3 The Measuring Principle
C76IB003EN-E
13
3 The Measuring Principle
Definition of density and specific gravity
The density
ρ
of a sample is defined as mass divided by volume:
The specific gravity SG is calculated by dividing the density of a sample by the
density of pure water at 20 °C:
Density and Specific Gravity values are highly temperature-dependent.
The oscillating U-tube method
The sample is introduced into a U-shaped borosilicate glass tube that is being
excited to vibrate at its characteristic frequency. The characteristic frequency
changes depending on the density of the sample. Through a precise
determination of the characteristic frequency and a mathematical conversion, the
density of the sample can be measured.
The density is calculated from the quotient of the period of oscillations of the U-
tube and the reference oscillator:
Concentration measurement
In binary mixtures, the density of the mixture is a function of its composition. Thus,
by using density/concentration tables, the density value of a binary mixture can
be used to calculate its composition. This is also possible with so-called quasi
binary mixtures. These are mixtures containing two major components and some
additional components which are present in very small concentrations compared
to the two main components. Many decarbonated soft drinks, for example, can be
considered to be quasi binary solutions of sugar in water because the
concentration of flavors and acids are very small compared to sugar and water.
Thus, the sugar concentration can be measured with a density meter.
KA, KB...
Apparatus constants
Q ...........
Quotient of the period of oscillation of the U-tube divided
by the period of oscillation of the reference oscillator
f
1
, f
2
.......
Correction terms for temperature, viscosity and
nonlinearity
ρ
m
V
-----
=
SG
ρ
Sample
ρ
Water
-----------------
=
density
KA
Q
2
f
1
KB
f
2
×
–
×
×
=
