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In an earlier paper a new group of coordinate transformations was obtained for reference systems tied to massive bodies. In the present paper a relation is established between the metric coefficients of such systems and the energy of the signal. The
1. The relative method of measuring the flow rates of water through a turbine is realized by simple means and provides a sufficient accuracy for the needs of hydrostation operation. 2. Further works of design organizations, operating services, an
In searching for a target letter while reading, participants make more omissions when the target letter is embedded in frequent function words than when it is embedded in less frequent content words. According to the guidance-organization (GO) model,
Tests have shown that at the instant the valves are switched pressure oscillations do arise both at the output of the system and in the space under the bell. The value of these oscillations at the output amounts to • (4-6) mm Hg, and in the spaces under the bell to ~: (10-15) m m Hg. These oscillations occur at a frequency of about 4 cps and die out very quickly; as a rule their duration does not exceed 1 sec. The oscillations are due to the inertia of the bells and the rapid opening of the valves which connect the space under the bells to the tested gas meter. These oscillations can undoubtedly be reduced by a slower opening of the valves, and if necessary by using a smoothing volume provided between the valves and the tested gas meter. However, even without suppression the above short oscillations cannot produce any appreciable effect on the checking of the gas meters. SUMMARY The experimental equipment made at the VNIIM has vessels in a continuous automatic operation. With pipes 50 purposes a continuous flow of air at the rate of 40 mS/hr at pipe diameter to 100-150 m m it is possible to increase still
OF T E M P E R A T U R E
shown the possibility of using two bell-type metering mm in diameter this equipment can provide for checking a maximum error of the order of 0.2%. By raising the further the size of the controlled flows.
ON T H E R E A D I N G S
OF D I F F E R E N T I A L -
S. S. K i v i l i s
V. E. O l e i n i k o v
Translated from Izmeritel'naya Tekhnika, No. 3, pp. 53-55, March, 1962 It is customary in the USSR to calibrate and check differential-manometer flowmeters at normal temperatures (20 • 8" C) [1, 2, 3]. Additional errors in the readings of the instrument, however, arise under operating conditions when the temperature of the ambient air differs from normal. This effect is patticularly pronounced when float-type differential-manometer flowmeters axe used. The additional error in them is due to the effect of temperature on the density of the liquid which fills the differential manometer, on the volume of the instrument containers and the float, and on the depth of the immersion of the float in the liquid. It should, however, be noted that the problems related to the temperature error in the float-type differential manometers are inadequately and at times incorrectly dealt with in literature. Thus, in [4, 5, 6] it is suggested that in designing constricting devices, it is possible to account for the effect of temperature on the liquid which fills the instrument by using an appropriate coefficient in the flow equation. The values of this coefficient which are given in the table with respect to the temperature of the differential manometer are calculated from t h e formula
ap= cht ('r162
where Ap is the pressure difference; C is the coefficient of proportionality; h t is the difference in the height of the balancing liquid columns in the differential manometer at temperature I ; 7h and 7 are the specific gravities of the balancing and of the operating * liquids respectively at temperature t . It is obvious that it is only possible to determine directly the value of h t in a tubular U-shaped manometer. It is impossible to determine the value of h t for float-type differential manometers which ate calibrated at a normal temperature (i.e., with a known value of hz0), and thus in practice (1) cannot be applied.'* 9 Bo-"--~here and henceforth the operating liquid is understood to be the liquid located above the balancing liquid. 9 * Formula (1) is also given in German standards for measuring flows , but there it is clearly stated that it can only be applied to U-shaped manometers. 250
The above problem is further confused in  by recommending on the one hand the application of (1) in calculating constricting devices, and on the other hand by providing for calculating the relative temperature error an equation* in which the variation of the specific gravity of liquids in a differential manometer is taken into account for a second time. The formulas given in  for computing the flow in float-type differential manometers only hold in the case when the temperature of the instrument is equal to 20* C. For other temperature values of the ambient medium it is recommended in  to multiply the reading by a correcting coefficient: f k= V
vy.t-~t Yy. 20 - y2o
where ), and Yt are the specific gravities of the balancing and the operating liquids, respectively at temperature t_ ; 7 y . Y" rand Z0 720 are the corresponding specific gravities at 20* C.
hr o . . ~
Coefficient (2) is obtained in the assumption that if the readings of the instrument are the same at different temperatures, the cormsponding differences in the height of the balancing liquid columns are also the same. In fact, the constant reading, for instance, when the temperature of the differential manometer is raised, means that the float (owing to its rising at a zero pressure difference) has been displaced by a greater amount than at a normal temperature, i.e., the displaced volume of the balancing liquid and, hence, the difference in the heights of its columns in the instrument vessels is greater than at normal temperature. The defect of expression (2) consists in the fact that it does not take account of the thermal expansion either of the instrument vessel or of the float, and of the variation in the depth of immersion of the float. Thus, the use of (2) does not provide the required correction.
