{{no footnotes, date=March 2014 U-Tube

The oscillating U-tube is a technique to determine the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...

liquid A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter (the others being solid, gas, ...

s and gases based on an electronic measurement of the

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...

of oscillation, from which the density value is calculated. This measuring principle is based on the Mass-Spring Model. The sample is filled into a container with oscillation capacity. The eigenfrequency of this container is influenced by the sample's

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...

. This container with oscillation capacity is a hollow, U-shaped

glass tube Glass tubes are mainly cylindrical hollow-wares. Their special shape combined with the huge variety of glass types (like borosilicate, flint, aluminosilicate, soda lime, lead or quartz glass), allows the use of glass tubing in many applications. Fo ...

(oscillating U-tube) which is electronically excited into undamped oscillation. The two branches of the U-shaped oscillator function as its spring elements. The direction of oscillation is normal to the level of the two branches. The oscillator's eigenfrequency is only influenced by the part of the sample that is actually involved in the oscillation. The

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...

involved in the oscillation is limited by the stationary oscillation knots at the bearing points of the oscillator. If the oscillator is at least filled up to its bearing points, the same precisely defined

always participates in the oscillation, thus the measured value of the sample's

can be used to calculate its density. Overfilling the oscillator beyond the bearing points is irrelevant to the measurement. For this reason the oscillator can also be employed to measure the density of sample media that flow through the tube (Continuous Measurement). In modern digital density meters, Piezo elements are used to excite the U-tube whereby optical pickups determine the period of oscillation. This period τ can be measured with high resolution and stands in simple relation to the

ρ of the sample in the oscillator: :

\rho = A \cdot \tau^2 - B

A and B are the respective instrument constants of each oscillator. Their values are determined by

calibrating In measurement technology and metrology, calibration is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known a ...

with two substances of the precisely known densities ρ1 and ρ2. Modern instruments calculate and store the constants A and B after the two calibration measurements, which are mostly performed with

air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing f ...

and

water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...

. They employ suitable measures to compensate various parasitic influences on the measuring result, e.g. the influence of the sample's

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the int ...

and the non-linearity caused by the measuring instrument's finite mass as well as aging effects of the glass (reference oscillator). In 1967 the company Anton Paar GmbH presented the first digital density meter for liquids and gases employing the oscillating U-tube principle at ACHEMA.

Sources

* Otto Kratky et al., ''Device for density determination.'' US Patent 3523446, https://patents.google.com/patent/US3523446 *Stabinger, Hans: "Density Measurement using modern oscillating transducers", South Yorkshire Trading Standards Unit, Sheffield 1994 * ISO 15212-1

External links

Anton Paar GmbH

Dr. Hans Stabinger
Measuring instruments