An Examination of the Uncertainty in Pressure of Industrial Dead-Weight Testers Used For Pressure Calibrations in Different Environments

Transcription

1 An Examination of the Uncertainty in Pressure of Industrial Dead-Weight Testers Used For Pressure Calibrations in Different Environments Author: Michael Bair Speaker: Mike Collins Fluke Calibration 4765 E. Beautiful Lane, Phoenix, AZ PH: FAX: Abstract The industrial dead-weight tester (IDWT) is traditionally a dead weight pressure gauge that is designed, built and calibrated to be used without having to make corrections or calculate pressure. In practice, different levels of corrections are used from no corrections, i.e. depending on the pressure value engraved on the weights, to using the full pressure equation to calculate a reference pressure. Parallel to this IDWTs are used in different environments. Some IDWTs are portable enough to be used in an open environment, many are used on production floors and many are used in laboratories as references with a good environment. It is not always clear what the uncertainty specifications are in the variety of levels of corrections and environment. This paper carefully examines these levels of corrections made and applies them to an industrial environment and provides the tools to be able to perform a valid uncertainty analysis in pressure. 2.0 Learning Objectives Readers and attendees will gain knowledge on the use and influences of industrial dead-weight testers. They would also gain knowledge on this type of uncertainty analysis. 3.0 Introduction The IDWT is a type of instrument that is described in a number of references including Dadson, Lewis and Peggs The Pressure Balance, Theory and Practice [1], NCSLI s RISP4 Deadweight Pressure Gauges [2], EA 10/03 Calibration of Pressure Balances (formerly EAL-G26) [3], and OIML s R 110 Pressure Balances [4]. These references suffice to describe the use and

2 calibration of IDWTs as long as the pressure equation, as defined in each document, is used to calculate pressure. For a long time IDWTs have been designed and used in such a way that the calculations recommended in the references given in the previous paragraph are not used or are only partially used. The pressure measurement industry has embraced this design and method of use for several reasons. One is that they can be used without electrical power or computer and still experience very good pressure control and relatively low uncertainty in pressure. Another is ease of use. Normally the masses supplied with an IDWT are marked with nominal pressures and with nominal starting pressure marked on the carrier so that operators only need to add nominal pressure values to document the standards output. In addition to the fact that the method suggested in the previous paragraph is used in place of the full calculations, IDWTs are often used in industrial environments. Large fluctuating ambient temperatures or large deviations from calibration temperature can have a significant effect on the uncertainty in pressure as defined by the nominal mass loads. Because of a need to support lower uncertainties on these types of pressure balances it was decided to perform a product uncertainty analysis that took into account three modes of use. One is the normal recommended method of calculating pressure using the pressure equation, the second is an interim calculation that accounts for temperature and gravity, and the last was for no corrections. These were called full correction (method 1), partial correction (method 2) and no correction (method 3) methods of use. This paper does not focus specifically on these instruments but on the method used to calculate uncertainty. The examples given are generic and are not intended to be a product specification. The intent is to help an operator of any IDWT to know what the uncertainty is based on the mode of use and environment with which it is used. 4.0 Methods of Use 4.1 Full Correction (method 1) The equation below gives the full calculation for a Pressure Balance as described in the introduction of this paper. If pressure is being calculated for an IDWT using this equation then the uncertainty is more straightforward and is performed in the classical way such as what is described in numerous uncertainty publications for Pressure Balances. Because most IDWTs measure gauge or negative gauge pressure, there is no term for residual pressure under a bell jar for absolute mode and is neglected in this paper.

3 Whether or not the method of use is using the full equation or no corrections the full equation is used to determine the uncertainty for all three modes. Section 5.0 will step through all the influences of uncertainty and discuss the influences on the different methods of use. M g l (1 ρ (air) ρ(mass) ) + πdτ A (23,0) [1 + (α p + α c ) (θ 23)] (1 + λp) (ρ (fluid) ρ (air) ) g l h where: M = Total true mass load [kg] gl = Local acceleration due to gravity [m/s 2 ] ρ(air) = Ambient air density [kg/m 3 ] ρ(mass) = Average density of mass load [kg/m 3 ] Τ = Surface tension (considered 0 with gas) [N/m] D = Diameter of the piston [m] ρ(fluid) = Density of the test medium (gas or oil) [kg/m 3 ] h = Difference in height between DWT [m] reference level and test reference level A(23,0) = Piston-cylinder effective area at 20 C and [m 2 ] 0 pressure αp = Linear thermal expansion coefficient of piston [ C -1 ] αc = Linear thermal expansion coefficient of cylinder [ C -1 ] θ = Temperature of the piston-cylinder [ C] λ = Elastic deformation coefficient of the [Pa -1 ] piston-cylinder P = Pressure applied to the piston-cylinder [Pa] 4.2 IDWT Design To manufacture an IDWT for use with nominal pressure values (partial or no correction) the pressure equation in 4.1 is used. The equation is set to calculate masses to be manufactured so that when they are used they produce a pressure that is the nominal value indicated on the mass within an uncertainty. The equation is filled with the following variables: M =1 kg gl = Customer s local or standard gravity ρ(air) = 1.2 kg/m 3 (sometimes referred to as standard density) ρ(mass) = Some apparent density value such as 8000 kg/m 3

