NISTIR 7383
 

Selected Procedures for Volumetric 

Calibrations 

(2013 Ed) 

Harris, Georgia L. 

 

 

 

NISTIR 7383 

Selected Procedures for Volumetric 

Calibrations 

(2013 Ed) 

Harris, Georgia L. 

Office of Weights and Measures 

April 2013 

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 

Foreword 

This NIST IR of Selected Publications was updated from the 2006 version in 2012 and 

included Good Laboratory Practices, Good Measurement Practices, and Standard 

Operating Procedures for volumetric calibrations. Procedures were reviewed at 2012 

Regional Measurement Assurance Program meetings with input provided by working 

metrologists who have implemented these procedures in their laboratories. As a result, 

additional updates were required in 2013. 

Updates to this edition include the latest CIPM accepted equations for the calculation of 

water density in GLP 10. SOP 17 and 20 have been modified so that they apply to 

control charts for check standards, standard deviation charts, and range charts for any 

process with replicate measurements (versus only those for volume transfer calibrations 

as previously written.) 

The following Practices and Procedures that were included in the 2006 edition were 

removed in the 2012 publication: 

Standard Operating Procedures for: 

 Gravimetric Volume Calibrations Using a Single-Pan Balance (13) and Using 

Equal Arm Balances (15). Contents specific to glassware calibrations have been 

included in SOP 14. Few laboratories maintain mechanical balances or equal arm 

balances for gravimetric calibrations, therefore, these procedures will no longer be 

updated. 

The calibration procedures for Small Volume Provers (SOP 26, Volumetric, and SOPSVP, Gravimetric) have been revised and are replacing SOP 26 for generic “Gravimetric 

Calibrations of Dynamic Volumetric Standards” which includes Small Volume Provers 

and alternative standards in this 2013 edition. 

Many of these procedures are updates to procedures that were originally published in 

NBS Handbook 145, Handbook for the Quality Assurance of Metrological 

Measurements, in 1986, by Henry V. Oppermann and John K. Taylor. The 2006 updates 

incorporated many of the requirements noted for procedures in ISO Guide 25, 

ANSI/NCSL Z 540-1-1994, and ISO/IEC 17025 laboratory [quality] management 

systems. The 2006 changes incorporated 1) uncertainty analyses that comply with current 

international methods in the Guide to the Expression of Uncertainty in Measurements 

(GUM) and 2) measurement assurance techniques using check standards. The 2012 

updates included updated terminology consistent with the International Vocabulary of 

Metrology (VIM), primarily associated with metrological traceability. The 2013 update 

includes data sheets and example uncertainty budget tables in all SOPs. 

Note regarding SI units: This publication conforms to the concept of primary use of the 

International System of Units (SI) recommended in the Omnibus Trade and 

Competitiveness Act of 1988 by citing SI units before customary units where both units 

appear together and placing separate sections containing requirements for SI units before 

iii 
corresponding sections containing requirements for customary units. In some cases, 

however, laboratory standards and/or trade practice are currently restricted to the use of 

customary units (e.g., retail sale of gasoline in the United States is still sold by U.S. 

gallons); therefore, some procedures in this publication specify only customary units. 

Non-SI units are predominately in common use in State legal metrology laboratories, 

and/or the petroleum industry for many volumetric measurements, therefore non-SI units 

have been used to reflect the practical needs of the laboratories performing these 

measurements as appropriate. SI units are used where practical, and where use or 

potential conversion errors, will not likely impact the quality of laboratory measurement 

results. 

Endorsement Disclaimer 

Certain commercial equipment, instruments, or materials are identified in this publication 

in order to specify the experimental procedure adequately. Such identification is not 

intended to imply recommendation or endorsement by the National Institute of Standards 

and Technology, nor is it intended to imply that the materials or equipment identified are 

necessarily the best available for the purpose. 

iv 
 

Table of Contents 

Foreword iii 

Good Laboratory Practices 

10 Purity of Water GLP 10-1 

13 Drying “To Contain” Volume Standards GLP 13-1 

Good Measurement Practices 

3 Method of Reading A Meniscus Using Water or Other Wetting GMP 3-1 

Liquid 

6 Cleaning Metal Volumetric Measures GMP 6-1 

7 Cleaning Precision Glassware GMP 7-1 

Standard Operating Procedures 

14 Gravimetric Calibration of Volumetric Ware Using an Electronic SOP 14-1 

Balance 

16 Calibration of Measuring Flasks, Volume Transfer Method SOP 16-1 

17 Control Charts of Laboratory Owned Check Standards for SOP 17-1 

Calibration of Measuring Flasks or Small Provers using Volume 

Transfer Methods 

18 Calibration of Graduated Neck-Type Metal Volumetric Field SOP 18-1 

Standards, Volumetric Transfer Method 

19 Calibration of Large Neck-Type Metal Provers, Volume Transfer SOP 19-1 

Method 

20 Control Charts for Calibration of Neck Type Provers, Volume SOP 20-1 

Transfer Method 

21 Calibration of LPG Provers SOP 21-1 

26 Gravimetric Calibration of Dynamic Volumetric Standards SOP 26-1 

v 
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vi
 
 

Good Laboratory Practices 
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April 2013 

GLP 10 

Good Laboratory Practice 

for the 

Purity of Water 

Water is used in two ways in the metrology laboratory. It may be used as a cleaning fluid. It may 

also be used as a transfer medium in volume transfer calibrations, or as standard reference 

material for gravimetric volume calibrations. In each case of these cases, the water must be 

clean; in the case of gravimetric volume calibrations it must be pure, as well. 

Dirty water can cause a number of problems, including depositing residues in a volumetric 

vessel that could cause volumetric errors or could soil its interior. When in doubt of the 

cleanliness of the water supply, filters should be attached to the supply lines used. 

Cleanliness of water may be achieved by removal of physical contaminating substances, 

especially by filtration. City water is ordinarily clean but may become dirty from the distribution 

system and especially from prolonged standing in some kinds of pipes and tubing. Hoses used to 

transfer water from and into large vessels and tanks may need internal cleaning, as well. 

Flushing to remove visible contamination is all that is usually required prior to use in volume 

transfer calibrations or prior to further purification. 

Clean Water used in Volume Transfer Calibrations 

Clean water is all that is necessary when making measurements by volumetric transfer since 

volumetric comparisons are involved. When the water density value is used in a volume transfer 

equation, the ratio of the density values of clean water versus pure water is essentially 

unchanged, despite impurities. The coefficient of expansion for distilled water and pure water 

are also essentially the same. 

Note: the equations used in gravimetric calibrations do not use ratios and systematic errors will 

result in the calibration relative to impurities in the water. The use of low resolution density 

meters for evaluating the quality of clean water (instead of using pure water as described) is 

discouraged for use in gravimetric calibrations. 

Pure Water used in Gravimetric Volume Calibrations 

Pure water is needed for gravimetric volume calibrations. For gravimetric calibrations, filtration 

systems alone are not adequate. Pure water requires the removal of chemical contaminants and 

this may be achieved by distillation, reverse osmosis, ion exchange systems, or combinations of 

these systems. The purity of the water from any given system and maintenance requirement is 

often dependent on the quality of the source water. Source water should be tested to determine 

the best type of system to meet laboratory needs. Density calculations may be accurate even 

when appreciable levels of dissolved salts remain in the water. However, since it is very difficult 

to know what type and quantity of salts are tolerable before density is affected, it is prudent to 

use the best system practical within budgetary constraints. 

GLP 10 Page 1 of 5 
 

April 2013 

Water Quality Specifications and Purification Methods 

ASTM Type III or IV Reagent Water1

* is recommended as adequate for gravimetric calibration 

purposes. Such water may be produced by distillation or by ion exchange with relatively 

inexpensive equipment. Type III grade of reagent water may be prepared by distillation, ion 

exchange, continuous electrodeionization reverse osmosis, or a combination thereof, followed by 

polishing with a 0.45 μm membrane filter. Type IV grade of reagent water may be prepared by 

distillation, ion exchange, continuous electrodeionization reverse osmosis, electrodialysis, or a 

combination thereof. 

The ASTM D-1193 specifications for conductivity and resistivity are noted in Table 1. 

Table 1. Conductivity and resistivity specifications for water. 

Type I Type II Type III Type IV 

Electrical conductivity, max, 

μS/cm at 298 K (25 °C) 0.056 1.0 0.25 5.0 

Electrical resistivity, min, 

MΩ·cm at 298 K (25 °C) 18 1.0 4.0 0.20 

Conductivity or resistivity (along with other water quality measurements) are often used to 

assess the water quality used in cooling towers, boilers, relative humidity systems, micro and 

nanoelectronic systems and in pharmaceuticals, to ensure water of sufficient purity and to 

minimize corrosion or build-up within such systems. 

Conductivity and resistivity measurements do not have a direct correlation to water density, 

which is the critical attribute of concern for gravimetric volume calibrations. However, 

conductivity or resistivity measurements are a good indicator of water quality and whether the 

system is in good operating condition or needs service. Conductivity is simply the reciprocal of 

resistivity. For water quality specifications and assessment purposes, conductivity is usually 

measured in microSiemens per centimeter (μS/cm) and resistivity is usually measured in 

megaohms-centimeter (MΩ·cm), both usually at a reference temperature of 25 oC. Conductivity 

is greatly influenced by temperature and is not linear. However, this is not a major concern for 

typical laboratory applications requiring pure water. Either a meter or indicator light should be 

included in laboratory systems to monitor water quality output. Standard reference materials are 

available to test conductivity and resistivity units. But, because the measurement values are not 

used to perform corrections to volume calibrations, traceable calibrations of the units are not 

essential. 

Most manufacturers of systems at this level indicate that the resulting water will meet Type I 

specifications. Sales literature will usually specify whether the equipment will provide water of 

the above quality. Additionally, many manufacturers will provide a source water quality test and 

recommend a system to meet the purity and volume requirements of the laboratory. 

1

 ASTM D 1193 - (06)2011, Standard Specification for REAGENT WATER, ASTM, http://www.astm.org, 1916 

Race St., Philadelphia, PA 19103. 

GLP 10 Page 2 of 5 
 

April 2013 

A cartridge-type ion-exchange system is recommended for its simplicity and ease of operation. It 

can operate intermittently (on demand) and requires little or no maintenance except for change of 

cartridges, the need for which will be indicated. A relatively small system (2 L/hr to 30 L/hr) is 

adequate for laboratories calibrating glassware and test measures up to and including 20 L (5 

gal) standards. It may be used on demand or to fill a small (20 L to 40 L) storage bottle to assure 

a continuous supply of calibration water. 

There are two broad types of ion-exchange systems. Pressure cartridge systems (PCS) operate 

directly from line pressure (up to 700 kPa) and need no special operation precautions. The less 

expensive type operates from the water line through a needle valve to produce a specified flow 

through the cartridge(s). In this system, the outlet must not become blocked or turned off to 

prevent the water pressure from building up and bursting the cartridge. It is common practice to 

plumb directly from the output of this cartridge to a storage tank without using a valve in 

between. The unit is operated by simply turning the shut-off valve located at the water supply. 

Water Density Measurements 

Water density may be measured with a five- or six-place oscillation-type density meter 

calibrated using suitable standard reference materials that are representative of the range of use. 

These systems typically measure the density at a specific reference temperature (generally 20 

oC). However, density meters are generally not needed if an appropriate water purification 

system is used that includes a way to measure conductivity or resistivity and where outside 

validation of water quality has been obtained. 

One method that may be used in the laboratory for monitoring water over time is to maintain a 

quality assurance reference flask (QARF) that is calibrated at any time a gravimetric calibration 

is performed. If the results of a proficiency test (interlaboratory comparison) that is conducted at 

the same time are found acceptable, one can assume that the quality of the water was acceptable 

on that day. In this way, the reference value for the flask may be monitored over time. Glassware 

is unlikely to change with use of pure water; thus, significant changes on a control chart for a 

QARF indicate other problems that may need to be investigated such as water quality or other 

changes in the calibration system or process. 

Exposure of pure water in storage to air will likely cause degradation in the conductivity and/or 

resistivity measurements. However, pure water has been stored for over a year with little 

degradation in the density quality (provided that storage containers and lines are clean and that 

there is no bacterial growth, algae, or other contamination). 

Temperature equilibrium is a critical factor in the density stability of water. This is especially 

important for large volumes. Water temperatures must be stable throughout the container. 

Temperature accuracy is as important as purity for a correct density determination. If water is 

coming straight from the tap through the purification system into the prover, the temperature 

may fluctuate appreciably. Therefore, it is important to store an adequate volume of water to 

complete a calibration either already purified or ready to go through the system. 

GLP 10 Page 3 of 5 
 

April 2013 

Water Density Calculations 

Water density tables (see Table 9.8 in NISTIR 6969) or calculations are required for most 

gravimetric calculations. For use in computer programs (most often spreadsheets), the use of 

calculations are preferred to the use of look-up tables. 

The following equation provides the density for air-free water and is recommended for use 

between 0 °C and 40 °C.2 This equation provides results in kg/m3. Therefore, divide by 1000 to 

convert the value to g/cm3 . 

2  (t  a1 ) (t  a2 )

(t )  a5 1  Eqn. 1 w  a3 (t  a4 ) 

where: 

a1 = -3.983 035 C 

a2 = 301.797 C 

a3 = 522528.9 C2 

a4 = 69.348 81 C 

a5 = 999.974 950 kg/m3 

tw is the temperature of the water in C. 

In Excel Format: 

=999.97495*(1-(((G8-3.983035)^2*(G8+301.797))/(522528.9*(G8+69.34881)))) 

where, G8 is the cell with the Celsius temperature and units are given in kg/m3 . 

Pure water that is used in the laboratory is generally air-saturated, so the density must be 

corrected. The impact is approximately between 1 and 4 parts per million (or several times the 

uncertainty of the water density calculation). To adjust the air-free water density in Equation 1 

between 0 °C and 40 °C to air-saturated water (the standard laboratory condition), use the 

following equation, 

3  / kg m  s0  s1t Eqn. 2 

where, 

S0/(10-3 kg m-3)= -4.612 

and 

S1/(10-3 kg m-3 °C-1)= 0.106. 

In Excel Format: 

2

 M. Tanaka, G. Girard, R. Davis, A. Peuto, and N. Bignell, Recommended table for the density of water between 

0 °C and 40 °C based on recent experimental reports, Metrologia, 38, 301-309 (2001). 