It is shown in  that on the basis of a scheme corresponding to the actual operating conditions of a differential manometer working with a constricting device, when the pressure difference measured by 0,8 the instrument remains constant with a varying temperature of the ambient medium, the referred temperature correction 6 q for the readings (of the flow) of a float-type differential manometer can be determined from the expression:
+ t/(1 + an a t ) . 0 ( 1 - 3 a n At)--Oo (l--Po. At) Qy (l--I~bt)--Oo (1--13o AI)
haa D~Td~ - lOy--Oo ,
4 V. at (fl--2a) ~t(Dt+d~)(1T2aAt)
where Q/Qmax is the ratio of the measured flow to the upper measurement limit, %; Hma x is the displacement of the float for a maximum pressure difference hmax; Oy and p o are the densities of the balancing and operating liquids respectively at 20* C; t is the temperature of the ambient medium; At = t - 20; B and B0 are the coefficients of the bulk expansionof the balancing and operating liquids respectively; h is the difference in the height of the balancing liquid columns for a given pressure difference at a temperature of 20* C; D and d are the internal diameters of the float vessel and replaceable vessel respectively at 20* C; V is the volume of ~ e balancing liquid at 20* C; cx is the mean linear expansion coefficient of the vessels; an is the linear expansion coefficient of the float; I is the height of the float at 20* C; p is the density of the float at 20* C. Without analyzing the essence of this equation we shall simply observe that in our view in this instance the expressions obtained for U-shaped manometers cannot be applied to the float-type differential manometer.
An analysis of (3) leads to the conclusion that the temperature error in the readings of a float-type mercury differential manometer calibrated at a normal temperature is affected to a negligible extent by the properties of the operating liquid, i.e., that its temperature error can be determined with sufficient accuracy by means of the following equation derived for the case when air is above the mercury :
at Dt+a t
. H ma x Q max The attached Iigure illustrates graphically the calculations made by means of (4) for mercury differential manometers with standard values for the limiting pressure difference. The raising of the temperature by 30 ~ C with respect to normal has been adopted in order to correspond to the maximum permissible temperature of the ambient medium specified in . It will be seen that at a maximum temperature the additional error can be completely neglected in instruments with a limiting pressure difference of 40 and 63 mm Hg and for the remaining pressure difference ranges it can be neglected over the scale range extending approximately from 55 to 100% of the full-scale reading. For smatler temperature deviations from the normal this error can obviously be neglected for all the pressure difference ranges. Thus, the flowmeter constricting devices should be computed by means of the limiting pressure difference in differential manometers at a normal temperature, and the additional error in measuring the flow under operating conditions at different temperatures should be accounted for by means of the above computing data. The effect of the ambient air temperature can be reduced to a negligibly small quantity by the appropriate selection of the maximum measured pressure difference. 1. 2. 3. 4. 5. 6. 7. 8.
LITERATURE CITED Regulation 27-54 for Applying and Checking Flowmeters with Normal Diaphragms. Nozzles and Venturi Tubes [in Russian] (Mashgiz, 1955). GOST (All-Union State Standard) 3720-54. Differential Manometers. COST 3720-60. Differential Manometers. P.P. Kremlevskii, Flowmeters [in Russian] (Mashgiz, 1955). A.N. Pavlovskii, Measurement of the Flow and Quantity of Liquids, Gases and Vapors [in Russian] (Mashgiz, 1951). V . P . Preobrazhenskii, Thermotechnical Measurements and Instruments [in Russian] (Gosenergoizdat, 1953). DiN (1952); V D I - Durchflussmessregeln (1948). S.S. Kivilis and V. E. Oleinikov, "Investigation of errors in float-type differential-manometer flowmeters, Report of the All-Union Scientific Research Institute of the Committee of Standards, Measures and Measuring Instruments on the subject of Zh- 1/26-60 (1961).