4 A(23,mid pressure) = Effective area at 23 C and midscale pressure Neglecting the surface tension and head corrections, the result is a mass to pressure conversion coefficient, Kn or Kl (Kx), at standard conditions and either at the customer s local gravity or standard gravity. As an example this could be Pa/kg. This value is then converted to a desired pressure unit. If it is psi then the mass to pressure conversion coefficient is psi/kg. Masses, both main and incremental are then calculated by simply dividing the desired nominal pressure value by Kx. For example there could be 10 main masses that are 1000 psi each. The target value for manufacturing would be kg for each of the main masses. If the lowest pressure in this example is 50 psi, i.e. the pressure with the lowest possible mass load, then the same equation is used to calculate the expected mass or in the case of the example in the previous paragraph kg. This value can then be adjusted for constants such as hydraulic pressure head, surface tension and hydraulic fluid buoyancy by expressing them in terms of mass. The reason for using a midscale pressure value for effective area is to split in half the uncertainty due to not accounting for changes in pressure. In the case of very high pressure hydraulic IDWTs it may be such that the change in effective area with increasing pressure is so great that using a single effective area at midscale to calculate all mass values introduces too much uncertainty. In this case it is a common practice to calculate main masses with incremental mass changes to account for this change in area. The only stipulation is that the masses be used in sequence. In some designs of IDWTs a single weight set can be used with either a high or low pressure piston-cylinder installed in the same base. In this case a common practice would be to split the difference between the nominal values of two piston-cylinders. As an example, if the previous example of psi/kg is matched with a piston-cylinder that is psi/kg, the difference between the nominal values are % and % respectively. Averaging these differences gives a value of 0.034%, hence the Kx values would be changed to and psi/kg and adds uncertainty to the nominal pressure values that is equal to the change in the Kx values, in this case 0.011%. 4.3 Partial correction (method 2) As is indicated in the previous section much of the pressure equation is taken into account during manufacturing. But this is using the assumption that the piston temperature is at 23 C and at some predetermined gravity. The partial correction is derived from the full pressure equation and may include a correction for gravity and piston-cylinder temperatures. In some IDWTs this may also include a correction for

5 air density. This depends on the manufacturer and the level of uncertainty trying to be achieved. In this paper the assumption is that only piston-cylinder temperature and gravity are corrected. The partial correction is defined as: Pcorrg = Pnom g l gc Pcorr = Pcorrg [1 + (23 θ) (α p + α c )] where: Pcorr = Complete corrected pressure [Pressure Unit on Mass] Pcorrg = Corrected nominal pressure for gravity [Pressure Unit on Mass] Pnom = Nominal pressure [Pressure Unit on Mass] gl = Local gravity [m/s 2 ] gc = Calibration gravity (manufactured) [m/s 2 ] If the assumed temperature of the piston-cylinder is consistent, then the correction becomes a constant that is applied to all nominal pressures. 5.0 Uncertainties The following sections provide information on each uncertainty and how they affect all three methods of use, (1) full correction, (2) partial correction and (3) no correction. 5.1 Gravity It does not matter if the device is a piston gauge or an IDWT, or whether the method IDWT is 1, 2 or 3, the uncertainty in gravity affects them the same. Method 1 and 2 use gravity in an equation and with method three it is assumed that the gravity correction is manufactured into the masses. The only additional uncertainty that might be included is if an IDWT is being used with no corrections and is moved from the original location with which the masses were corrected. Since gravity can be as much as 0.4% different throughout global occupied locations, a change in location is not considered as an uncertainty here, however a calculation is given to estimate errors due to moving an IDWT without the correction. The services offered by the National Geodetic Survey [5] (USA only) and PTB Gravity Information System [6] provide gravity predictions with uncertainties that are normally acceptable to be used with IDWTS. It is possible to calculate gravity based on latitude and elevation using the World Geodetic System calculation (WGS84) [7] but does not have an uncertainty prediction. Table 1 gives some examples of gravity predictions by PTB, NGS and calculated using the WGS for three US and three international locations with significant