GLP 10 Page 4 of 5 
 

April 2013 

=(-4.612+0.106*G8) 

where, G8 is the cell with the Celsius temperature. (Add this value to the density. Air-saturated 

water density will be less than air-free water density.) 

Note: The units in Equation 2 are 10-3 kg/m3 or “parts per million,” so divide by 1 000 000 to 

find the change to the water density in g/cm3. Equation 1 and Equation 2 may be combined, 

taking care to match units. 

Uncertainty in Water Density Values 

The uncertainty in water density given by the references for the equation itself may be calculated 

using Eqn. 3. The calculated uncertainty for all of the values in the example data shown below is 

0.000 000 83 g/cm3 . 

2 3 4 -3 3

u( w )  0.8394  0.00128t  0.000110t  0.00000609 t  0.000000116t (10 kg / m ) 

Eqn. 3 

Example Data 

Temperature (°C) Air-Free Water Density 

(g/cm3

) 

Correction for Air 

Saturation 

(g/cm3

) 

Air-Saturated Water 

Density 

(g/cm3) 

10 0.999 702 70 -0.000 003 55 0.999 699 15 

15 0.999 102 57 -0.000 003 02 0.999 099 55 

20 0.998 206 75 -0.000 002 49 0.998 204 26 

25 0.997 047 02 -0.000 001 96 0.997 045 06 

Additional References: 

ASTM D 1125 – (95)2009, Standard Test Method for Electrical Conductivity and Resistivity of 

Water, ASTM, http://www.astm.org, 1916 Race St., Philadelphia, PA 19103. 

ISO 15212-1:2002, Oscillation-type density meters – Part 1: Laboratory instruments, ISO, 2002. 

GLP 10 Page 5 of 5 
 

 

 

 

 

 

April 2013 

GLP 13 

Good Laboratory Practice 

for 

Drying “To Contain” Volume Standards 

Vessels calibrated "to contain" must be dried of all measurable water in order to obtain an 

"empty" weight. The drying process should not contaminate the container; otherwise, it will need 

to be re-cleaned before further calibration or volumetric use. The following is presented as 

guidance when drying is required. 

Drain as much of the residual water as practical before starting any drying process. If time is not 

a consideration, a glass tube may be inserted into the container to blow clean dry air (or 

nitrogen) through it to evaporate the residual water film. A filter or dust trap may be necessary to 

pre-clean the air used. Air lines must be selected to ensure that aging and wear do not introduce 

contaminants. Air may be drawn through a tube connected to a vacuum pump, but with some 

danger of drawing in dirty air from the surroundings. Clean absorbent cotton placed at the neck 

opening can minimize the entrance of foreign matter. Compressed air systems may introduce 

finely atomized oils or moisture into the air which may not be visible. If laboratory quality air is 

not available, nitrogen may be used. 

Safety Note: Material Safety Data Sheets (MSDSs) must be available in the laboratory and 

should be reviewed to ensure safe handling and disposal of all chemicals noted in this procedure. 

Care must be taken to avoid mixing chemicals such as acetone and alcohols in the laboratory. 

Cleaning with solvents may be performed; ethanol is the preferred medium. Preliminary rinsing 

with acetone will remove large amounts of water, with which it is infinitely miscible, but this 

solvent often contains impurities such as traces of oils that could deposit on the container walls 

and be a disposal problem. Thus, a final alcohol (preferably ethanol or methanol) rinse is 

recommended, even if acetone is used to remove most of the water. Care must be taken to ensure 

that the alcohol is not mixed with acetone, and that the alcohol is not denatured with oils to an 

extent that will leave residue on the standard. The alcohol is allowed to drain as much as 

possible, followed by air drying as described above. 

Some metal containers may be internally coated to minimize corrosion. When present, it should 

be ascertained that such coatings are not affected by alcohol or acetone; otherwise, solvent 

treatments should not be used. 

The external surfaces of all containers should be clean when gravimetric calibrations are 

performed. Otherwise, any removal of external dust or dirt during the measurement process 

could cause errors of unknown magnitude. 

Analytical glassware should not be dried by heating in an oven as the glass may suffer nonelastic expansion and put the glassware out of calibration. 

GLP 13 Page 1 of 2 
April 2013 

Calibration Tip: Cover a vessel after it is clean and dry to minimize contaminants from 

collecting inside the vessel. Clean and dry the flask one to two days prior to the calibration and 

allow the flask to come to equilibrium with the environment. Obtain an initial baseline “dry 

weight” of the clean container for use as a dry reference weight on subsequent weighing and 

drying cycles. 

GLP 13 Page 2 of 2 
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Good Measurement Practices 
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April 2013 

GMP 3 

Good Measurement Practice 

for 

Method of Reading a Meniscus Using Water or Other Wetting Liquid 

The meniscus of most liquids used in volumetric calibrations is concave-up, with the lowest 

point in the center that is used to determine the meniscus reading. The curvature of a meniscus 

is related to the surface tension of the liquid and inversely related to the diameter of the tubing in 

which it is formed. When reading any meniscus, it is important to ascertain that it is in an 

equilibrium position. Tapping of sight glasses and/or small motions of containers may be used to 

induce slight displacements of the meniscus. Return to the same reading is evidence of a stable 

meniscus. 

The meniscus formed by a non-wetting liquid, such as mercury (Hg), is convex with the highest 

point in the center and is no longer regularly used for volumetric calibrations. In the case of a 

convex meniscus, the highest point is used to make the reading. The reading of a mercury 

barometer or thermometer is a classic example of this kind. 

In all apparatus where the volume is defined by a concave-up meniscus, the setting or reading is 

made on the lowest point of the meniscus. In order that the lowest point may be observed, it is 

necessary to place a shade of some dark material immediately below the meniscus, which 

renders the profile of the meniscus dark and clearly visible against a light background. A 

convenient device for this purpose is a collar-shaped section of thick black rubber tubing, cut 

open at one side and of such size as to clasp the tube firmly. 

Two common methods are used for setting and visually reading a meniscus: Options A and B. 

The method used in calibration should be consistent with the intended use of the volumetric 

standard. For interlaboratory comparisons, the method to be used should be defined during the 

planning stages of the comparison. The width of the graduation on the neck scale will affect the 

readability of the meniscus and should be estimated to the nearest 1/10 of a division when using 

either Option A or Option B. 

Several types of meniscus readers are available. These include black/white meniscus card 

readers, magnifying glasses with cross-hairs, and collar shaped tubes that may be placed around 

the graduated neck of the volumetric container. Black/ white meniscus card readers are simple to 

create as shown in the figure below. 

This type of meniscus reader is generally preferred for the Option A method of reading the 

GMP 3 Page 1 of 5 
 

April 2013 

meniscus. More elaborate card readers may be purchased that allow placement around the neck 

of a flask. 

Another type of meniscus reader consists of a clear lens (plastic or glass) with etched lines on the 

front and back that are aligned to prevent parallax errors in reading. This type may or may not 

include magnification. This type of reader is preferred for Option B. 

Option A 

Option A is suitable when graduation lines extend more than 75 percent of the circumference of 

the sight gage area, for example with graduated neck type flasks or single mark flasks. 

The position of the lowest point of the meniscus with reference to the graduation line is such that 

it is in the plane of the middle of the graduation line. This position of the meniscus is obtained by 

making the setting in the center of the ellipse formed by the graduation line on the front and the 

back of the tube as observed by having the eye slightly below the plane of the graduation line. 

This is illustrated below. The setting is accurate if, as the eye is raised and the ellipse narrows, 

the lowest point of the meniscus remains midway between the front and rear portions of the 

graduation line. By this method it is possible to observe the approach of the meniscus from either 

above or below the line to its proper setting. 

Meniscus Surface 

Front Side of Index Line 

Rear Side of 

Index Line 

Observer’s View From Slightly Below the 

Horizontal Level of the Graduation Line.
 

FRONT VIEW 

Exaggerated Curvature 

Meniscus Surface 

Fraction of a Millimeter Below the 

Graduation Line (or a Card Reader with the 

Black Side on the Bottom.) 

Circumferential 

Graduation Line 

Line-of-Sight to Front 

Side of Index 

Observer’s Eye 

Line-of-Sight to Rear 

Side of Index Line-of-Sight to 

Meniscus 

Black Rubber Opaque Screen Placed a 

SIDE VIEW 

GMP 3 Page 2 of 5 
 

 

April 2013 

Option B 

Option B, is typically used with opaque liquids or when the graduation mark does not extend 

around the circumference of the volumetric standard. (Option B is also referenced in a number of 

ISO and OIML standards for glassware, thus it is important to review meniscus reading practices 

with the user.) 

In setting the meniscus or taking a reading, the observer's eye should be normal to and in the 

same horizontal plane as the meniscus. The illumination is adjusted to get a sharp definition of 

the meniscus. Elimination of parallax error is very important and can be judged by slight 

fluctuations of eye level that do not affect the reading. 

The position of the lowest point of the meniscus with reference to the graduation line is 

horizontally tangent to the plane of the upper edge of the graduation line. The position of the 

meniscus is obtained by having the eye in the same plane of the upper edge of the graduation line 

as shown below. Offsets from reading in the same plane will produce parallax errors. 

Observer’s Eye Graduation Line 

Comparison of Option A and Option B Methods 

For most practical applications the difference between these two methods is insignificant 

compared to the tolerances of the volumetric standards. However, a component for measurement 

uncertainty should be included as appropriate. When performing calibrations, using the 

glassware as precision standards with clear liquids, or when comparing results among 

laboratories the difference in meniscus setting is directly related to the visible thickness of the 

meniscus and the volume of liquid contained in the neck between the top of a graduation line and 

the middle of the graduation line as shown in the following diagram as 1) which results with 

Option B when clear liquids are used and 2) which results with Option A and is only possible 

when clear liquids are used. 

Graduation Line 

Graduation Mid-point 

Option A, Mid-point of the meniscus. Option B, Top of the meniscus. 

When opaque liquids are used, an additional error or correction factor based on the volume 

contained between the upper and lower edges of the meniscus may need to be considered. The 

curve of the meniscus and impact of this error is dependent on the diameter of the meniscus and 

surface tension of the liquid being used. 

GMP 3 Page 3 of 5 
 

April 2013 

Uncertainty and Error Analysis in Meniscus Readings 

The standard deviation of replicate meniscus readings of volumetric measures provides an 

estimate of precision that can be used in the uncertainty analysis. However, potential errors in 

reading a meniscus may be caused by poor eye alignment according to Option A or B, by lack of 

cleanliness on material surfaces, by variations in visual acuity, by lighting, by the use of cameras 

or other optical tools, and by the thickness of the graduation line and characteristics of the 

meniscus itself. Repeatability, or precision, provides an estimate of the process variability, but 

the potential errors may result in systematic inaccuracies or biases. 

“Precision” in the following graphic illustrates the repeatability of the measurement process and 

“Accuracy” demonstrates the possible systematic inaccuracy of the mean value versus a 

reference value, due to uncorrected errors. 

The sensitivity of the volume measurement to the meniscus reading uncertainty may be 

calculated using the equation for the volume of a cylinder and the neck diameter. 

Vol   r 

2 h where r is the radius of the internal diameter and h is the height of the line or 

meniscus reading uncertainty. Units will be determined based on the dimensional units that are 

used. For example radius in cm2

 and height in cm, will provide results in cm3 or mL. The 

meniscus itself often has an observed “thickness” that is larger than the graduation lines so this 

should be considered as well. The potential error in meniscus reading may 

be treated as a triangular distribution. 

Example for a Glass Flask 

If the internal diameter of a flask is 1.5 cm (15 mm) and the height of the 

graduation line is 0.50 mm, the volume associated with the line can be 

15 2 calculated as follows: Vol   ( ) 0.5= 88.36 mm3

 (0.088 mL). These 2 

values are rounded for illustrative purposes only; significance must be 

GMP 3 Page 4 of 5 
 

April 2013 

evaluated based on measuring instruments and flask resolution. Experimental data obtained by 

reading a meniscus among multiple laboratory staff members may also be used to incorporate an 

estimate of uncertainty in meniscus reading. 

Example for a Test Measure or Prover 

In a test measure or prover, the volume inside the gauge also represents the volume inside the 

neck. So, two volumes can be calculated and added together to determine the impact. 

If the internal diameter of the gauge tube is 13 mm 

(0.5 in) and the height of the graduation line is 

0.50 mm, the volume associated with the line 

inside the gauge tube can be calculated as follows: 

13 2 Vol   ( ) 0.5 = 66.4 mm3

 (0.066 mL). This 2 

amount alone is generally not readable on the test 

measure or prover. But, the equivalent amount of 

volume that this gauge tube volume represents in 

the neck (given a 3 in neck) can be calculated as 

76.2 2 follows: Vol   ( ) 0.5 = 2.28 mL. These

2 

two volumes are added together, giving a sum of 

2.346 mL, or about 0.143 in3 . In the case of a 5 

gal test measure, the typical calibration 

uncertainty is about 0.35 in3

, so this potential error 

is significant. 

These values are rounded for illustrative purposes only; actual significance must be evaluated 

based on measuring instruments and resolutions. Experimental data obtained by reading a 

meniscus among multiple laboratory staff members may also be used to incorporate an estimate 

of uncertainty in meniscus reading. 

GMP 3 Page 5 of 5 
 

 

 

April 2013 

GMP 6 

Good Measurement Practice 

for 

Cleaning Metal Volumetric Measures 

All volumetric test measures, including laboratory standards and those submitted for calibration 

must be clean at the time of measurement. Drainage is altered by greasy and oily surfaces. 

Corroded surfaces raise questions that impair future use, so corrosion-damaged containers may not 

be worth testing. Maintaining clean volumetric test measures improves reproducibility of delivered 

volume between calibration and usage. 

Many laboratories will not accept test measures and provers for calibration unless they have been 

suitably cleaned to remove contents such as petroleum or other chemical residues. In those cases, 

all surfaces (inside and out), drain lines, pumps, and hoses that may be used during the calibration 

process must be cleaned so that no petroleum or other product residue remains that would 

otherwise spill onto the laboratory floor or drain into the sewer/waste-water system. 

Metal measuring vessels are best cleaned by using a non-foaming dishwashing detergent. Warm 

water is most effective both for cleaning and rinsing, which must be thorough. If warm water 

cleaning and rinsing is used, the vessel must be equilibrated to calibration temperatures before use 

or calibration. 

The cleaning operation involves the use of a liberal amount of the detergent solution and vigorous 

shaking, swirling, or other motion so that the solution contacts the entire inner surface of the vessel. 

