4 Density Determination Using The Displacement Method; 4.1 Physical Principle - Sartorius YP50K Betriebsanleitung

4 Density Determination using the Displacement Method

4.1 Physical Principle

In density determination according to the displacement method,
the quantity of a fluid of known density (reference density) as
displaced by a test specimen is determined. The density of
reference weights is determined by weighing.
Figure 1: Displacement Method Principle
The following measurement values are to be determined:
– The total mass m of the Pycnometer of specific volume V
0
which is filled with a reference fluid of density p
capacity V .
0
– The total mass m1 of the Pycnometer, which contains the test
specimen of known mass mt and is filled to cubic capacity V
with the reference fluid of density p
In order to take account of the buoyancy in air in both cases,
it is necessary to know the air densities p
balance was operated.
Since the object is a solid body, its volume V
volume of the displaced fluid quantity. If volumes V
known, it is possible to deduce the object volume from the mass
values m and m as determined by weighing. Finally, the desired
0 1
density p results from the values for mass and volume.
t
The accuracy of the density determination method is heavily
dependent on the accuracy to which mass values m
be determined. Therefore, high demands are placed on weighing
for the determination of density. Thus balances are required
which, due to their high resolution, can also be used to compare
the mass of weights (mass comparators).
6
,
p
to cubic
0
1
.
1
and p at which the
a0 a1
is the same as the
t
and V are
0 1
and m can
0 1
Fundamentally, it is necessary to take two weight measurements
in order to determine the quantity of weight displaced. Figure 1
shows the actual measurement task and the physical variables
involved.
As in the case of comparing the mass of weights, the following
physical influences must also be taken into consideration or
eliminated during the determination of density:
– The zero point drift of the balance due to changes of tempera-
ture at the installation location, because the possibility of small
temperature changes cannot be ruled out even with the best of
air conditioning.
– Linearity deviations of the balance, because even in the case of
the finest linearization of the characteristics by the manufacturer
certain residual deviations must be assumed.
For these reasons the following possible methods are available
for the determination of density:
1. Absolute weighing with elimination of drift. Consideration of the
linearity deviations when assessing density if the characteristics
of the balance are known; otherwise in the uncertainty analysis
only.
2. Mass comparison through substitution weighing as a highly
accurate method suitable for cases where the balance is used for
density determination in individual cases only.