6 dispersions in locations. Note that there is one value where the difference between PTB and NGS is greater than either of the respective reported uncertainties. This was Anchorage, Alaska. But this difference would probably be an insignificant error for most IDWTs. Also note that the calculated WGS84 prediction has a dispersion of agreement with the PTB values of approximately ±105 ppm at k=2. Table 1. Examples of gravity predictions and associated uncertainty predictions. Location PTB PTB Ugl(95) NGS NGS Ugl(95) Difference from PTB WGS84 Difference from PTB m/s 2 [ppm] m/s 2 [ppm] [ppm] m/s 2 [ppm] US US US INT INT INT As mentioned it might be useful to know what the error is when changing location of a predetermined gravity when not making corrections. The WGS84 is useful in the prediction of error in gravity due to a change in latitude and elevation. Change in gravity with change in altitude depends on where the IDWT is being moved. If location of the IDWT changed within a 100 km change in latitude the error in gravity in ppm can be roughly predicted as: Error ppm = (L L ) D where: L = Absolute value of latitude [degrees] D = latitude change in distance [km] As an example, in Phoenix, AZ where the latitude is approximately 33 degrees N, a change in 50 km (31.6 miles) calculates to about 36 ppm change in gravity. The same change in latitude in Singapore is less than 1 ppm. For changes in elevation the error is approximately 0.31 ppm per meter of elevation change. This is the same no matter where your location is and a difference in 12 meters of elevation can have as much of an effect as 50 km change of latitude in Phoenix. Though it is not typical for IDWTs, gravity can be determined by surveying the location and uncertainties can be lower than 1 ppm. 5.2 Mass

7 There are two possible uncertainties in mass when considering all three methods of use. For the determination of the mass value it is fairly common to use a direct weighing method to achieve an uncertainty of ±20 to 50 ppm. This applies to all three methods. For methods 2 and 3 there is an additional uncertainty due to the manufacturing of the mass. Since the mass values are intended to generate an exact nominal pressure when used, any deviations from the target mass value is an additional uncertainty. The second uncertainty due to manufacturing is not correlated with the determination of uncertainty in mass. However the uncertainty in manufacturing can be considered to have a high confidence since the mass would be rejected if outside the manufacturing tolerance. One approach might be to guardband the manufacturing tolerance with the uncertainty in the mass determinations. This way for methods 2 and 3 there is one uncertainty in mass. 5.3 Air Buoyancy If calculated as in method 1, there is very little uncertainty contributed by the air buoyancy correction. Table 2 gives the sensitivity coefficient for temperature, pressure and humidity with respect to the air buoyancy correction. Using ambient sensors with uncertainties of ±1 C, 0.5 kpa and 20% RH, the uncertainty would be negligible to IDWT specifications. Table 2. Sensitivity in ppm for ambient measurements as they apply to air buoyancy. Measurement Sensitivity to Pressure Ambient Temp 0.55 ppm/ C Ambient Pressure Ambient Humidity 1.5 ppm/kpa ppm/%rh Uncertainty in the air buoyancy when considering methods 2 and 3 depends on the difference in air density used to calculate the Kx value for the mass determinations and the density of the air the IDWT masses are surrounded by at the time of measurement. A common practice is to use standard air density to determine Kx. In a way this is a little unfortunate because standard air density is at sea level and is close to the maximum value. This means that deviations in air density from what was designed into the Kx value are almost always in the negative direction and is more of an asymmetrical distribution. As a possible worse case almost all industry is conducted below an altitude of 2500 m (8200 ft) where the air density is an average of 0.93 kg/m 3. If using 1.2 kg/m 3 for an air density at this location the error is 34 ppm. At a 1000 m