Depending on the condition of the surface, this operation should be repeated one or more times to 

ensure removal of oily films and residues. As much as possible of the detergent solution should be 

drained prior to the water rinses to facilitate complete removal of the detergent from the prover. 

Ordinarily, three rinses will be sufficient, but this should be confirmed by testing the final rinse for 

any visual evidence of detergent or other residues. 

When detergents are not sufficient to remove oily or greasy deposits, solvents may be used, 

provided it is ascertained that they do not affect any coatings on the container. The surfaces should 

be dry before any calibrations are attempted. 

If lime or scale build-up has occurred (usually only in standards that are primarily used with water), 

they may be cleaned with a suitable lime or scale remover. Many of these chemicals contain acids 

and may react with metals, so appropriate care should be taken and these chemicals should not be 

allowed to soak for extended periods of time. Many lime and scale removers have safety and 

handling requirements and may have special disposal requirements. The material safety data sheet 

(MSDS) should be reviewed prior to using or disposing of scale and lime removers. 

After cleaning or use, vessels should be drained completely and stored in a dry place. They should 

be covered to prevent entrance of dust and foreign matter. Metal containers further should be 

protected from damage by denting and/or dropping. Once such a vessel has been visibly dented, it 

GMP 6 Page 1 of 2 
April 2013 

is difficult to ascertain whether additional changes have occurred. Even when dents have been 

removed and the vessel has been calibrated, visual deformities can compromise future use. 

Accordingly, protection from damage while stored and when in use should be a major concern of 

the metrologist or owner of the device. 

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April 2013 

GMP 7 

Good Measurement Practice 

for 

Cleaning Precision Glassware 

The volume contained in or delivered from precision glassware depends on the cleanliness of the 

container. Glassware must be sufficiently clean to ensure uniform wetting of the entire internal 

surface of the standard. When clean, the walls will be uniformly wetted and the water will adhere 

to the surface in a continuous film. If films of dirt or grease are present, the meniscus may 

crinkle at the edges and liquids will not drain properly and will leave water drops on the internal 

walls. Lack of cleanliness can cause errors in setting a meniscus and incomplete 

wetting/drainage of the calibration liquid (generally water.) 

Glassware that is submitted for calibration should be cleaned (and autoclaved if needed) prior to 

submission to the laboratory to ensure removal of all chemical, biological, radiological, or other 

contaminants. 

If glassware is cleaned by the laboratory, appropriate inquiries should be made to determine 

prior and subsequent uses along with implications of certain cleaning methods. Some methods of 

cleaning glassware prior to calibration or use are ineffective or detrimental and may leave 

chemical contamination deposits that can be detected in some chemical analysis operations. 

There are a number of suitable detergents (both liquid and powder), available from laboratory 

supply houses that do not contain phosphates. The catalog descriptions usually indicate whether 

or not they contain phosphates. Laboratory detergents that contain phosphates can leave a 

deposit on the glass that will cause water to "bead" on the surface making it appear to be dirty, 

and making it difficult to properly set a meniscus. Once a phosphate deposit has occurred, it is 

very difficult to remove. It may be removed with hot (approx. 65 °C) sodium dichromate-sulfuric 

acid cleaning solution. However, use of this hot solution is hazardous, is a problem for safe 

disposal, and is not recommended unless proper safety equipment is available (see the next 

section). 

If acetone is used to remove oil or grease film, always follow with alcohol (ethanol) before 

drying or rinsing with water. Denatured methanol can leave an oily residue due to the denaturing 

process. Acetone, if allowed to dry, may also leave a film deposit. 

The above solvents need not be used if the glass does not have oil or grease film. Mechanical 

shaking of water and suitable non-phosphate detergents is usually adequate for cleaning 

glassware. 

These cleaning agents do not preclude the use of other suitable methods, of which there are 

several. Some have special applications that would not normally be encountered by metrologists 

or field inspectors. 

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See GLP 13, Good Laboratory Practice for Drying Containers for appropriate drying techniques. 

It is not necessary to dry any container marked “to deliver.” 

Cleaning Methods 1 

Safety Note: Material safety data sheets (MSDS) should be available, studied, and carefully 

followed before using any of the following cleaning methods. Chromic acid solutions are not 

recommended for routine use because it is a hazardous waste and hazardous to health! Suitable 

education or training in the handling of chemicals is highly recommended. 

Frequently it is desirable to give glassware a preliminary rinse or soak with an organic solvent 

such as xylene or acetone to remove grease, followed by a water rinse. The rinsing with water 

must be done thoroughly if acid will be used later to clean the glassware. 

Unless autoclaving is necessary, glassware should be cleaned as soon as possible after use to 

avoid setting and caking of residues. Pipets, for example, may be placed in a jar containing a 

weak antiseptic solution immediately after use. Autoclaving is necessary to disinfect glassware 

that may have been used to contain potentially dangerous biological fluids. 

A selection of general cleaning methods follows: 

1. Fill with sulfuric acid-dichromate mixture and let stand. After removal of the mixture, 

rinse with distilled water at least six times. To make the cleaning mixture, dissolve (60 to 

65) g of sodium- or potassium-dichromate by heating in (30 to 35) mL of water, cool and 

slowly add concentrated sulfuric acid to make one liter of solution. This solution is 

available from laboratory supply companies. 

Note: Extreme care should be exercised in handling acidic solutions. 

2. Scrub with a 1 % to 2 % hot solution of a detergent. Rinse well after brushing. A number 

of suitable, commercial washing compounds are available. 

3. Fuming sulfuric acid (very hazardous material) is an excellent cleaning agent. Usually, 

cleaning can be accomplished by use of a comparatively small amount of acid, 

manipulating the vessel so that the acid comes in contact with the entire surface, and 

immediately emptying and rinsing. 

When a piece of glassware is badly contaminated with stopcock grease (except silicone grease), 

it may be necessary to rinse with acetone once or twice before using one of the above methods. 

For silicone grease, the acetone can be omitted and the piece soaked for 30 min in fuming 

sulfuric acid. Warm decahydronaphthalene (decalin) also has been suggested as a solvent for 

silicone grease. In this case, let the piece soak for 2 h, drain, and rinse once or twice with 

1 While the metrologist is not ordinarily faced with the problems for which these procedures are necessary, they are 

given here in the event that they are needed. 

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acetone, followed by a water rinse. 

Cautions 

Care should be exercised when using most cleaning solutions because they can cause skin 

irritations or severe burns on contact. Dilute solutions become concentrated as the water 

evaporates; therefore, always flush the exposed area immediately with large quantities of water. 

Suitable chemical-specific-resistant goggles or a face mask should be worn to protect the eyes 

from splashes and rubber gloves should be worn to protect the hands. It is advisable to wear an 

acid resistant laboratory coat or a rubber apron to protect clothing when using strong acids for 

cleaning. The glassware should be handled gently to avoid breakage and also to prevent spilling 

acids and other cleaning fluids. All cleaning should be done in a laboratory sink or on an 

acid-proof laboratory bench, preferably within a fume hood, to the extent possible. 

Some of the cleaning materials mentioned leave minute traces or residues unless the rinsing 

process is carried out thoroughly. While such traces may not be harmful if the purpose of 

cleaning is to prepare the glassware for calibration, they can give trouble when the glassware is 

used in certain laboratory operations. For example, manganese and chromium compounds, even 

in extreme dilution, may retard or inhibit growth of micro-organisms, and traces of phosphorus 

may interfere with delicate tests for this element. When glassware is to be calibrated, final 

rinsing must be with pure distilled or deionized water. 

If an article is to be dried after cleaning, as is necessary for all vessels marked "To Contain", 

acetone, followed by ethyl alcohol (American Chemical Society Specification) may be used. 

Drying may be hastened by blowing clean, dry air into the vessel (or drawing the air through the 

vessel). Be sure not to mix acetone with alcohol. (See GLP 13.) 

Efficient air filters must be provided to remove any particles of oil or dirt from compressed air 

used for drying purposes. 

GMP 7 Page 3 of 3 
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Standard Operating Procedures 
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1 

April 2013 

SOP No. 14
 

Recommende d Standard Ope rating Procedure
 

for
 

Gravimetric Calibration of Volumetric Standards Using an Electronic Balance
 

Introduction 

1.1	 Purpose of Test 

This procedure is a precision mass calibration converting mass values to volumetric 

values using pure water as a standard reference material. The results provide calibration 

of either the "to deliver" or "to contain" volume of measuring containers that may be 

used as volumetric measuring standards. The procedure uses gravimetric calibration 

principles to minimize calibration uncertainties. Accordingly, the procedure is especially 

useful for high accuracy calibrations. The procedure references measurement control 

standards to ensure the validity of the standards and the measurement process; 

however, additional good measurement practices such as those required for precision 

mass calibrations must be used. The procedure makes use of an electronic balance and 

is suitable for all sizes of gravimetric calibrations only limited by the capacity and 

resolution of the balance and handling capabilities. Standards that are calibrated for use 

in legal weights and measures applications should be evaluated for conformance to the 

appropriate specifications and tolerances that apply. This procedure calculates the 

average volume based on two runs. NOTE: NIST calibrations generally make use of 

the average of five replicates. 

1.2	 Prerequisites 

1.2.1	 Verify that valid calibration certificates with appropriate values and uncertainties 

are available for all of the standards used in the calibration. All standards must 

have demonstrated metrological traceability to the international system of units 

(SI), which may be to the SI through a National Metrology Institute such as 

NIST. 

1.2.2	 Verify that the mass standards to be used have sufficiently small standard 

uncertainties for the level of calibration. Reference mass standards should not be 

used for gravimetric calibration due to the risk of water contamination. Weights 

of ASTM Class 2 or 3 or OIML Class F1 or F2 are recommended for this 

procedure. Working standards of other classes are generally not designed to 

maintain adequate stability needed; however, corrections obtained within a few 

days of the volume calibration may provide adequate stability and may be used 

if the uncertainty is sufficiently small and the density is available for performing 

buoyancy corrections. 

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1.2.3	 Verify that the balance used is in good operating condition with adequate 

capacity, sufficiently small resolution, and sufficiently small process standard 

deviation, as verified by a valid control chart or preliminary experiments using 

this procedure. NOTE: standard deviations obtained from mass calibrations do 

not reflect the process repeatability of gravimetric calibrations; therefore 

process repeatability must be obtained using this procedure! The accuracy of 

the balance and weighing procedures should be evaluated to minimize potential 

bias in the measurement process. 

1.2.4	 Verify that the operator is experienced in precision weighing techniques and has 

had specific training in SOP 2, SOP 4, SOP 29, GMP 3, GMP 10, and 

gravimetric calibrations. 

1.2.5	 Verify that an adequate quality and supply of distilled or deionized water (see 

GLP 10) is available. Note: Do not use tap water for this procedure! 

1.2.6	 Verify that air currents are minimized in the laboratory when weighing is 

performed. Verify that the laboratory facilities meet the following minimum 

conditions to enable meeting the expected uncertainty that is achievable with this 

procedure: 

Table 1. Laboratory environme ntal conditions. 

Procedure Temperature Relative Humidity 

Gravimetric 20 C to 23 C 

Stable to ± 1 C / 1 h, during the calibration 

40 % to 60 % 

Stable to ± 10 % / 4 h 

Methodology 

2.1	 Scope, Precision, Accuracy 

The procedure is applicable for the calibration of any size of measuring container that, 

when filled with water, will not overload the electronic balance used. Typical containers 

range in capacity from 1 mL to 20 L; however, this procedure is also applicable for 

larger provers provided that facility, equipment and standards meet the requirements in 

this SOP. When larger provers (e.g., 100 gal or more) are tested, also see the Test 

Notes in the Appendix. The procedure is generally only appropriate for micropipettes 

when additional evaporation corrections are made. The precision of calibration depends 

on the care exercised in adjusting the various volumes and strict adherence to the 

various steps of the procedure. The accuracy attainable depends on the ability of the 

operator to read and set the meniscus, uncertainties of the standard weights, the air 

buoyancy corrections, and thermal expansion corrections that are made. 

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2.2	 Summary 

The electronic balance used is calibrated by incorporating standard masses into the 

procedure. The volumetric vessel to be calibrated is then weighed dry or “wetted 

down,” depending on whether the calibration is to be made on a “To Contain” or “To 

Deliver” basis. The container is filled with pure water of known temperature and reweighed. The difference in mass is used to calculate the capacity of the container at the 

nominal capacity and at various capacities when multiple neck graduations are present. 

Transfer vessels may be used for all procedures except for flasks and containers 

marked “To Contain” (TC). 

2.3	 Standards and Equipment Requirements 

2.3.1	 An electronic balance having sufficient capacity to weigh the loaded vessel is 

required. The balance selection affects the potential measurement errors 

associated with this procedure. Prior to use and where available, it is 

recommended to use the adjust/calibrate feature on balances. Option A 

provides a single point calibration factor for the balance. In general, concerns 

are greater for balances or mass comparators larger than 5 kg due to corner 

loading errors, non-linearity, and repeatability over the range of use. Option B 

as described in the calculation section for larger volumes corrects for balance 

non-linearity in both the filled and empty/drained ranges of use. Option B will 

also likely be required on mass comparators that have multiple ranges. It also 

provides corrections for variations in air density that may occur over a longer 

weighing process on larger volumes. For all procedures in this SOP, the balance 

should be zeroed prior to each measurement to minimize possible effects due to 

balance drift. The sensitivity or resolution of the balance may be a limiting factor 

in the accuracy of the measurement. The resolution and repeatability must be 

smaller than the accepted uncertainty of the calibration. Linearity errors or 

additional uncertainties may need to be considered when the mass standards are 

slightly less than the volume or container being measured. 

2.3.2	 Sufficient quantity of calibrated mass standards. Mass standards are selected so 

that they are slightly larger than the combined mass of the volume and container 

or transfer vessel that will be weighed. When summations of masses are used, 

the summation mass is used, and the “effective density” must be calculated, 

taking care not to use “average” density values. 

2.3.3	 Thermometer with resolution and uncertainty less than 0.1 °C to determine 

water temperature. 

2.3.4	 Thermometer with resolution and uncertainty less than 0.50 °C to determine air 

1 temperature. 

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April 2013 

2.3.5	 Barometer with resolution and uncertainty less than 135 Pa (1 mm Hg) to 

determine air pressure.1 

2.3.6	 Hygrometer with resolution and uncertainty less than 10 % to determine relative 

humidity.1 

2.3.7	 Distilled or deionized water (See GLP 10) of sufficient quality and quantity for 

the calibration. Note: Do not use tap water for this procedure! 

