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Archimedes Principle, Gaspycnometer and Geopycnometer


von Amalia Aventurin (Autor)

Praktikumsbericht / -arbeit 2013 11 Seiten

Geowissenschaften / Geographie - Sonstiges


Table Of Contents

I. Archimedes Principle measurement

II. Gaspycnometer measurment

III. Geopycnometer measurment

IV. Conclusion

V. References

I. Archimedes Principle measurement

The Archimedes method is used to determine the volume of an irregular shaped solid object. This is done by determining the dry mass of an object (which is given), the fully water saturated mass, measured with the Kern 572, and the mass of the sample when hanging in a water-filled bowl. Both measurements – the saturated and hanging-mass in a water-bowl – were done five times each by about 19.5°C air temperature and about 18°C water temperature. For this experiment we used two samples: G1 is a black stone with small mica particles and bigger white quartz inclusions. This stone is coarse-grained and compacted and therefore it could be a gabbro. G2 is a greenish sandstone with small particles and lesser compaction. The results of the measurements are shown in table 1.

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Tab. 1: Measured masses by the Archimedes principle. The “saturated weights” is the mass of the sample by a water-saturation over one week. The “immerged weights” show the mass by hanging the sample in a water-filled bowl.

The Archimedes principle is based on the fact that an object immersed in a fluid will displace a certain amount of fluid. The amount of given fluid displaced depends on the density of the object. If the density of the fluid (ρfluid) and the mass of the object (mdry) is known, you can write the formula like this:

ρobj = mdry/vb = mdry / [(msat- mimm )/ρfluid] (1)


G1: ρobj = 1674.5 / 1063.6 = 1.574 g/cm3

G2: ρobj = 1901.6 / 1210.17 = 1.571 g/cm3

In order to determine the object's density (ρobj), the parameter to determine is the mass of the object immersed in the fluid (mimm). In case of a rock sample with certain porosity you can use equation (1) to determine the bulk density (correlates to ρobj) or bulk volume of the sample. In order to calculate the matrix density (ρma) the following equation can be written like this:

ρma = msat / vma = (msat .ρfluid) / [ mdry – ( msat -mimm)] (2)

Examples (with used ρfluid= 0.9982 g/cm3):

G1: ρma = (1676.4 * 0.9982) / [1674.5-(1676.4-612.8)] = 2.737 g/cm3

G2: ρma = (1985.4 * 0.9982) / [1901.6 - (1985.4-777.4)] = 2.853 g /cm3

Where msat is the mass of a core sample saturated with a given fluid, vma is the matrix volume and mimm the mass of displaced fluid. With these formulations you can write:

Ø= vp /vb = (vb - vma) / vb = (msat - mdry) / mimm (3)

to determine the porosity.


G1: Ø = (1676.4 - 1674.5) / 612.8 = 0.0031= 0.35%

G2: Ø = (1985.4-1901.6) / 777.4= 0.1077 = 10.79%

Vp = (msat -mdry) / ρfluid (4)

Displaced water mass = msat – mimm/ ρfluid (density of water = 0.9982 g/cm³ at 20°C).


G1: Vp = mdw= (1676.4- 612.8)/0.9982 = 2.14 cm³

G2: Vp= mdw= (1985.4-777.4)/0.9982 = 83.95 cm³

All results with the used formulas are shown in table 2.



ISBN (eBook)
ISBN (Buch)
522 KB
Institution / Hochschule
Rheinisch-Westfälische Technische Hochschule Aachen – Lehrstuhl für Geologie, Geochemie und Lagerstätten des Erdöls und der Kohle
archimedes principle gaspycnometer geopycnometer petrophysics


  • Amalia Aventurin (Autor)



Titel: Archimedes Principle, Gaspycnometer and Geopycnometer