8 (3300 ft) this calculates to an error of 17.5 ppm. These errors, depending on the level of uncertainty of the IDWT, will most likely be insignificant. 5.4 Effective Area Determination The uncertainty in effective area of the piston-cylinder used with an IDWT has an equal affect on all three methods and is one of the most dominant uncertainties. The results and uncertainty in effective area will be dependent upon the performance of the piston-cylinder throughout its range and the uncertainty of the reference used. It is sufficient to say here that the uncertainty in effective area over its range should be documented. For this example a simple ±100 ppm at k=2 is common and acceptable for many ranges and suffices as an example in the final section of this paper. 5.5 Change in Effective Area with Temperature Since the effective area of the piston-cylinder is dependent upon its temperature there is an uncertainty associated with the measurement of the temperature, the uncertainty in thermal expansion coefficient and in this uncertainty analysis the uncertainty when not making the correction. In this case methods 1 and 2 have the same influences. Method 3 has only the influence of not making a correction and is dependent solely on the thermal expansion properties of the materials of the piston-cylinder. Table 3 gives some examples of thermal expansion coefficients. In general the thermal expansion coefficients have an uncertainty of no worse that 5% at k=2. The uncertainty associated with the thermal expansion coefficient depends on how much of a correction is made, i.e. how far from the reported effective area reference temperature of the piston-cylinder. For laboratory applications for IDWTs this uncertainty can be considered insignificant. Even with a difference of 10 C from the piston-cylinder reference temperature, 5% uncertainty only contributes ±11 ppm worse case at k=2. Table 3. Linear thermal expansion coefficients for materials commonly used with IDWT piston-cylinders. Piston/Cylinder (α p + α c ) [1/ C] Tungsten/Tungsten 11 x 10-6 Tungsten/Steel 16 x 10-6 Steel/Steel 21 x 10-6 Ceramic/Steel 22 x 10-6

9 C For most IDWTs there is not a sensor included to measure the temperature of the piston-cylinder. A common approach is to use an existing ambient temperature measurement and assume the piston-cylinder is at that temperature. In this case there are two uncertainties to consider, the uncertainty of the thermometer measuring ambient temperature, which is easily quantified and the uncertainty of the assumption that the piston-cylinder is at this temperature which is dependent upon the stability of the environment and the amount of thermal change influenced by pressure excursions. In both cases the uncertainty is calculated as the uncertainty in temperature multiplied by the thermal expansion coefficient. A study was performed to try to determine the errors obtained when trying to predict the temperature of the piston-cylinder by using the ambient temperature. Two separate instances were looked at, a controlled laboratory and an uncontrolled environment. This was accomplished by inserting a thermistor with an uncertainty lower than ±0.03 C at k=2 in an IDWT mounting post to simulate piston-cylinder temperature. The different environments were monitored at the same time the simulated piston-cylinder temperature was observed. Figure 1 shows a 6 hour excursion in a laboratory environment. The maximum difference in temperature was approximately 1 C Ambient Temperature Mounting Post Temperature :43:12 1:55:12 3:07:12 4:19:12 5:31:12 6:43:12 Elapsed time Figure 1. Simultaneous log of temperatures of an IDWT mounting post and Ambient temperature in a controlled environment.

10 C In figure 2 the same setup was taken to a room where the air conditioning was turned off and the environment was left to drift. In this case the worse case difference was observed when the rate of change of the ambient temperature was at its highest. In this example the maximum rate of the change in ambient temperature was approximately 2.5 C per hour. Even at that rate the maximum difference between the mounting post temperature and the ambient temperature was 1 C Ambient Temperature Mounting Post Temperature :00:00 2:24:00 4:48:00 7:12:00 9:36:00 12:00:00 14:24:00 Elapsed Time Figure 2. Simultaneous log of temperatures of an IDWT mounting post and ambient temperature in an uncontrolled environment.. For this IDWT the uncertainty for method 1 and 2 would be two uncertainties included separately, one for the uncertainty of the ambient thermometer and one for the assumption it is the piston-cylinder temperature. For method 3 the uncertainty is the maximum deviation of the anticipated piston-cylinder temperature and the effective area reference temperature. If the reference temperature is 23 C a possible assumption is that the piston-cylinder temperature is no larger than ±5 C from that value or 18 to 28 C. Table 4 gives the uncertainties for the different thermal expansion coefficients shown in Table 3 for an assumed ambient temperature range of 18 to 28 C (64.4 to 84.4 F) and a rate of change of no more than 2.5 C (4.5 F) per hour.