2.3.8	 Stopwatch or other suitable timing device (does not need to be calibrated.) 

2.4	 General Considerations 

2.4.1	 Cleanliness checks 

Verify that all containers to be calibrated are clean as evidenced by uniform 

drainage of water. No water droplets should remain on any interior surface as 

the water drains from the container. A reproducible “wet-down” weight is 

evidence for cleanliness in cases where it is not possible to visually check for 

uniform drainage. Use GMP 6 or 7 to clean vessels as necessary. All glassware 

must be meticulously cleaned, prior to calibration. When clean, the walls will be 

uniformly wetted. Instructions for cleaning are given in GMP 6 and GMP 7. An 

exception is plastic ware, which will not be wetted. Follow manufacturer's 

instructions for cleaning such vessels. Do not use cleaning agents that will attack, 

discolor, or swell plastic ware. 

2.4.2	 Use water that is thermally equilibrated with the laboratory environment. 

Equilibration can be achieved by storing the water in clean containers in the 

laboratory. It is important to use water that is equilibrated in the laboratory as 

much as possible to minimize potential calibration errors and convection 

currents during the calibration. Consider water to be equilibrated when within ± 

5 °C of the laboratory temperature. 

2.4.3	 Volumetric calibrations to a marked volume (graduation line) are critically 

dependent on the setting of a meniscus. See GMP 3 for guidance in reading a 

meniscus. 

2.4.4	 Use GLP 13 as the procedure to dry any container to be calibrated on a “To 

Contain” basis. 

2.4.5	 Wet down (not used for any container calibrated “To Contain”) 

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For glassware and hand-held test measures: Fill the container to capacity with 

distilled or deionized water, then empty over a 30 s period while avoiding 

splashing. Drain for 10 s unless another drain time is specified. (This is 

commonly called a “30 s pour, 10 s drain” emptying procedure.) A 30 s (± 5 

s) pour followed by a 10 s drain, with the measure held between a 10 degree 

and 15 degree angle from vertical is required during calibration and use for glass 

flasks. A wet-down is not required for a transfer vessel that is used to weigh a 

delivered volume of water. 

For stationary provers: Fill the container to capacity with distilled or deionized 

water, then empty. Time the drain once the cessation of the main flow is 

complete for 30 s and close the valve. 

2.5	 Calibration Procedure for Burets 

2.5.1	 Clamp the buret vertically on a support stand. Also clamp a plain glass test tube 

or beaker, large enough to hold a thermometer, in the vicinity of the buret. 

2.5.2	 Fill the buret with water and test for absence of leaks from the tip and 

stopcock. Drain and fill several times to condition the buret. Fill when ready to 

test. 

2.5.3	 Drain and record the delivery time, defined as the time of unrestricted flow from 

the zero mark to the lowest graduation mark with the stopcock fully open. 

2.5.4	 Fill the buret slightly above the zero mark with temperature-equilibrated water 

and also fill the test tube that holds the thermometer. Record the water 

temperature. 

2.5.5	 Set the meniscus on the zero mark and touch the tip with the wetted wall of a 

beaker to remove any excess water. The buret tip must be full. 

2.5.6	 Measure and record the air temperature, air pressure, and relative humidity. 

2.5.7	 Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the empty transfer vessel or flask 

when filled with water. Record the reading as O1. 

2.5.8	 Zero the balance and then weigh an empty transfer vessel or flask including the 

stopper or cover to be used. Record as O2. 

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2.5.9	 Fully open the stopcock and discharge the contents of the buret into the 

previously weighed flask or transfer vessel. The tip of the buret should be in 

contact with the wall of the flask. When the level in the buret is within a few 

millimeters above the line being calibrated, slow the discharge and make an 

accurate setting. When the setting is completed, move the flask horizontally to 

break contact with the tip. Recheck the setting. 

2.5.10 Stopper (or cover) the filled transfer vessel or flask. Check to make sure that 

the outside of the transfer vessel or flask is not wet. Zero the balance and then 

weigh the filled transfer vessel or flask. Record the balance reading as O3. 

2.5.11 Measure and record the temperature of water in the container. 

2.5.12 Test the next interval in the same manner	 - from the zero mark to the next 

interval of test. 

2.5.13 For burets with a specified waiting time, empty as in 2.5.9 to within a few 

millimeters of the calibration mark. Pause for the specified waiting time (e.g., 10 

s), then adjust the meniscus to the graduation line as in 2.5.9. 

2.5.14 Measure and record the air temperature, air pressure, and relative humidity. 

2.5.15 Make a duplicate determination for each interval (Run 2). 

2.5.16 Calculate the volume for each interval as described in Section 3, Option A. 

2.6	 Calibration Procedure for Pipets (One-Mark) 

2.6.1	 Measure and record the air temperature, air pressure, and relative humidity. 

2.6.2	 Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the empty transfer vessel or flask 

when filled with water. Record the reading as O1. 

2.6.3	 Zero the balance and then weigh an empty transfer vessel or flask, including the 

stopper or cover that will be used. Record the balance reading as O2. 

2.6.4	 Fill the pipet to the index mark and measure the delivery time with the tip in 

contact with the internal surface of a beaker (not the transfer vessel that will be 

used.) 

2.6.5	 Refill the pipet by suction, slightly above the index line. Record the water 

temperature. Wipe tip with filter paper, then slowly lower level to the index line, 

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April 2013 

using a stopcock or pinch clamp for fine control. The tip must be in contact with 

the wetted wall of the beaker while this setting is being made. Do not remove 

any water remaining on tip at this time. 

2.6.6	 Hold the pipet in a vertical position and deliver water into the previously 

weighed transfer vessel or flask, with the tip in contact with the inside wall or 

neck. 

2.6.7	 After flow has ceased, wait two seconds then remove the pipet from contact 

with the flask. Check to make sure that the outside of the transfer vessel or flask 

is not wet. 

2.6.8	 Stopper (or cover) the filled transfer vessel or flask. Zero the balance and then 

weigh the transfer vessel or flask. Record the balance reading as O3. 

2.6.9	 Measure and record the temperature of water in the container. 

2.6.10 Measure and record the air temperature, air pressure, and relative humidity. 

2.6.11 Make a duplicate determination for the pipet (Run 2). 

2.6.12 Calculate the volume as described in Section 3, Option A. 

2.7	 Calibration of Flasks (To Contain) – Transfer vessel must not be used. 

2.7.1	 Clean and dry the flask to be calibrated as described in GLP 13. Then stopper 

the flask. 

2.7.2	 Measure and record the air temperature, air pressure, and relative humidity. 

2.7.3	 Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the flask when filled with water. 

Record the reading as O1. 

2.7.4	 Zero the balance and then weigh the dry flask including its stopper or cover. 

Record the balance reading as O2. 

2.7.5	 Place an appropriate sized funnel in neck and fill the flask to just below the 

reference graduation while maneuvering the flask to wet the entire neck below 

the stopper. Let stand for two minutes then adjust the meniscus to the reference 

graduation line, taking care to avoid wetting the neck above the capacity 

graduation. 

2.7.6	 Check that the outside surface of the flask, and its internal surface above the 

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water level are dry, and that neither bubbles or foam are present in the water. 

Remove visible water droplets if needed with a laboratory wipe. Stopper or 

cover the flask. 

2.7.7	 Zero the balance and then weigh the filled flask and its stopper or cover, and 

record the balance reading as O3. 

2.7.8	 Measure and record the temperature of the water in the flask or other container. 

2.7.9	 Measure and record the air temperature, air pressure, and relative humidity. 

2.7.10 Make a duplicate determination (Run 2) after drying the flask per GLP 13. 

2.7.11 Perform volume calculations as described in Section 3, Option A. 

2.8	 Calibration of Flasks (To Deliver) 

2.8.1	 Clean but do not dry the flask to be calibrated. Condition the flask by filling and 

emptying the flask over a 30 s period by gradually inclining it to avoid splashing. 

When the main flow has ceased, hold the flask in a nearly vertical position for 

10 seconds unless another drain time is specified, then touch off the drop of 

water adhering to the tip of the flask. 

2.8.2	 Measure and record the air temperature, air pressure, and relative humidity. 

2.8.3	 Zero the balance and then place a known mass standard on the balance pan 

that is slightly larger than the filled capacity of the flask when filled with water. 

Record the reading as O1. 

2.8.4	 Zero the balance and then weigh the drained (empty) flask including its stopper 

or cover. Record the balance reading as O2. 

2.8.5	 Fill the flask to just below the reference graduation. Let the flask stand for two 

minutes, then adjust the meniscus to the reference graduation line. Do not dry 

the inside of the flask above the graduation line, but take care to ensure that the 

outside of the flask is dry. 

2.8.6	 Zero the balance and then weigh the filled vessel, with cap or stopper. Record 

the balance reading as O3. 

2.8.7	 Measure and record the temperature of the water in the flask. 

2.8.8	 Measure and record the air temperature, air pressure, and relative humidity. 

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2.8.9	 Make a duplicate determination (Run 2). 

2.8.10 Calculate the volume of the flask as described in Section 3, Option A. 

Note: The order of weighing the filled and drained flask in Section 2.8 may be reversed . In that case, 

the filled vessel is still weighed and recorded as O 3, the flask is drained as in 2.8.1, and the properly 

drained vessel is weighed and recorded as O2. 

2.9	 Calibration of Other Volumetric Glassware 

2.9.1	 Measuring Pipets (non-single-mark) – Calibrate in a manner similar to that used 

to calibrate burets (2.5). 

2.9.2	 Graduated Cylinders – Calibrate in a manner similar to that used for flasks (To 

Deliver cylinders, use section 2.8; To Contain cylinders, use section 2.7). 

2.10	 Calibration of Slicker-Plate Type Standards 

2.10.1 This calibration makes use of Option B where equivalent mass standards are 

used at both the filled and empty loads on the balance. A transfer vessel is 

recommended. 

2.10.2 Condition the slicker-plate type standards with several wet-down runs to fully 

ensure wet down and smooth valve operation. 

2.10.3 Measure and record the air temperature, air pressure, and relative humidity. 

2.10.4 Zero the balance and then place a standard mass, MS1, on the balance platform 

(MS1 should be slightly larger than the mass of the drained vessel, dry vessel, or 

empty transfer vessel.) Record reading as O1. 

2.10.5 Zero the balance. Place the dry or “wet-down” transfer vessel on the balance 

platform, as appropriate, and record reading as O2. Caution: all containers must 

be dry on the outside for all weighing. 

2.10.6 Fill the slicker-plate standard to just above the rim of the standard. Record the 

water temperature. Slide the slicker plate across the level top. Set the transfer 

vessel below the nozzle to ensure all volume is transferred into the vessel and 

that no splashing occurs. 

2.10.7 Open the slicker-plate standard valve and remove the plate simultaneously and 

smoothly to deliver the water into the transfer vessel. Time the drain for 30 s 

after cessation of the main flow and close the valve. Cover the transfer vessel 

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and move it from beneath the standard to ensure additional drops of water are 

not transferred. Note: never fill the transfer vessel while it is sitting on the 

balance platform to ensure that the balance is not damaged with water and to 

avoid errors associated with balance drift and hysteresis. 

2.10.8 Zero the balance and then place a standard mass, MS2, on the balance platform 

(MS2 should be slightly larger than the mass of the filled vessel.) Record the 

balance reading as O3. 

2.10.9 Zero the balance and then weigh the filled transfer vessel and record the balance 

reading as O4. 

2.10.10 Immediately after weighing, check the temperature of the water in the filled 

container. Ensure that the water has not changed by more than 0.2 °C during 

the measurement process or repeat the run. 

2.10.11 Measure	 and record the air temperature, barometric pressure, and relative 

humidity. 

2.10.12 Make a duplicate determination (Run 2). 

2.10.13 Calculate the volume as described in Section 3, Option B. 

2.11	 Calibration of Hand-held Graduated Neck Type Provers 

2.11.1 A hand-held test measure is weighed empty and filled much like the procedure 

for To Deliver flasks (section 2.8). However, this calibration makes use of 

Option B where equivalent mass standards are used at both the filled and empty 

loads on the balance. 

2.11.2 Condition the test measure by filling and draining using a 30 s pour followed by 

a 10 s drain. Take care to avoid splashing of water on the outside of the 

measure. The wet-down will help equilibrate the test measure with the water 

temperature. 

2.11.3 Measure and record the air temperature, air pressure, and relative humidity. 

2.11.4 Zero the balance and then place standard masses, MS1, on the balance platform 

(MS1 should be slightly larger than the mass of the drained vessel.) Record 

reading as O1. 

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2.11.5 Zero the balance and then place the “wet-down” test measure on the balance 

platform, and record the balance reading as O2. Caution: all containers must be 

dry on the outside for all weighing. 

2.11.6 Fill the	 graduated neck type test measure to just below the nominal volume 

mark. Record the water temperature. Adjust the meniscus to nominal. 

2.11.7 Zero the balance and then place standard masses, MS2, on the balance platform 

(MS2 should be slightly larger than the mass of the filled vessel.) Record the 

balance reading as O3. 

2.11.8 Zero the balance and then weigh the filled transfer vessel and record the balance 

reading as O4. 

2.11.9 Immediately	 after weighing, check the temperature of the water in the filled 

container. Ensure that the water has not changed by more than 0.2 °C since 

step 2.11.6 or repeat the run. 

2.11.10 Measure	 and record the air temperature, barometric pressure, and relative 

humidity. 

2.11.11 Make a duplicate determination (Run 2). 

2.11.12 Calculate the volume as described in Section 3, Option B.	 You may use the 

average water temperature in calculations. If a neck scale plate verification is 

performed, additional weighings may be performed after setting the meniscus at 

each level. 

2.12	 Calibration of Large Volume Graduated Neck Type Provers 

2.12.1 This calibration makes use of Option B where approximately equivalent mass 

standards are used at both the filled and empty loads on the balance. A transfer 

vessel is recommended. The unknown vessel to be calibrated must be elevated 

to facilitate transfer of water into the transfer vessel. 

2.12.2 Condition	 the prover with a wet-down run to fully ensure smooth valve 

operation, temperature equilibration, and wet-down of the delivery system. 

2.12.3 Measure and record the air temperature, air pressure, and relative humidity. 

2.12.4 Zero the balance and then place standard masses, MS1, on the balance platform 

(MS1 should be slightly larger than the mass of the drained vessel, dry vessel, or 

empty transfer vessel.) Record reading as O1. 

