NMISA
Volume/Density
Measurements of Irregular
Objects at NMISA
Name: Bongani Ndlovu
Date: 26 September 2016
TQM-5126-1
CONTENTS
• Introduction
• Experimental details
• Volume determination
• Results
• Conclusion
TQM-5126-1
INTRODUCTION
• Volume of regular objects
• Measure dimensions and apply the formula
𝑉=
𝜋𝑟 2 ℎ
𝑉 = 𝑙𝑏ℎ
𝑉=
4
𝜋𝑟 3
3
INTRODUCTION
• Volume of Irregular
objects
• OIML-shaped
• Not always possible
to measure
dimensions
• Use Archimedes’
Principle
ARCHIMEDES’ PRINCIPLE
𝐹𝐵
m
𝑚𝑔
• The buoyancy force 𝐹𝐵 on a
submerged object equals the
weight of the displaced fluid
• 𝐹𝐵 = 𝑉𝜌𝑓 𝑔
• 𝐹𝑔 = 𝑚𝑔
• Can find the submerged volume
of the object
• 𝑉=
Fluid
𝑚
𝜌𝑓
ARCHIMEDES’ PRINCIPLE APPLIED
• Technique (a): weighing in fluid, most accurate
•
S. W. Hughes, “Archimedes revisited: a faster, better, cheaper method of accurately
measuring the volume of small objects,” Physics Education, vol. 40, no. 5, pp. 468-474,
2005.
EXPERIMENTAL DETAILS
• NMISA uses automated VC1005
• NMISA’s VC1005 rests on the stable granite table
• Minimal vibrations
FLUID BATH
• Inner bath: FC-40 fluid thermally stable, single phase liquid (-57 to 165 degC)
• Heavy (density ~1870 kg/m^3): More buoyancy, less weighing errors, can break
glass
• Outer bath: Sterilized distilled water, prevents glass breaking
• FC-40 fluid calibrated for density before measurements
EXPERIMENTAL SETUP
• Temperature sensor mounted close to where weighing
occurs
• ClimaLog to measure air T, P, RH
• Data processing on a computer
HOW IT WORKS
• Uses conventional masses
• For a mass piece taken at a temperature of 20 0C, the conventional
mass 𝑚𝑐 is defined as the mass of a reference of density 8000 kg/m3
that the mass piece balances in air density of 1.2 kg/m3
• 𝑚 = 𝑚𝑐 1 −
1.2
8000
+ 𝑉(1.2)
• Compares the test mass to the reference mass
(known volume)
• Detects volume difference
• Results include volume and density
VOLUME DETERMINATION
1.2
(𝑚𝑐𝑡 −𝑚𝑐𝑟 ) 1 −
𝐵∆𝑚𝑤
8000
∆𝑉 =
−
𝜌𝑓 − 1.2
𝜌𝑓 − 1.2
• 𝑚𝑐𝑡 , 𝑚𝑐𝑟 : conventional mass for the test,
reference
𝑚𝑤𝑟1 +𝑚𝑤𝑟2
2
• ∆𝑚𝑤 = 𝑚𝑤𝑡 −
weighing difference
• 𝐵= 1
𝜌𝑎𝑖𝑟
−
𝜌𝑏𝑤
: drift eliminated
: balance correction factor
• 𝑉𝑡𝑒𝑠𝑡 = 𝑉𝑟𝑒𝑓 + ∆𝑉
Mettler Toledo, Switzerland: Operating instructions Volume Comparator VC1005, vol. Ver. 2.9, 2009.
RESULTS – DENSITY SPHERES
• Volume:
• Density:
RESULTS – OIML WEIGHTS
Volume:
• KRISS volume was calculated from the calibration
certificate values for mass and density
RESULTS – OIML WEIGHTS
Density:
• KRISS density and uncertainty were obtained from
the calibration certificate
• −1 < 𝐸𝑛 < 1
CONCLUSION
• Calculated density uncertainties show significant
improvement from the current NMISA’s CMCs
• Volume and density results are in agreement with
those found at KRISS
• Therefore we have accurately measured the
volumes and densities of mass pieces (50 g – 1 kg)
THANK YOU!