{{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 ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

liquid Liquid is a state of matter with a definite volume but no fixed shape. Liquids adapt to the shape of their container and are nearly incompressible, maintaining their volume even under pressure. The density of a liquid is usually close to th ...

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. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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 In linear algebra, an eigenvector ( ) or characteristic vector is a Vector (mathematics and physics), vector that has its direction (geometry), direction unchanged (or reversed) by a given linear map, linear transformation. More precisely, an e ...

of this container is influenced by the sample's

mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...

. 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 regions in 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 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 An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...

and

water Water is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...

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

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

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 The International Organization for Standardization (ISO ; ; ) is an independent, non-governmental, international standard development organization composed of representatives from the national standards organizations of member countries. Me ...

15212-1

External links

Anton Paar GmbH

Dr. Hans Stabinger
Measuring instruments