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April 2013 

2.12.5 Zero the balance. Place dry or “wet-down” transfer vessel including cover on 

balance platform, as appropriate, and record reading as O2. Caution: all 

containers must be dry on the outside for all weighing. 

2.12.6 Fill the	 graduated neck type prover to just below the nominal volume mark. 

Record the water temperature. Adjust the meniscus to nominal. Set the transfer 

vessel below the nozzle to ensure all volume is transferred into the vessel and 

that no splashing occurs. Use hoses and piping of minimum length to avoid 

errors associated with retention during delivery. Hoses should be translucent so 

that cessation of the main flow is visible. Care should be taken to ensure that 

there are no loops or sags in the hose that may hold water. When using hoses or 

piping, be sure to include them as part of the wet-down process. 

2.12.7 Open the unknown prover valve to deliver the water into the transfer vessel. 

Time the drain for 30 s after the cessation of the main flow and close the valve. 

Cover the transfer vessel and move it from beneath the prover to ensure 

additional drops of water are not transferred. 

2.12.8 Zero the balance and then place standard masses, MS2, on the balance platform 

(MS2 should be slightly larger than the mass of the filled vessel.) Record the 

balance reading as O3. 

2.12.9 Zero the balance and then weigh the filled transfer vessel and its cover. Record 

the balance reading as O4. 

2.12.10 Immediately after weighing, check the temperature of the water in the filled 

container. The temperature should not change by more than 0.2 °C if the prover 

and water have been equilibrated in the laboratory environment. 

2.12.11 Measure	 and record the air temperature, barometric pressure, and relative 

humidity. 

2.12.12 Make a duplicate determination (Run 2). 

2.12.13 Calculate the volume as described in Section 3, Option B. You may use the 

average water temperatures for calculations. 

Calculations 

3.1	 Option A – One-point balance calibration. Compute the volume at the temperature 

under test, Vt, for each determination using the equation: 

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3 
 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

  

































 

















 

1

 1 

1

23

s w a

s a

t O

M

OOV





Eqn. 3.1 

Note: the O3 value is the filled volume container or transfer vessel and O 2 is the dry, 

empty, or drained value. If the order of any weighing operations were changed, the 

calculated volume may indicate a negative value. 

3.2	 Option B – Two point balance calibration. Compute the volume, Vt, for each 

determination using the equation: 















































  















 

 

1

1 

O

O

1 

O

O

 

1

1

1

2

2

2

3

4

s aw

a

s

s

a Vt Ms M









Eqn. 3.2 

Table 2. Variables for volume equations . 

Variable Description 

Ms, Ms1, 

Ms2 

mass of standards (i.e., true mass, vacuum mass) (g) 

s density of MS (g/cm3) 

w density of water at the temperature of measurement (g/cm3) 

a density of air at the conditions of calibration (g/cm3) 

Vt 

represents either the “to contain” or “to deliver” volume (depending on 

whether O2 represents a dry or a “wet down” container at the temperature 

of the measurement) (cm3 or mL) 

3.3	 Glassware is typically calibrated to 20 °C. Compute V20, the volume at 20 C, for each 

run, using the expression: 

 - t ( - 1 V V 20 )  20 

t 

 1   20  20 VV t  t 

Eqn. 3.3 

where  is the cubical coefficient of expansion of the container being calibrated (°C-1), (see 

NISTIR 6969, Table 9.10), and, t, is the temperature (oC) of the water. Compute the mean V20 

for the duplicate measurements. 

3.4	 Test measures and provers are typically calibrated to 60 °F. Compute V60, the volume 

at 60 F, for each run, using the expression (taking care to use the cubical coefficient of 

expansion in °F-1): 

 1   60  60 VV t  t 

Eqn. 3.4 

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3.5	 If using a different reference temperature, use the following equation and take care to 

match the cubical coefficient of expansion units with the units of temperature: 

 1   t  ef  ref VV t

tr 

Eqn. 3.5 

3.6. Other Reference temperatures may be used. Common reference temperatures for other 

liquids follow: 

Commodity Reference 

Temperature 

Frozen food labeled by volume (e.g., fruit juice) -18 oC (0 oF) 

Beer 3.9 oC (39.1 oF) 

Food that must be kept refrigerated (e.g., milk) 4.4 oC (40 oF) 

Distilled spirits or petroleum 15.56 oC (60 oF) 

Petroleum (International Reference) 15 oC (59 oF) 

Compressed Natural Gas (CNG) 15 °C (60 oF) 

Wine 20 oC (68 oF) 

Unrefrigerated liquids (e.g., sold unchilled, like soft drinks) 20 oC (68 oF) 

Hydrogen (H2) 21 oC (70 oF) 

Petroleum (Hawaii) 26.67 oC (80 oF) 

4	 Measurement Assurance 

4.1	 Duplicate the process with a suitable check standard (See GLP 1, SOP 30, in 

NISTIR 6969, or Sec. 7.4, in NBS Handbook 145) or conduct replicate 

measurements per SOP 17 or 20. Average values of the range or standard 

deviation of similarly sized flasks or volumetric standards may be tracked on a 

single range chart or standard deviation chart according to SOP 17 or 20 . A 

minimum of 12 replicate measurements are required to establish initial process 

limits and 25 to 30 points are required for reporting valid uncertainty values. 

4.2	 Plot the check standard volume and verify it is within established limits. A t-test 

may be incorporated to check the observed value against an accepted value. 

4.3	 The mean of the check standard is used to evaluate bias and drift over time and 

may be used to identify or signify problems with the volume standard or changes 

in water quality. 

4.4	 Check standard observations are used to calculate the standard deviation of the 

measurement process, sp. 

5 Assignment of Uncertainties 

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of the mass 

standards used, uc, plus the measurement process repeatability, sp, at approximately a 95 

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percent level of confidence. See SOP 29 for the complete standard operating procedure for 

calculating the uncertainty. 

5.1	 The standard uncertainty for the standards, us, is obtained from the calibration 

report. The combined standard uncertainty, uc, is used and not the expanded 

uncertainty, U, therefore the reported uncertainty for the standard will usually 

need to be divided by the coverage factor k. Multiple mass standards are often 

used, so see SOP 29 for treatment of dependencies and correlations. 

5.2	 Standard deviation of the measurement process from control chart performance 

(See SOP No. 17 or 20.) 

The value for sp is obtained from the control chart data for check standards when 

a check standard is available using this procedure. It may also be estimated based 

on replicate measurements over time. Replicate measurements over time may 

provide a pooled standard deviation that may be used or the average range is 

used to estimate the standard deviation per SOP 17 or 20. This standard 

deviation value is a repeatability factor related to the precision of the weighings 

and the setting of the meniscus when present, but does not include uncertainties 

associated with errors in reading the meniscus (See GMP 3.) 

5.3	 Include uncertainties associated with the reading of the meniscus when one is 

present. See GMP 3 for details. 

5.4	 Other standard uncertainties usually included at this calibration level include 

uncertainties associated with water temperature measurements, thermometer 

accuracy, calculation of air density, standard uncertainties associated with the 

density of the mass standards, coefficients of expansion, viscosity or surface 

effects on the volume of liquid clinging to vessel walls after draining, improper 

observance of drainage times, and the lack of internal cleanliness. 

5.5	 Example components to be considered for an uncertainty budget table are shown 

in Table 3. Multiple values may need to be considered in some cases. 

Table 3. Example uncertainty budget table. 

Uncertainty Component 

Des cription S ymbol S ource Typical Dis tribution 

Uncertainty of the s tandard 

mas s (es ) (5.1) us Calibration report 

Rectangular or 

Normal divided by 

coverage factor 

Accepted s tandard deviation of 

the proces s (5.2) sp 

Control chart, s tandard 

deviation chart Normal 

W ater temperature utx 

Cons ider accuracy, res olution, 

and gradients Rectangular 

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W ater dens ity uρw GLP 10 Rectangular 

Cubical Coefficient of Expans ion uCCE 

5 % to 10 % 

(EURAMET CG-19) Rectangular 

Menis cus reading (when pres ent) 

(5.3) um GMP 3 Triangular 

Drain time effects ud From experimental data Rectangular 

Air temperature (for air dens ity) ut SOP 2 Rectangular 

Air pres s ure (for air dens ity) up SOP 2 Rectangular 

Air relative humidity (for air 

dens ity) uRH SOP 2 Rectangular 

Air dens ity (equation) uρa SOP 2 Rectangular 

Mas s dens ity uρm

0.05 g/cm3 

NIST Reference Rectangular 

6	 Report 

6.1	 Report results as described in SOP 1, Preparation of Calibration/Test Results, 

with the addition of the following: 

6.1.1	 “To Contain” or “To Deliver” volume, reference temperature, uncertainty, 

material, thermal coefficient of expansion (assumed or measured), 

construction, any identifying markings, tolerances (if appropriate), 

laboratory air temperature, water temperature(s) at time of test, 

barometric pressure, relative humidity, and any out-of-tolerance 

conditions. 

Additional Re fe rence s: 

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S. D., and Johnson, A. N., NIST 

Calibration Services for Liquid Volume, NIST Special Publication 250-72, National Institute of 

Standards and Technology, Gaithersburg, MD, (2009). 

EURAMET Calibration Guide 19, Guidelines on the Determination of Uncertainty in Gravimetric 

Volume Calibration, (Version 2.1, 03/2012). 

SOP 14	 Page 16 of 19 
 

 

 

April 2013 

Appendix A (Single -Point Balance Calibration) 

Gravimetric Calibration Data Sheet (Option A) 

Laboratory data and conditions: 

Vessel ID Op erator 

M aterial Date 

Cubical Coefficient of Exp ansion Before After 

Balance Identification Temp erature 

Load Pressure 

Standard deviation of the p rocess, 

from control chart, sp 

Relative Humidity 

Degrees of Freedom Reference water 

temp erature 

Mass standard(s) data: 

ID (Not e ID and for Filled 

or Emp ty Load) Nominal M ass Correction* Exp anded Unc: From cal. rep ort 

Unc: 

k factor 

Density 

g/cm3 

S 

S 

S 

S 

S 

*M ass Correction = True Mass values are required. 

Observations: 

Run 1 Weights – Zero balance before each weighing. Balance Observations, Units______ 

MS O1 

Emp t y or Drained O2 

Filled O3 

tw 

Run 2 Weights – Zero balance before each weighing. Balance Observations, Units______ 

MS O1 

Emp t y or Drained O2 

Filled O3 

tw 

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Appe ndix B (Two-Point Balance Calibration) 

Gravimetric Calibration Data Sheet (Option B) 

Laboratory data and conditions: 

Vessel ID Op erator 

M aterial Date 

Cubical Coefficient of Exp ansion Before After 

Balance Temp erature 

Load Pressure 

Standard deviation of the p rocess, 

from control chart, sp 

Relative Humidity 

Degrees of Freedom Reference water 

temp erature 

Mass standard(s) data: 

ID (Note ID for Emp ty 

(MS1) or Filled (MS2) 

Loads) 

Nominal M ass Correction* Exp anded Unc: 

From cal. rep ort 

Unc: 

k factor 

Density 

g/cm3 

S 

S 

S 

S 

S 

S 

S 

*M ass Correction = True Mass values are required. 

Observations: 

Run 1 Weights – Zero balance before each weighing. Balance Observations, Units______ 

Ms1 O1 

Emp t y or Drained O2 

MS2 O3 

Filled O4 

tw in standard: tw in unknown: Temp erature change is less than 0.2 °C? Y/N 

Run 2 Weights – Zero balance before each weighing. Balance Observations, Units______ 

Ms1 O1 

Emp t y or Drained O2 

MS2 O3 

Filled O4 

tw in standard: tw in unknown: Temp erature change is less than 0.2 °C? Y/N 

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Appendix C 

Test Notes for Large Provers 

1	 Pour and drain times. 

It is impractical to completely drain a filled container, because some of the contents will remain 

as a film. By strict adherence to a specified procedure, the residual contents can be held 

essentially constant so that, reproducible calibration constants can be obtained . The 

conventionally selected conditions are as follows: 

a.	 For bottom-drain containers: open drain valve fully and allow contents to discharge at 

maximum rate. When flow ceases, wait 30 s, close valve, and touch off any drops 

adhering to spout. 

b.	 For pour-type containers: pour contents by gradually tilting container to an 85o angle, so 

that virtually all liquid is delivered in 30 s. Allow to drain for an additional 10 s, then 

touch off any drops adhering to the lip. 

The instructions described above must be precisely followed during calibration and use of the 

calibrated vessels. 

2	 Evaporation losses. 

A suitable cap should be placed on the top of open vessels to minimize evaporation losses. If 

used, the cap must be included in all weighings. 

3	 Slicker-plate. 

When a slicker-plate standard is calibrated, the plate should be used to fix the water level in it. 

A transfer vessel is recommended for use when calibrating a slicker-plate type standard. But if 

the standard is weighed, the plate must be weighed with the standard during each such 

operation. 

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SOP 16
 

Standard Ope rating Procedure for
 

Calibration of M e asuring Flasks
 

Volume Transfe r Method
 

Introduction 

1.1	 Purpose of Test 

This procedure describes a method for volume transfer calibration of the "to deliver" 

volume of measuring flasks from calibrated volumetric standards. The test items are then 

used as volumetric measurement standards, often for packaged commodity verification. 

If “to contain” calibrations are to be performed, appropriate modifications are needed in 

the procedure to ensure complete drying of the flask between calibration runs. 

1.2	 Prerequisites 

1.2.1	 Verify that valid calibration certificates are available for all of the standards used 

in the calibration. All standards must have demonstrated metrological 

traceability to the international system of units (SI), which may be to the SI 

through a National Metrology Institute such as NIST. 

1.2.2	 Verify that the standards to be used have sufficiently small standard uncertainties 

for the intended level of calibration. 

1.2.3	 Verify that the standard burets and pipets are clean, free of leaks, and in good 

operational condition. 

1.2.4	 Verify the availability of an adequate supply of pure distilled or deionized water 

(See GLP 10) of sufficient quality and quantity for the calibration. Do not use 

tap water for this procedure to ensure the reference glassware is maintained 

with valid reference values! 

1.2.5	 Verify that the operator has had specific training and is proficient in SOP 16, 

GMP 3, GMP 7, and is familiar with the operating characteristics and 

conditioning of pipets and burets. 

1.2.6	 Verify that the laboratory facilities meet the minimum conditions shown in Table 

1 to meet the expected uncertainty that is achievable with this procedure. 

