Supplement - Sartorius YDK 01-0D Betriebsanleitung

Supplement

This supplement should help you to
better understand how the formulas and
allowance factors used here have been
derived.
Fundamental Principles
Mass (g)
Density =
Volume (cm
The Archimedean Principle:
A solid immersed in a liquid is exposed to
the force of buoyancy (G). This value is the
same as that of the weight of the liquid
displaced by the volume of the solid. The
volume of an immersed solid V (s) equals
the volume of the displaced liquid V (fl).
The following are determined:
1. The weight of the sample in air: W (a)
2. The buoyancy of the solid in liquid: G
The specific gravity of a solid is:
sample mass
ρ =
=
sample volume
If the density ρ (fl) of the displaced liquid
is known, then
Mass (fl)
V (fl) = =
ρ (fl)
Therefore:
W (a) · ρ (fl)
ρ =
G
3
)
W (a) W (a)
=
V (s) V (fl)
G
ρ (fl)
Calculation
The specific gravity of a solid
is calculated from the ratio
ρ : W (a) = ρ (fl) : W (a) – W (fl),
where:
W (a) · ρ (fl)
ρ =
W (a) – W (fl)
W (a) – W (fl) = G =
buoyancy of the sample
The density of a liquid is determined
from the buoyancy of the plummet, which
has a defined volume
G
V (fl) =
V
where:
ρ
= specific gravity of a solid
ρ (fl)
= density of the liquid
W (a) = weight of the solid in air
W (fl) = weight of the solid in liquid
G = buoyancy of the plummet
V = volume of the solid
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