The oscillating U-tube is a technique to determine the density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 of liquid

Liquid

Liquid is one of the three classical states of matter . Like a gas, a liquid is able to flow and take the shape of a container. Some liquids resist compression, while others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly...

s and gas

Gas

Gas is one of the three classical states of matter . Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point , boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons...

es based on an electronic measurement of the frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 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

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

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

Glass tube

Glass tubes or glass tubing are hollow pieces of borosilicate or flint glass used primarily as laboratory glassware. Glass tubing is commercially available in various thicknesses and lengths. Glass tubing is frequently attached to rubber stoppers....

 (oscillating U-tube) which is electronically excited into undamped oscillation (at the lowest possible amplitude). 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

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

 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 volume

Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

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

Mass

Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 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 the digital density meter, the mechanic oscillation

Oscillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

 of the U-tube is e.g. electromagnetically transformed into an alternating voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

 of the same frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

. The period τ can be measured with high resolution and stands in simple relation to the density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 ρ of the sample in the oscillator:


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 and water

Water

Water is a chemical substance with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. Water is a liquid at ambient conditions, but it often co-exists on Earth with its solid state, ice, and gaseous state . Water also exists in a...

. They employ suitable measures to compensate various parasitic influences on the measuring result, e.g. the influence of the sample’s viscosity and the non-linearity caused by the measuring instrument’s finite mass.

In 1967 the company Anton Paar GmbH presented the first digital density meter for liquids and gases at ACHEMA. It was the first instrument to employ the oscillating U-tube principle by Dr. Hans Stabinger and Prof. Hans Leopold for density determination.

Sources

• Stabinger, Hans: "Density Measurement using modern oscillating transducers", South Yorkshire Trading Standards Unit, Sheffield 1994
• ISO 15212-1