The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite polynomials must be carried until the fourth order to correctly describe the energy equation. The viscosity and thermal coefficients, previously obtained by J.Y. Yang et al 1,2 through the Uehling-Uhlenbeck approach, are also derived here. Thus the construction of a lattice Boltzmann method for the quantum fluid is possible provided that the Bose-Einstein and Fermi-Dirac equilibrium distribution functions are expanded until fourth order in the Hermite polynomials.

A key comparison was performed in order to compare national measurement systems to determine volume of liquids, particularly at fixed volumes of 20 L and 100 mL. The participants were CENAM (Mexico), NIST (United States of America), NRC/MC (Canada), SP (Sweden), PTB (Germany), INRIM (former IMGC, Italy), NMIA (Australia) and INMETRO (Brazil). CENAM acted as pilot laboratory. The measurements were carried out from December 2003 to March 2005.The chosen values of volume (20 L and 100 mL) are both representatives of the Calibration and Measurement Capabilities (CMCs) declared by most of the participating national metrology institutes.The transfer standards (TSs) were three stainless steel pipettes for volume at 20 L and six commercially available glass pycnometers for volume at 100 mL. Prior to the beginning of the key comparison, the 20 L TSs were tested by CENAM, SP and NMIA The results of the test phase showed excellent values for both repeatability and reproducibility.During the CCM.FF-K4, the results of most of the laboratories showed good agreement with the reference values. The best estimation of the measurands, as reported by the participants showed a general agreement better than ±0.0025% for volume of liquids at 100 mL and 20 L.Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (MRA).

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This work presents an electronic circuit for double-timing pulse interpolation applied to compact piston provers (also referred as small volume provers). Compact provers are usually employed to prove meters with pulsed outputs. API and ISO standards [1,2] recommend a minimum of 10.000 pulses per run to obtain a resolution better than ± 0.01%. Since the volume of fluid displaced by a compact prover is relatively small, the number of pulses produced during a proving run is often considerably less than 10.000 pulses. Pulse interpolation techniques are commonly used to increase resolution and to diminish uncertainty during a proving run by estimating the fractional part of meter pulses within the time interval of the calibration. In this way, pulse interpolation techniques are essential to obtain accurate flow measurements and to allow the calibration of meters with compact provers. Our implementation uses a compact piston prover with an internal volume of 12 L and maximum flow capacity of 180 L/min. In order to implement the double-timing pulse interpolation method, we have used a Pentium D, 2.80 GHz installed with a 16-bit counter/timer board. Data acquisition and control software were written using VB .Net. An electronic circuitry was built to activate/deactivate counters gates, and to collect pulses. Some requirements and limitations of pulse interpolation techniques such as circuitry testing and pulse stability are also discussed in this work.

Abstract. The necessity of standardizing and traceability to SI in micro scale flow has been subject of intense discuss in the metrology community. The Bureau International of Poids et Mesures (BIPM) has encouraged National Metrology Institutes to be prepared to participate, in 2024, of the first Key Comparison event planned in this area. With this aim, the present work describes a standard system based on gravimetric method for fluid delivery and respective quantification, which was developed by the National Institute of Metrology, Quality and Technology (INMETRO) in order to provide traceability for microflow rate measurement. The system performance and capability were evaluated. An important goal of the work is contribute to the establishment and advancement of researches on microfluidic issues in the Institute.