Noel Bignell

Using small sonic nozzles as secondary flow standards

Abstract When using sonic nozzles as secondary laboratory standards they must be calibrated. Standard methods of calculating discharge coefficient values are not useful with small nozzles of uncertain geometries. Calibration against primary standards is discussed. Alternatively, one nozzle can be directly compared with another by several techniques using ratios of pressure and temperature and sometimes flow. Several factors change the nozzle coefficient. Estimates of the changes due to pressure and humidity are given. Adiabatic cooling produces temperature changes that affect the nozzle coefficient by changing the throat area. Depending on the nozzle holder the inlet gas can also be cooled with an effect on the flow. Nozzles may be made by metal machining or by shrinking glass tubes. Sapphire cutting heads, which may be bought, can be used as sonic nozzles. An example of a promising but unsuitable form of nozzle having a square throat is given. The pressure dependence of these is discussed. The use of nozzles in arrays, for automatic operation as flow standards, is described.

Comparison techniques for small sonic nozzles

Abstract Two techniques are described that allow small sonic nozzles to be compared. The first allows one nozzle to be compared easily and accurately with another at the same inlet conditions. The second allows a nozzle with a particular inlet pressure to be compared with the same nozzle at a different inlet pressure. A description of the calibration of two sets of sonic nozzles is given in some detail. The first is a set of nominally equal nozzles and the second is a set of nozzles of varying sizes used to produce a range of closely spaced flows for the calibration of flow meters. The redundant measurement scheme with its design and variance-covariance matrices is described, and some results of actual measurements given. Results of the measurement of the change of discharge coefficients with Reynolds number for nozzles of throat diameters 0.7, 1.0 and 1.4 mm are given and compared with previous work.

Final report on key comparison CCM.P-K4 of absolute pressure standards from 1 Pa to 1000 Pa

A key comparison of low absolute pressure standards, organized under the auspices of the Consultative Committee for Mass and Related Quantities (CCM), was carried out at seven national metrology institutes (NMIs) between March 1998 and September 1999 in order to determine the degrees of equivalence of the standards at pressures in the range 1 Pa to 1000 Pa. The primary standards, which represent two principal measurement methods, included five liquid-column manometers and four static expansion systems. The transfer standard package consisted of four high-precision pressure transducers: two capacitance diaphragm gauges to provide high resolution at low pressures, and two resonant silicon gauges to provide the required calibration stability. Two nominally identical transfer packages were used to reduce the time required for the measurements, with Package A being circulated among laboratories in the European region (Istituto di Metrologia G. Colonnetti, Italy; National Physical Laboratory, UK; Physikalisch-Technische Bundesanstalt, Germany) and Package B in the Asia-Pacific region (CSIRO-National Measurement Laboratory, Australia; Korea Research Institute of Standards and Science; National Physical Laboratory of India). The results obtained were normalized using data obtained from simultaneous calibrations of the two packages at the pilot laboratory (National Institute of Standards and Technology, USA). The degrees of equivalence of the measurement standards were determined in two ways: deviations from key comparison reference values and pairwise differences between these deviations. Apart from results from one NMI that were identified as outliers, the absolute-pressure standards of the participants were generally found to be equivalent and the results revealed no significant relative bias between the two principal methods tested.

The Effect of Dissolved Air on the Density of Water

An experiment to measure the change in density of water which has been saturated with air is described and the results given. The 80 points taken in the range 4°C to 20°C have been fitted to the equation Δρ = -4.612 + 0.106 t with density in 10-3 kg m-3 and t in °C, and confidence limits have been given. Other results are discussed.

Thermal effects in small sonic nozzles

Abstract A study has been made of the effect of temperature on the coefficient used to characterise small sonic nozzles. Due to adiabatic cooling of the gas stream to −30 °C in the throat, the body of the nozzle is also cooled. The temperature drop of several bodies during operation was measured. Using a gas flow standard that can operate in continuous mode, measurements were made of the change of the nozzle coefficient with temperature. The real gas correction factor, the discharge coefficient and the area of the throat are investigated to explain the observed change in the nozzle coefficient. Changes in these quantities are inadequate to explain the results. The maximum percentage changes likely to be experienced are estimated for a range of nozzle throat diameters.

Volumetric positive-displacement gas flow standard

Abstract A new volumetric standard system has been developed capable of calibrating gas flow meters continuously. It is made of double concentric spheres. The inner sphere defines a basic volume that is divided into two parts by a flexible diaphragm. A water draw method used to measure this volume gave 25.343 l with 1 ml uncertainty. A changing pressure signal causes a change of flow direction every cycle. A careful treatment of this transient signal provides corrections to the basic formula for the mass flow rate. An uncertainty analysis of the new standard system shows that the most important factor is air temperature. Multiple nozzles were calibrated singly and in parallel by the new system to check the upper limit of the flow rate which is about 2 m 3 /h with 0.15% expanded uncertainty.

Reproducibility of E-class weights

In the uncertainty of E-class weights the need is recognized for an additional component, termed reproducibility, that comes from a time dependence slower than that of the repeatability of the balance but shorter than that of the drifts in mass values that are sometimes seen. The observed scatter over times of the order of one year in the values of check weights is assumed to be due to the repeatability, which is calculable, and the reproducibility which can hence be found by subtraction. Values are given for weights used in this laboratory. The possible origin of this reproducibility uncertainty is discussed and the conclusion reached that it is not related solely to surface phenomena.

A fixed point on the pressure scale: carbon dioxide vapor pressure at 273.16 K

The vapor pressure of carbon dioxide in equilibrium with the liquid at 0.01 °C has been measured; the value is found to be 3.48608 ± 0.00017 MPa. Results were found to depend on the purity of the carbon dioxide. The relatively simple procedures reported herein produced carbon dioxide samples of sufficient purity to be suitable for use of this vapor-pressure value as a pressure fixed point.

The change in water density due to aeration in the range 0-8°C

The observation, by Kozdon, Dammermann and Wagenbreth, of a minimum at 3 °C in the density change when water is saturated with air has been investigated by a magnetic float technique. The results presented for the range 0-8 °C do not confirm this minimum nor an earlier one reported by Marek whose results have been re-analysed. When the new low-temperature results are combined with earlier ones the relationship found between density change Δ (t), and temperature t °C, for the range 0-20 °C, is Δ (t) = (-4.873 + 0.1708 t - 0.003108 t2) g/m3 with an estimated uncertainty, 99%, of 0.2 g/m3.

The H2O (I) - H2O (III) - H2O (L) Triple Point of Water as a Fixed Pressure Point

An apparatus to utilize the H2O (I) - H2O (III) - H2O (L) triple point as a pressure fixed point is described. A technique to establish the three phases simultaneously in the cell is described. The value of the pressure was measured with a piston gage and was found to be (208.829 ? 0.025) MPa at the 99.7 percent confidence level.