11 Table 4. Contributing temperature uncertainties Application All Methods Method 1,2 Method 1,2 Method 3 (α p + α c ) UTalpha UTdevice UTp-c UT no correction [1/ C] [ppm] [ppm] [ppm] [ppm] 11 x x x x The last consideration for temperature is the influence of the addition or removal of heat due to pressure changes in the media. For the most part there is enough thermal inertia in the mounting posts of most IDWTs to absorb any heat changes occurring during use of the IDWT. A study was completed using IR thermometry to determine if this was true. A subject IDWT was pressurized to 5000 psi (35 MPa) as quickly as possible as a likely maximum temperature excursion while monitoring different exposed parts of the IDWT to look for significant changes in temperature. In this example there was nothing detected that would need to be added to the uncertainties shown in Table Change in Effective Area with Pressure The uncertainty in effective area is given in 5.4 and includes the uncertainty due to changes in pressure, the elastic deformation coefficient, and need not be included for method 1. For method 2 and 3 there is no compensation for changes in pressure with the exception of what is done at the time the masses are manufactured. As mentioned in 4.2 there are two ways to compensate for the elastic deformation coefficient when manufacturing the masses. One is by choosing an effective area at midscale pressure to cut the influence in half, and the other, normally reserved for very high pressure applications, is where the masses are adjusted sequentially to account for the change in area. In the latter case the assumption is that the masses are used sequentially. For many low pressure applications the uncertainty is insignificant because the change in effective area is not large. For some manufacturers a re-entrant mounting design is used for higher pressures to effectively counter the changes in effective area. However there are limitations on how high a re-entrant design can be used with the intent to obtain an elastic deformation coefficient close to zero. Finally the use of tungsten carbide and larger cylinders can help play a role in reducing the amount of deformation for free deformation mounting systems. Table 5 gives examples of elastic deformation coefficients and their influence on methods 2 and 3.

12 Table 5. Influences of pressure deformation for tungsten piston and steel and tungsten cylinders in free deformation mounting system Pressure Pressure WC/ST WC/WC 1/2 Total Change [MPa] [psi] [1/MPa] [1/MPa] [ppm] [ppm] E E E E E E E E E E Surface Tension, Hydraulic Fluid Heads and Fluid Buoyancy The full correction equation in section 4.1 gives the calculation of surface tension and head pressure. Not shown is the calculation for fluid buoyancy which is accounted for in the height reference level of the IDWT. For method 1, as long as height measurements are performed within ±2 mm, the uncertainties may be insignificant even for hydraulic systems. For methods 2 and 3 these corrections are not made. For hydraulic IDWTs, as with other variables, these corrections are significant and instead of being calculated at the time of measurement are accounted for in the manufacturing of the mass carrier (weight sleeve). For gas IDWTs these variables are considered insignificant as calculated to the defined reference level of the IDWT. The reference level of the IDWT may be a line on a post attached to the base, a mark on the mounting post or possibly defined as the top of the test port. Head pressure calculations outside of the design of the IDWT are not considered here. As is mentioned in 4.2 surface tension, hydraulic heads and hydraulic fluid buoyancy corrections are accounted for by considering them constant and calculating a mass value that equal the correction. The mass value of the mass carrier is then modified at the time of manufacturing to account for the piston mass and these corrections to get to a nominal starting value. The uncertainty then becomes the same as what is assumed in method Level Level is an influence on the output of IDWTs. Many models of IDWTs have levels on their base that can be used to level the piston-cylinder. In almost all cases the levels on the bases need not be used because the level can be set using an external level on top of the piston. But there are certainly some cases, such as with reversed hanging piston-cylinder assemblies used for negative