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Table 1. Laboratory environmental conditions . 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 C to 27 C, 

Stable to ± 1 C / 1 h during the calibration 

40 % to 60 % 

Stable to ± 20 % / 4 h 

2 Methodology 

2.1	 Scope, Precision, Accuracy 

The method is applicable for the calibration of any size of measuring flask for which 

standard pipets of comparable volume are available. Typical flasks have volumes in the 

range of 100 mL to 5 L (1 gill to 1 gallon). The precision of calibration depends on the 

care exercised in adjusting the various volumes and strict adherence to the various steps 

of the procedure. The accuracy will depend on the accuracy of calibration of the 

volumetric standards used, accuracy in reading the meniscus, together with the precision 

of the comparison. Clean glassware and strict adherence to the drainage instructions are 

essential for precise and accurate results. 

2.2	 Summary 

The flask to be calibrated is given an initial wet-down using the correct drain procedure, 

then nearly filled with water delivered from a calibrated pipet. (This procedure relies on 

calibrated pipets that deliver slightly less than the full nominal volume.) Additional water 

is added to the test flask from a calibrated buret until the meniscus in the test item 

coincides with the calibration graduation mark. The sum of the volumes delivered into 

the wetted flask is equivalent to its "to deliver" volume. The process described assumes 

that the flask is marked with a 10-second drain time. If the flask is marked with a drain 

time other than 10 s, the specified drain time should be used rather than the 10 s drain 

time described. A 30-second drain time should be used when a flask has no drain time 

specified. 

2.3	 Standards and Equipment 

2.3.1	 Calibrated standard pipet(s) of suitable volumes. These standards are typically 

made of borosilicate glass. 

2.3.2	 Calibrated standard buret(s) of 10 mL (or 120 minim1

) capacity. These 

standards are typically made of borosilicate glass. 

1 1 [US] minim = 0.061615496 milliliter (mL). 120 minim s tandards were provided to the States as reference s tandards 

for us e in volume trans fer calibrations . Thes e s tandards have higher res olution than metric s tandards provided at the 

s ame time. 

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2.3.3	 Calibrated thermometers, with resolution and uncertainty to ≤ 0.1 °C to 

determine water temperature. 

2.3.4	 Meniscus reading device (See GMP 3). 

2.3.5	 Stopwatch or other suitable timing device (does not need to be calibrated). 

2.4	 Procedure 

2.4.1	 Cleanliness check 

Verify that all glassware, including the standards used and the vessels to be 

calibrated, are internally clean, as evidenced by uniform drainage of water. No 

water droplets should remain on the internal surfaces as the water drains from 

the vessels. If this occurs, the glassware must be cleaned with suitable agents 

and rinsed with pure water until uniform drainage is obtained. (See GMP 7). 

2.4.2	 Wet-down of pipet and flask 

2.4.2.1 Fill the	 standard pipet to until water flows from the top tip, then 

completely drain into an empty vessel. Check for uniform drainage. 

Touch off the pipet outlet tip against the container wall to remove 

excess droplets and to establish a constant tip retention volume. The 

pipet and bore of the delivery side of the stopcock should appear to be 

"empty" and the delivery tip should contain a small volume of water 

retained in it. This is the "wet-down" condition of the pipet. It must be 

done at the beginning of each test sequence. Ensure that the outside of 

the standard pipet is free of water droplets that may fall into the 

unknown flask. 

2.4.2.2 Refill the pipet and use it to fill the flask to be calibrated. Empty the 

flask using a gentle pour in a 30 s  5 s period by gradually inclining the 

flask so as to avoid splashing of the walls as much as possible. When 

the main drainage stream has ceased, the flask will be nearly vertical. 

Allow an additional 10 second drainage after discharge of the flask 

contents while holding the flask at a 10 to 15 angle from vertical, then 

touch off the rim of the flask to remove any drops adhering to it. At the 

same time, check that uniform drainage has been achieved. This 

establishes the "to deliver" condition of the flask. Note that some small 

amount of water will remain in the flask. Each flask to be calibrated 

must be given this "wet-down" treatment immediately before the start of 

the test. 

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2.4.3
 

2.4.4
 

Conditioning the buret 

2.4.3.1 Fill the standard buret to overflow and drain several times to verify 

uniform drainage. Refill with water. Note that the stopcock bore and 

delivery tip should be filled with water at all times, in contrast to the 

condition for the pipet. 

2.4.3.2 Touch off the delivery tip against the wall of the receiving vessel, to 

remove any droplet adhering to the external surface of the tip. This is an 

operation that must be done every time a measured volume of water is 

delivered from the buret to ensure consistent volume delivery. 

Calibration 

2.4.4.1 Run 1. Fill the standard pipet to overflow. The delivery bore and the 

delivery tip will be empty, except for the small volume retained in the 

tip. Place the inside of the flask neck in contact with the tip of the pipet 

or buret, to avoid splashing but in a manner that does not block the flow 

of water. 

2.4.4.2 Deliver the contents of the pipet into the "wet-down" flask. Repeat as 

necessary to nearly fill the flask to the calibration line. The value 

recorded for the standard pipet will be the total of the deliveries used. 

2.4.4.3 Add water to the flask from the buret until the meniscus coincides with 

the calibration mark. (See GMP 3 for instructions on how to read a 

meniscus.) Read the volume of water delivered from the buret and 

record on a suitable data sheet such as the one in the Appendix. Note: 

If multiple deliveries of the complete buret contents are required, ensure 

that at no time the buret water level drops below the lowest graduation 

mark, or the entire process must be started over. The value recorded 

for the standard buret will be the sum of the delivered volumes. 

2.4.4.4 Empty the measuring flask as described in 2.4.2.2 to re-establish "wetdown." 

2.4.4.5 Record all data using the form given in the Appendix or a similar format. 

2.4.4.6 Run 2. Replicate Measurement. Repeat the procedure described in 

2.4.4. The test measure must be capable of repeating to 0.01 % of the 

test volume during calibration. Repeatability problems may be due to 

contamination, poor meniscus readings, lack of cleanliness, or conduct 

SOP 16	 Page 4 of 8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3 

April 2013 

of the calibration in an unstable environment. Repeatability problems 

must be corrected before calibration can be completed. 

2.4.4.7 Calibration Note:	 If the test vessel has a graduated neck (in addition to 

the nominal mark) additional graduations should be inspected for proper 

marking and calibrated as well. 

Calculations 

3.1	 Compute the individual "to deliver" volumes, VTD, for Run 1 and Run 2. 

Eqn. 1
 TD  VVV BP

Table 2. Variables for volume equation. 

Variable Description 

VTD “To deliver” Volume 

VP "To deliver" calibrated volume of the standard pipet 

VB 

Volume of water delivered from the buret, corrected for any calibration 

values 

3.2	 Temperature correction 

For calibration of glassware that is not made of borosilicate glass, not only should the 

above temperature conditions be realized but the water temperature must also be 

known. The water used must be stored in the laboratory until its temperature is 

equilibrated with its surroundings and the temperature of the discharged water is 

measured, using the calibrated thermometer. The "To Deliver" volume of the flask, 

corrected to the reference temperature of 20 C, VTD20, is computed, using the 

expression: 

 1    20  TD 20 VV TD  t 

Eqn. 2 

Table 3. Variables for volume temperature correction e quation. 

Variable Description 

VTD observed delivered volume as computed in 3.1 

VTD20 “To deliver” volume at the reference temperature of 20 C 

t Temperature of water at time of calibration 



Cubical coefficient of expansion of glass of standard (e.g., 0.000010 °C -1 for 

borosilicate glass) 

 Cubical coefficient of expansion of glass of flask (e.g., 0.000025 °C -1 for soda-lime 

glass) 

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The volumetric standards are typically made of borosilicate glass. If borosilicate flasks 

are calibrated, no temperature correction is required. This procedure relies on the fact 

that since deliveries are made over a short period of time, the temperature remains the 

same in the standard as in the unknown. When standards and flask s are not of the 

same material, the water temperat ure change must be less than 0.5 C while the 

water is in the standards and the flask . 

3.3	 Report the average volume VTD20 as the value for the flask after the temperature 

correction has been applied to each Run. 

4	 Measurement Assurance 

4.1	 Duplicate this process with a suitable check standard (Quality Assurance Reference 

Flask, QARF) or have a suitable range of check standards for the laboratory with 

similar size graduations and neck diameters. See SOP 17 and SOP 30. 

4.2	 Plot the check standard volume and verify that it is within established limits. Alternatively 

a t-test may be incorporated into the process to check the observed value against an 

accepted reference value. (See NISTIR 6969, Section 8). 

4.3	 The mean of the check standard value is used to evaluate bias and drift over time. 

4.4	 Check standard observations are used to calculate the standard deviation of the 

measurement process. 

5	 Assignment of Uncertainties 

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of the laboratory 

volumetric standards used, us, plus the standard deviation of the process, sp, at the 95 percent level of 

confidence. See SOP 29 for the complete standard operating procedure for calculating the uncertainty. 

5.1	 The standard uncertainty for the standard, us, is obtained from the calibration reports for 

the pipet and buret used for the calibration. The combined standard uncertainty, uc, 

from the calibration report must be used and not the expanded uncertainty, U. 

Therefore, the reported uncertainty for the standard will usually need to be divided by a 

coverage factor, k. Multiple standards are used in this procedure; however, they are 

typically calibrated independently. Multiple standard uncertainties are handled according 

to SOP 29. 

5.2	 The standard deviation of the measurement process, sp, is obtained from control chart 

performance (See SOP 17 or 20, and SOP 30) for a suitable QARF using the same 

volume transfer procedures on flasks of comparable size and neck dimensions. 

5.3	 Other standard uncertainties usually included at this calibration level include uncertainties 

associated with the ability to read the meniscus, only part of which is included in the 

process variability (See GMP 3), the cubical coefficient of expansion for the flask under 

test, use of proper temperature corrections, the accuracy of temperature measurements 

taking into consideration potential gradients in the glassware during calibration, round 

robin data showing reproducibility, environmental variations over time, and bias or drift 

of the standard. 

SOP 16	 Page 6 of 8 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

6	 Report 

6.1	 Report results as described in SOP 1, Preparation of Calibration/Test Results, with the 

addition of the following items: 

6.1.1	 “To Contain” or “To Deliver” volume, applicable reference temperature, 

uncertainty, material, thermal coefficient of expansion (assumed or measured), 

construction, any identifying markings, tolerances (if appropriate), laboratory 

temperature, water temperature at time of test, barometric pressure, relative 

humidity, and any out-of-tolerance conditions. 

7	 Alternative Reference Temperatures 

7.1	 Reference temperatures other than 20 oC (68 oF) may occasionally be used . Common 

reference temperatures for other liquids follow: 

Commodity Reference Temperature 

Frozen food labeled by volume (e.g., fruit juice) - 18 oC (0 oF) 

Beer 3.9 oC (39.1 oF) 

Food that must be kept refrigerated (e.g., milk) 4.4 oC (40 oF) 

Distilled spirits or petroleum 15.56 oC (60 oF) 

Petroleum (International Reference) 15 oC (59 oF) 

Wine 20 oC (68 oF) 

Unrefrigerated liquids (e.g., sold unchilled, like soft drinks) 20 oC (68 oF) 

Petroleum (Hawaii) 26.67 oC (80 oF) 

7.2	 When alternative reference temperatures are used, at the request of the user of the field 

standard, and when the glassware is not marked with a reference temperature, the 

calibrated value of the standard may be reported at a different reference temperature, 

tref, by using this equation: 

V  V     t t  TD reft TD 1   ref

Eqn. 3 

Additional Re fe rence s: 

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S. D., and Johnson, A. N., NIST 

Calibration Services for Liquid Volume, NIST Special Publication 250-72, National Institute of 

Standards and Technology, Gaithersburg, MD, (2009). 

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1    20  TD20 VV TD  t 

April 2013 

Appendix 

Calibration of M e asuring Flasks 

(Volume Transfe r M ethod) 

Laboratory data and conditions : 

Tes t Number Date 

Ves s el ID Operator 

Nominal Volume Before After 

Coefficient of Expans ion Temperature 

Proces s s tandard deviation 

from control chart, sp 

Pres s ure 

Degrees of Freedom Relative Humidity 

Volume s tandard(s ) data: 

ID 

(enter interval if needed) Nominal Calibrated Volume 

Volume 

Correction 

Coefficient of 

Expans ion Uncertainty k factor 

Pipet 

Buret 

Buret 

Buret 

Obs ervations : 

Run 1 Run 2 

Calibrated Pipet Volume: Vp 

Buret Volume: 

Final Reading 

Initial Reading 

Difference 

Calibration Correction (if required) 

Corrected Buret Volume, VB 

VTD = VP + VB 

Water temperature at time of tes t (t) 

Average VTD20 

SOP 16 Page 8 of 8 
 

 

April 2013 

SOP 17 

Standard Operating Procedure for 

Control Charts of Check Standards 

1 Introduction 

1.1 Purpose 

This procedure may be used to develop and maintain control charts to monitor the statistical 

control of laboratory check standards when replicate measurements are made as a part of the 

standard operating procedure. This procedure may be used for volume, length, time, or other 

calibrations when replicate measurements are made. 

1.2 Prerequisites 

1.2.1The procedure to be monitored must match the calibration procedure that is used. 

1.2.2 Either a check standard at each nominal value is used or a set of check standards are 

selected to monitor the range of items that are calibrated by the laboratory. 

2 Summary 

A check standard is obtained and calibrated several times initially to establish a reliable mean value 

and to estimate the standard deviation of calibration. All such calibrations are made using the 

applicable procedure that is used for calibration. A reference value may be obtained from a suitable 

calibration laboratory or by using a more accurate and precise calibration than the one that will be 

monitored. Directions for preparing and using a control chart for monitoring the mean ( x ) and the 

standard deviation chart are given. The x control chart monitors the process with respect to both the 

standard and the variability, while the standard deviation chart monitors its short-term precision. 

When the calibration process is determined to be in a state of statistical control, the calibrations 

made at that time may be considered to be valid and the standard deviation of the measurement 

process may be included in uncertainty calculations using SOP 29. 

Note: If a full evaluation of potential bias is desired, it is best if the reference value of the check 

standard is provided by an outside laboratory accredited to perform the applicable calibrations taking 

care to ensure that the source calibration has a sufficiently small uncertainty. 

