sample volume of no more than 1 ml and are easy to handle.