13 gauge ranges, where that cannot be done and the level is dependent upon the manufacturer s level on the base. Level is an asymmetrical uncertainty that is always in the negative direction. For ease of understanding the level uncertainty can be calculated in minutes and using [1 cosine] of the angle the uncertainty is estimated to be. As an example if the level is within 5 arc minutes the error is -1 ppm, 10 minutes is -4.2 ppm and 20 minutes is -17 ppm. 5.9 Performance Performance of an IDWT may be characterized in three different influences. These are changes in pressure with change in piston position (straightness of the piston), changes in pressure with changes of rotation, and sensitivity of the piston-cylinder. Performance affects all three methods of use the same and will vary greatly depending upon the quality of the piston-cylinder. Metrologists performing uncertainty analysis on IDWTs should be careful not include double influences. The effective area determination type A uncertainty will most likely be influenced by these characteristics. A possible approach is to determine the effective area under the best circumstances, i.e. from a pressure that is not too low, keeping the piston at the same level and rotating at a constant optimal level. Then at specific points test the piston straightness and rotation effects to ensure they are within parameters. Including sensitivity again is including this influence twice in the uncertainty analysis Piston-Cylinder match The final uncertainty to consider is only applicable to methods 2 and 3 and when there is one mass set used with two piston-cylinders. As was mentioned in section 4.2 when two pistoncylinders are used with a common mass set the masses are adjusted so that they share the difference in the effective areas. 6.0 Combining uncertainties for all three methods Table 7, at the end of this section, combines the all the uncertainties described in section 5 with emphasis on the three different methods. The example is for a common dual range of 70 MPa (10,000 psi) and 3.5MPa (500 psi) hydraulic IDWT. All uncertainties are included but there is an uncertainty that combines the deviations due to manufacturing tolerances of the masses. This combines the ability to manufacture the masses with the deviations from elastic deformation and piston-cylinder match. These deviations can only be determined from the calibration. In order to complete this section an example calibration

14 of the range above was used. Table 6 preceding the uncertainty budget provides these deviations for both of the piston-cylinders and may be thought of as uncorrected bias similar to what is described in section F from the GUM [8]. Considering the operator of the IDWT does not specifically know what the deviations are, the maximum value is used for the uncertainty. Table 6. Deviations of a dual range hydraulic IDWT Nominal Pressure Measured Pressure Difference 70 MPa (10000 psi) range [psi] [psi] [ppm] Maximum Deviation: MPa (500 psi) range Maximum Deviation: 93 For the uncertainty budget shown in Table 7 the environmental limitations are 18 to 28 C with changes in temperature no more than 2.5 C. For methods 1 and 2 the uncertainty due to temperature is listed twice, once for the uncertainty of the thermometer, assumed to be ±1 C at k=2, and the same uncertainty for the other temperature influence which is due to the assumption that the temperature measured is the temperature of the piston-cylinder. The uncertainty budget is simplified by not quantifying uncertainties that are constant. The largest influences of uncertainty at the low end is normally performance, mass and hydraulic head heights. For a product specification these would have to be quantified, but would most likely be applied using a threshold specification from 5 or 10% of the range. For example it might be ±(the maximum of, 0.02% of reading or 0.001% of full scale, whichever is greater) meaning it is a relative specification from 5 to 100% of range.

15 Table 7. Uncertainty Budget for a dual range hydraulic IDWT 70 Mpa (10000 psi) range 3.5 Mpa (500 psi) range Method Influence Section [ppm] [ppm] [ppm] [ppm] [ppm] [ppm] Gravity Mass Air Buoyancy Effective Area P-C temperature 5.5a P-C temperature 5.5b Level Performance Deviations 5.2, 5.6, [ppm] [ppm] [ppm] [ppm] [ppm] [ppm] Combined Expanded Conclusion Examining the results in Table 7 it is easy to see that method 1, full correction, provides the lowest uncertainty. However, within some reasonable industrial limits methods 2 and 3 provide a useful uncertainty with minimal or no corrections. It seems to be easier to conceive the fact that on a production floor or in the field method 2 would not be used because of the need to calculate a correction. This is emphasized by the fact that there is little difference between methods 2 and 3, assuming that gravity is not an issue. The IDWT is a very useful pressure instrument considering the fact that when the piston is floating it is controlling the pressure as well as some of the best automated controllers, without the need for electrical power, and provides very acceptable measurement uncertainties. However since method 2 and 3 depend on the manufactured values of the masses, as the materials change over time the only way to adjust is to adjust the masses. This can be done but is normally costly. But IDWTs are generally very robust and stable with intervals sometimes as long as 5 years. In addition to this an IDWT that is used using methods 2 or 3 must be calibrated as a whole. Whereas if method 1 is used the piston-cylinder and masses can be calibrated separately.

16 8.0 References 1. R.S. Dadson, S.L. Lewis and G.N. Peggs, The Pressure Balance, Theory and Practice, NPL Department of Industry, NCSLI s RISP4, Deadweight Pressure Gauges, Recommended Intrinsic/Derived Standard Practice, July EA 10/03, Calibration of Pressure Balances (formerly EAL-G26), EUROMET, July OIML R 110, Pressure Balances, National Geodetic Survey, Surface Gravity Predictions, 6. PTB Gravity Information System, 7. World Geodetic System, WGS84, Guide to the Expression Of Uncertainty in Measurement, ISO 1992