3 Equipment 

3.1 A check standard is required, and should be constructed of similar materials and design as 

the standards or devices under calibration. Check standards are maintained in the laboratory 

as a surrogate for items submitted for routine calibration. Examples of check standards 

might include a quality assurance reference flask (QARF), a test measure, an extra length 

SOP 17 Page 1 of 6 
4 

April 2013 

standard, or a stopwatch, taking care that all check standards are sufficiently similar to those 

submitted for calibration to obtain a suitable standard deviation of the measurement process 

and similar stability over time. 

3.2 All equipment designated in the applicable SOP. 

Procedure 

4.1 Initial Measurements 

4.1.1Calibrate the check standard a minimum of 12 times to establish the baseline chart. A 

calibration is defined as the result of replicate measurements as required by the SOP 

(i.e., a complete test consists of the number of runs specified in the SOP). Calibrations 

may be made on successive days, but no two complete tests should be made on any 

single day. Note: 25 to 30 points are recommended to determine uncertainties. 

4.1.2Tabulate the measurement data using the notation and a form such as the one contained 

in the Appendix of this SOP. The appendix provides an example for duplicate runs 

only; modifications would be needed when other replicates are used. The data may be 

maintained in a spreadsheet or other electronic program in lieu of a paper form. 

4.1.3 A standard deviation may be calculated for each set of runs according to the 

appropriate SOP. A pooled standard deviation is then determined for the measurement 

process. When all of the runs have the same number of replicates, each test will have 

the same number of degrees of freedom and an average of the standard deviations may 

be used. Use of a standard deviation of replicate measurements is preferred to the use 

of Range charts (see SOP 20 for guidance on Range charts.) 

4.2 Construction of Control Charts (See also SOP 9) 

4.2.1Construct the following control charts using the data of section 4.1. 

4.2.2Construct an x control chart for a check standard with the following control limits: 

Reference value (when available) 

Central Line x (mean of the average values) 

Lower warning limit (LWL) x  2s p 

Lower control (or action) limit (LCL) x  3s p
 

Upper warning limit (UWL) x  2s p
 

Upper control (or action) limit (UCL) x  3s p 

SOP 17 Page 2 of 6 
April 2013 

4.2.3Construct a Standard Deviation chart using the same approach. You should use 2 and 3 

as the respective multipliers for the Upper Warning Limit and Upper Control Limits. 

Note that there will be no negative numbers when calculating standard deviations. 

4.3 Use of Control Charts 

4.3.1An appropriate check standard is calibrated each time the laboratory performs 

calibrations using the SOP or on a set periodic basis if many calibrations are performed 

by the laboratory. If the calibrations extend over several days, the check standard is 

calibrated daily. The values of x and sp for each calibration of the check standard are 

plotted on the respective charts, preferably in sequential order. The limits on the charts 

are such that 95 % of the values should fall within the warning limits and rarely should 

a value fall outside of the control limits, provided that the system is in a state of 

statistical control. 

4.3.2If the plotted value of x lies outside of the control limits and the corresponding value 

on the standard deviation chart is within the control limits, a source of systematic error 

is suspected. 

4.3.3If the values for the standard deviation chart fall outside of the warning limits but 

inside of the control limits, a decrease in precision is indicated. Other problems should 

be investigated. 

4.3.4No calibration data should be accepted when the system is out of control. 

4.3.5If the plotted values for either x , or sp are outside of the warning limits but inside of the 

control limits, a second set of duplicate calibrations should be made. If the new values 

are within the warning limits, the process may be considered to be in control. If they lie 

outside of the warning limits, lack of control is indicated. Investigation actions should 

be taken and attainment of control demonstrated before calibration measurements are 

considered to be acceptable. 

4.3.6Even while the system is in an apparent state of control, incipient troubles may be 

indicated when the control data show short- or long-term trends, shifts, or runs. The 

t-test and F-test may be used to assess the significance of such observations (see NIST 

IR 6969 Sections 8.9, 8.10, and 8.11). 

4.4 Interpretation of Control Chart Data 

4.4.1Demonstration of "in control" status indicates that the calibration process is consistent 

with the past experience of the laboratory. That is to say, there is no reason to believe 

that excessive systematic error or changes in precision have occurred. 

SOP 17 Page 3 of 6 
April 2013 

4.4.2To the extent appropriate, the precision of measurement of the check standard may be 

extended to the calibration of other standards of similar nominal size made by the same 

measurement method. 

4.4.3Extension of the sp for the check standard to other calibrations assumes that all aspects 

of its calibration correspond to those for the other calibration. 

Figure 1. Example Control Chart 

SOP 17 Page 4 of 6 
April 2013 

Figure 2. Example Standard Deviation Chart 

Note: see point 8 that is outside of control limits. 

SOP 17 Page 5 of 6 
 

 

 

April 2013 

Appendix 

Control Chart Check Standard Data 

Check Standard Identification Nominal Value _____________ 

Test 

Number 

Date Run 1 Run 2* Average of 

Runs 

Standard 

deviation 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

* Additional columns will be needed when replicates runs beyond two are used. 

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SOP 18
 

Standard Operating Proce dure for
 

Calibration of Graduated Neck-Type M etal Volume tric Field Standards
 1 Using a Slicke r-Plate Type 

Introductio n 

1.1 Purpose of Test 

This procedure may be used to calibrate small non-pressurized, graduated necktype, metal field standards such as the 5 gal (or 20 L) standards used by weights 

and measures officials to test liquid dispensing equipment, gasoline pumps, for 

example. The test measure or prover being calibrated should be evaluated for 

conformance to appropriate specifications and tolerances (using the checklist 

provided in NIST Handbook 105-3, Specifications and Tolerances for Graduated 

Neck Type Volumetric Field Standards, 2010) if being used for legal weights and 

measures applications. (Alternatively, if requested by the customer, evaluation 

against OIML R 120 (2010), Standard capacity measures for testing measuring 

systems for liquids other than water, may be referenced.) 

This procedure uses a slicker-plate type standard to fill an unknown test measure 

of equal nominal volume. It requires water temperature stability during the 

transfer from the standard to the unknown test measure within the limits shown in 

Table 1. SOP 19 is a more appropriate procedure when temperature corrections 

are needed due to lack of water equilibration, temperature differences between the 

standard and unknown provers, or unstable environments. You may use water that 

is temperature-equilibrated with the laboratory environment. Equilibration can be 

achieved by storing the water in clean containers in the laboratory. 

Limiting factors: If the limits in Table 1 are exceeded, or materials other than 

stainless steel and mild steel are used, use SOP 19. These limits are to ensure that 

the impact of errors resulting from temperature differences on measured values is 

less than the resolution and repeatability on a 20 L or 5 gal test measure with 1 in3 

graduations. If smaller graduations are present, potential errors due to temperature 

variatio ns must be evaluated further and SOP 19 is recommended. 

Non-SI units are predominately in common us e in State legal metrology laboratories , and/or the petroleum indus try 

for many volumetric meas urements , therefore non -SI units have been us ed to reflect the practical needs of the 

laboratories performing thes e meas urements as appropriate . Mos t laboratory s tandards for this calibration procedure 

are 5 gal “s licker-plate” type s tandards . Very few laboratories have 20 L “s licker-plate” type s tandards . 

SOP 18 Page 1 of 9 

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Table 1. Te mpe rature limitations . 

Temperature 

Limitations Standard Material Unknown Material Temperature limit between s tandards (°C) 

1 Stainles s s teel Stainles s s teel < 0.5 °C 

2 Stainles s s teel Mild s teel < 0.2 °C 

1.2	 Prerequisites 

1.2.1	 Verify that the unknown prover has been properly cleaned and vented with 

all petroleum products removed prior to submission for calibration to 

ensure laboratory safety. 

1.2.2	 Verify that current calibratio n certificates with measurement values and 

uncertainties are availab le for all of the standards used in the test. All 

calibratio n values must have demonstrated metrological traceability to the 

internatio na l system of units (SI). Metrologica l traceability may be to the 

SI through a National Metrology Institute such as NIST. 

1.2.3	 Verify that the slicker-plate type standard has sufficiently small standard 

uncertainties for the intended level of calibration (i.e., less than 0.2 in3 

with an approximate 95 % level of confidence). 

1.2.4	 Verify the availab ility of an adequate supply of clean, preferably soft 

water (filtered and thermally equilibrated as appropriate) (GLP 10). Water 

does not need to be distilled or deionized for use in this procedure. The 

equations used in GLP 10 for the calculatio n of water density (air 

saturated) may be used without a significa nt impact on the measureme nt 

results. 

1.2.5	 Verify that the operator has had specific training and is proficient in SOP 

18, GMP 3, SOP 17 and is familiar with the operating characteristics and 

conditioning of the standards used. 

1.2.6	 Verify that the laboratory facilities meet the following minimum 

conditions to enable meeting the expected uncertainty achievable with this 

procedure: 

Table 2. Laboratory e nvironmental conditions . 

Procedure Temperature Relative Humidity 

Volume transfer 18 C to 27 C 

Stable to ± 2.0 C / 1 h 

35 % to 65 % 

Stable to ± 20 % / 4 h 

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1.3	 Field tests 

1.3.1	 A “field” calibration is considered one in which a calibration is conducted 

in an uncontrolled environment, such as out-of-doors. Calibrations 

conducted under field and laboratory conditions are not considered 

equivalent and uncertainties must reflect the conditio ns of the calibratio n. 

1.3.2	 SOP 19 is a more suitable procedure for non-laboratory conditions. The 

care required for field calibrations includes proper safety, a clean and 

bubble-free water supply, measurement control programs, and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and clean test liquid (water) to reach an equilibrium 

temperature with minimal evaporation. Environmental conditions must be 

selected to be within stated laboratory conditions as shown in Table 2, 

during the measurements. All data and appropriate environmental 

conditions must be documented regardless of test location. 

1.3.3	 An increased number of check standard verifications are required to 

ensure continued suitability of calibration values generated in field 

conditions as well as to verify the validity of any standards taken out of a 

secure laboratory environment once the standard(s) are returned to the 

laboratory. 

Methodology 

2.1	 Scope, Precision, Accuracy 

This procedure is applicable for the calibration of a small test measure within the 

limitations of the standards available. The precision attainable depends on the care 

used in the various volumetric adjustments and readings, in the strict observance 

of drainage times, and the internal cleanliness of the various volumetric vessels 

which can influence their drainage characteristics. The accuracy depend s on the 

uncertainties of the calibratio ns of the standards used. 

2.2	 Summary 

Water is delivered from the standard to the vessel under calibration. Because the 

"to deliver" volume of the latter is calibrated, the delivery must be into a "wetteddown" vessel. The wet-down also ensures consistent retention in the slicker-plate 

type standard. The gauge scale of the test vessel is adjusted to a correct reading, 

as necessary, and then sealed. 

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2.3	 Standards and Equipment 

2.3.1	 Calibrated slicker-plate type standard made of stainless steel. 

2.3.2	 Calibrated thermometer, with a resolutio n and uncertainty less than 0.1 C. 

2.3.3	 Meniscus reading device. (See GMP 3). 

2.3.4	 Timing device (Calibration is not required; uncertainty of the 

measureme nt only needs to be less than 5 s for a 30 s pour time.) 

2.4	 Procedure 

2.4.1	 Cleanliness Verification - Fill and drain both standard and vessel to be 

calibrated and check for any soiling that would affect drainage, as evidenced by clinging droplets, greasy films, and the like. Clean either or 

both with non-foaming detergent and water, as necessary, and rinse 

thoroughly. NOTE: Many laboratories have a policy regarding cleanliness 

of submitted volumetric standards to minimize water contamination with 

flammab le petroleum products. (See GMP 6). 

2.4.2	 Fill the unknown hand-held vessel with water to its nominal level and pour 

contents during a 30 s ± 5 s period then drain for a 10 s period after 

cessation of flow. Touch off any adhering drop from the neck. If a 

stationary test measure is being calibrated, the valve is opened and the 

measure is emptied, followed by a 30 s drain time after the cessation of the 

main flow. This constitutes the "wet-down" condition. Filling the vessel 

from the slicker-plate type standard following the instructions in steps 

2.4.3 and 2.4.4 will ensure that both the standard and vessel are properly 

“wetted-down”. 

2.4.3	 Run 1. Fill the slicker-plate standard with water by placing the fill tube or 

hose inside the standard near the bottom to minimize air bubbles. Fill the 

standard to slightly higher than the rim as the water level is raised by 

surface tension. Ensure that the reference standard is level to ensure 

consistent drain and retention characteristics. Measure and record the 

temperature in the standard. Use the slicker plate to strike off excess 

water, checking to see that no air bubbles are entrained in the water during 

this process. 

2.4.4	 Position the unknown vessel beneath the slicker-plate standard drain valve 

or piping to be sure no water is lost. Open the valve at the base of the 

standard at the same time as removing the slicker plate from the top of the 

standard to transfer water from the standard to the wet-down vessel. Allow 

a 30 s drain period after cessation of the main flow. Close the valve on the 

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slicker-plate standard and then move the unknown vessel from beneath the 

drain valve or piping to prevent additiona l water transfer. 

2.4.5	 Level the test measure and verify that the neck of the unknown test 

measure is vertical, or perpendicular to a level horizontal plane, by placing 

a level on the side of the neck as specified in NIST Handbook 105-3 (or 

suspend by its handle, if appropriate). Read and record the gauge reading. 

Measure and record the temperature of water in the unknown measure. If 

the temperature change between the standard and unknown test measure 

exceeds the allowable limits shown in Table 1, use SOP 19. 

2.4.6	 Adjust the graduated scale of the vessel as described in 3.3 if needed. Seal 

the scale adjustment device. 

2.4.7	 Run 2. Make a duplicate determinatio n. 

2.4.8	 Replicate runs of the test measure or prover must agree within ± 0.02 % of 

the test volume during calibration (± 0.2 in3 for 5 gal test measure). 

(Agreement value is calculated as the difference between Run 1 and Run 

2, divided by the nominal volume, and then multip lied by 100.) 

NOTE: If excess disagreement between the runs is observed, check all vessels for 

cleanliness, leaks, or other damage, identify and correct any problems. 

Agreement problems may be due to temperature changes, contamination 

or lack of cleanliness, or poor field conditions, such as when calibration is 

conducted in an unstable environment. Agreement problems must be 

corrected before calibratio n can be completed. 

Calculatio ns 

3.1	 When the water temperature is reasonably close to 60 F, the coefficients of 

expansion of the standard and the test vessel are sufficiently close together, and 

the deliveries and readings are made over a short period of time, temperature 

corrections are not made in this procedure. When conditions are not reasonably 

close to 60 oF and temperature corrections are needed, use SOP 19. Calculations 

provided in SOP 19 may be required for reporting volumetric results. 

3.2	 Within the accuracy requirements of Table 1, no temperature corrections arising 

from dissimilarities of the standard and vessel are used. If differences are 

suspected or observed, use SOP 19. 

3.3	 The reading of Run 1 is used to adjust the scale of the vessel, if necessary, to the 

correct reading, which is set at the calibrated volume of the slicker-plate standard 

at 60 F. Record the adjusted value as the “as left” value. Run 2 will validate the 

setting. Alternatively, the average of Run 1 and Run 2 may be used with the 

adjustment made after Run 2. In that case, a validation run should be conducted to 

ensure correct setting of the gage plate. 

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Note: When the accuracy requirements necessitate a temperature correction, the 

temperature of the water that has been recorded in both the standard and the 

unknown should be used to perform calculations according to the procedure given 

in SOP 19. 

3.4	 Determine and report the volume of the test vessel as follows: 

 -V volume Prover gauge reading  S

Eqn. 1 

where: VS = Volume of the slicker-plate standard at the appropriate reference 

temperature (usually 60 °F). 

4 Measurement Assurance 

4.1	 Duplicate the process with a suitable check standard. See SOP 17 or SOP 30. Plot 

the check standard volume and verify that it is within established limits. 

Alternatively, a t-test may be incorporated to check the observed value against an 

accepted value. The mean of the check standard observations may be used to 

evaluate bias and drift over time when a reference value for the check standard is 

available. Check standard observations are used to calculate the standard 

deviation of the measurement process which contributes to the Type A 

uncertainty components. 

4.2	 A standard deviation chart is also used for measurement assurance through the 

evaluation of replicate measurements. The standard deviation of each combination 

of Run 1 and Run 2 is calculated and the pooled (or average) standard deviatio n 

over time may be used to estimate the short-term variability in the measurement 

process. The short-term standard deviation may be used to incorporate an F -test 

(observed vs. accepted) into the measurement process. A standard deviation chart 

for unknown provers represents the variability in condition of test measures 

submitted for calibration as well as the short-term repeatability of the 

measurement process. 

5 Assignme nt of Uncertainties 

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of 

the laboratory volumetric standards used, us, plus the standard deviation of the process, sp, 

at an approximate 95 % level of confidence. See SOP 29 for the complete standard 

operating procedure for calculating the uncertainty. 

5.1	 The standard uncertainty for the standard, us, is obtained from the calibration 

report. The combined standard uncertainty, uc, is used and not the expanded 

uncertainty, U, therefore the reported uncertainty for the standard will usually 

need to be divided by the coverage factor k. 

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5.2	 The standard deviation of the measurement process, sp, is obtained from a control 

chart for the check standard so that it reflects performance over time (See SOP 17 

or 20, and SOP 30). The larger of the value from the standard deviation over time 

for a check standard from Section 4.1 or from the standard deviation chart taken 

from Section 4.2 should be used in the uncertainty calculatio ns. 

5.3	 Other standard uncertainties usually included at this calibration level primarily 

include 1) uncertainties associated with the ability to read the meniscus, only part 

of which is included in the process variability due to parallax and visual 

capabilities (See GMP 3), and 2) uncorrected temperature corrections related to 

the cubical coefficient of expansion for the prover under test, use of proper 

temperature corrections, and the accuracy of temperature measurements. 

Additional factors that might be included are: round robin data showing bias, 

environmental variations over time, and drift of the standard as noted in control 

charts. 

5.4	 To properly evaluate uncertainties and user requirements (tolerances), assessment 

of additional user uncertainties may be required by laboratory staff. Through 

proper use of documented laboratory and field procedures, additional uncertainty 

factors may be minimized to a level that does not contribute significantly to the 

previously described factors. Additional standard uncertainties in the calibration 

of field standards and their use in meter verification may include: how the prover 

level is established, how delivery and drain times are determined, the use of a 

proper “wet-down” prior to calibration or use, the cleanliness of the prover and 

calibration medium, prover retention characteristics related to inside surface, 

contamination or corrosion, total drain times, and possible air entrapment in the 

water. 

5.5	 Example components to be considered for an uncertainty budget table are shown 

in Table 3. 

Table 3. Example uncertainty budge t table . 

Unce rtainty Compone nt De s cription Symbol Source Typical 

Dis tribution 

Uncertainty of the standard (5.1) us Calibration report 

Rectangular or 

Normal divided by 

coverage factor 

Accepted standard deviation of the process 

(5.2) sp 

Control chart, 

standard deviation 

chart 

Normal 

Ability to read the Meniscus in S (5.3) um 

None if using a 

slicker-plate type 

standard 

Triangular 

Ability to read the Meniscus in X (5.3) um GMP 3 Triangular 

Uncorrected temperature errors (5.3) ute Calculated based Rectangular 

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6 

April 2013 

on limits and SOP 

19 equations 

Uncertainty of bias or drift of standards (5.3) ub From control chart Rectangular 

Water temperature (S) uts 

Consider 

accuracy, 

resolution, and 

gradients 

Rectangular 

Water temperature (X) utx 

Consider 

accuracy, 

resolution, and 

gradients 

Rectangular 

Cubical Coefficient of Expansion on S uCCE 

5 % to 10 % 

(EURAMET CG21) Rectangular 

Cubical Coefficient of Expansion on X uCCE 

5 % to 10 % 

(EURAMET CG21) Rectangular 

Uncertainty of drain time ud 

From 

experimental data Rectangular 

Report 

6.1	 Report results as described in SOP 1, Preparation of Calibration/Test Results, 

with the addition of the following: 

6.1.1	 “To Contain” or “To Deliver” volume, reference temperature, uncertainty, 

material, thermal coefficient of expansion (assumed or measured), 

construction, any identifying markings, tolerances (if appropriate), 

laboratory temperature, water temperature(s) at time of test, barometric 

pressure, relative humid ity, and any out–of-tolerance conditio ns. 

SOP 18	 Page 8 of 9 
 

 

 

 

 

 

 

 

 

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Appendix A 

Volume Transfer Data Sheet 

Laboratory data and conditions: 

Vessel Owner Op erator 

Vessel ID Date 

M aterial Air Temp erat ure 

Cubical Coefficient of Exp ansion Relative Humidity 

Standard deviation of the p rocess, 

sp 

Reference temp erature of 

unknown p rover 

sp from Control Chart or Standard 

Deviation Chart 

Degrees of Freedom 

Volume standard(s) data: 

ID (Not e ID of Standards) Nominal Volume/Correction Exp anded Unc: 

From cal. rep ort 

Unc: 

k factor 

Cubical Coefficient 

of Exp ansion 

S 

S 

S 

S 

Observations: 

Run 

Standard 

M aterial 

(M S/SS) 

Unknown 

M aterial 

(M S/SS) 

Water 

Temp in 

Standard 

(°C) 

Unknown 

Gauge Reading 

(in3) 

Water 

Temp in 

Unknown 

(°C) 

Adjustment 

M ade? 

Temp erature 

Difference 

Accep table for 

SOP 18? 

1 ___Yes ___No ___Yes ___No 

2 ___Yes ___No ___Yes ___No 

3 ___Yes ___No ___Yes ___No 

Temperature Difference Evaluation: 

If Standard is stainless st eel (SS) and Unknown is stainless st eel, the temp erature of the water between the standard and unk nown 

must not change more than 0.5 oC during the calibration. 

If the standard is st ainless steel and the unknown test measure is mild steel (M S), the change in water temp erat ure between 

standard and unknown must be less than 0.2 oC during the calibration. 

If t hese limits are exceeded, use SOP 19 calculations to determine the volume of the unknown volumetric measure. 

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1 

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SOP 19
 

Standard Operating Proce dure for
 

Calibration of Graduate d Neck-Type Metal Provers
 1 (Volume Transfer M ethod)

Introductio n 

1.1	 Purpose of Test 

This procedure is used to calibrate graduated neck type metal test measures and 

provers (20 L (5 gal) and larger) that are used in verification of petroleum, 

biodiesel, ethanol, milk, and/or water meters. The test measure or prover being 

calibrated should be evaluated for conformance to appropriate specifications and 

tolerances (using the checklist provided in NIST Handbook 105-3, Specifications 

and Tolerances for Graduated Neck Type Volumetric Field Standards, 2010) if 

being used for legal weights and measures applications. (Alternatively, if 

requested by the customer, evaluation against OIML R 120 (2010), Standard 

capacity measures for testing measuring systems for liquids other than water, may 

be referenced.) 

1.2	 Prerequisites 

1.2.1	 Verify that the unknown prover has been properly cleaned and vented , 

with all petroleum products removed prior to submission for calibration to 

ensure laboratory safety and compliance with environmental disposal 

requirements. The prover may be visually inspected to determine that 

residual liquid petroleum products are not present. Smell is not necessarily 

an adequate indicator of cleanliness. 

NOTE: Many laboratories have a policy regarding cleanliness of submitted 

volumetric standards to minimize water contamination with flammable petroleum 

products. 

1.2.2	 Verify that valid current calibration certificates with measurement values 

and uncertainties are available for all of the standards used in the test. All 

calibration values must have demonstrated metrological traceability to the 

international system of units (SI). Metrological traceability may be to the 

SI through a National Metrology Institute such as NIST. 

1.2.3	 Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of calibratio n. 

Non-SI units are predominately in common us e in State legal metrology laboratories , and/or the petroleum indus try 

for many volumetric meas urements , therefore non -SI units have been us ed to reflect the practical needs of the 

laboratories performing thes e meas urements as appropriate. . 

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1.2.4	 Verify the availability of an adequate supply of clean, preferably soft 

water (filtered and thermally equilibrated as appropriate) water (GLP 10). 

Water does not need to be distilled or deionized for use in this procedure. 

The equations used in GLP 10 for the calculation of water density (air 

saturated) may be used without a significant impact on the measurement 

results. 

1.2.5	 Verify that the operator has had specific training and is proficient in SOP 

17, SOP 19, SOP 20, GMP 3, and is familiar with the operating 

characteristic s and conditioning of the standards used. 

1.2.6	 Verify that the laboratory facilities meet the following minimum 

conditions to make possible the expected uncertainty achievable with this 

procedure: 

Table 1. Laboratory environme ntal conditions . 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 C to 27 C 

Stable to ± 2.0 C / 1 h 

35 % to 65 % 

Stable to ± 20 % / 4 h 

1.3 Field tests 

1.3.1	 A “field” calibration is considered one in which a calibration is conducted 

in uncontrolled environments, such as out-of-doors. Calibrations 

conducted under field and laboratory conditions are not considered 

equivalent. 

1.3.2	 The care required for field calibrations includes proper safety, a clean and 

bubble-free water supply, measurement control programs, and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and clean test liquid (water) to reach an equilibrium 

temperature with minimal evaporation. Environmental conditions must be 

selected to be within stated laboratory conditions during the 

measurements. All data and appropriate environmental conditions must be 

documented regardless of test location. 

1.3.3	 An increased number of check standard verifications are required to 

ensure continued suitability of calibration values generated in field 

conditions as well as to verify the validity of any standards taken out of a 

secure laboratory environment once the standard(s) are returned to the 

laboratory. 

Methodology 

2.1	 Scope, Precision, Accuracy 

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This procedure is applicable for the calibration of any size metal prover within the 

limitations of the standards available. The repeatability attainable depends on 

strict adherence to the procedure, the care in volumetric adjustments, and the 

number of transfers, in the case of multiple transfers. The accuracy depends on 

the standards used. 

2.2	 Summary 

Water is delivered from calibrated volumetric standard(s) into the unknown test 

measure or prover being calibrated. Depending on the respective volumes, 

multiple transfers may be required. While these should be minimized, a maximum 

number of 15 transfers are permitted to ensure that final uncertainties and 

systematic errors are sufficiently small for the intended applications. The 

temperature of the calibration medium (water) cannot be considered to be 

constant during transfers; hence, the temperature of the water for each transfer 

must be measured. Because of the large volumes, the difference in thermal 

expansion of the respective vessels must be considered. 

2.3	 Standards and Equipment 

2.3.1	 Calibrated volumetric standards of suitable sizes. 

2.3.2	 Calibrated flask(s) of suitable sizes to calibrate neck of prover. 

2.3.3	 A funnel for transferring water from the flask into the prover or test 

measure. 

2.3.4	 Meniscus reading device (See GMP 3). 

2.3.5	 Calibrated thermometer, with resolutio n and uncertainty less than 0.1 C. 

2.3.6	 Timing device (calibration is not required; uncertainty of the measurement 

only needs to be less than 5 s for a 30 s pour time.) 

2.3.7	 Sturdy platform, with appropriate safety conditions, with sufficient height 

to hold standard and to permit transfer of water from it to the prover by 

gravity flow. 

2.3.8	 Clean pipe or tubing (hoses) to facilitate transfer of water from the 

laboratory standard to prover. Pipe and hose lengths must be minimized to 

reduce water retention errors. Care must be taken during wet-downs and 

runs to ensure complete drainage and consistent retention in all hoses or 

pipes. 

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2.4	 Procedure 

2.4.1	 Cleanline ss verificatio n 

Fill and drain both the standard and unknown test measure or prover to be 

calibrated and check for visual evidence of soiling and of improper drainage. If necessary, clean with non-foaming detergent and water and rinse 

thoroughly (see GMP 6). 

2.4.2	 Neck scale plate verification. (This is generally only conducted for new or 

damaged measures or those that have not been calibrated by the laboratory 

in the past.) 

2.4.2.1 Fill the	 unknown prover with water from the standard. Adjust and 

check the prover level by placing a precision spirit or electronic 

digital level vertically on the neck on at least two locations, 90 

degrees apart around the circumference of the neck and adjust the 

orientation of the standard until the neck is as close to vertical 

(plumb or perpendicular to the horizontal plane) as possible. Verify 

and adjust any mounted levels that are on the prover to agree 

(when present and when possible). Check the prover system for 

leaks. This neck scale plate verification may be used as a wetteddown run. 

2.4.2.2 Bleed the liquid level down to a graduation near the bottom of the 

upper neck. "rock" the prover to "bounce" the liquid level, 

momentarily, to ensure that it has reached an equilibrium level. 

Read and record this setting to be used as the initial scale reading 

sri for verificatio n of the neck scale plate. 

2.4.2.3 Recheck the scale reading, and then add water from calibrated 

1 1 standards equal to approximately /4 or /5 of the graduated neck 

volume and record the scale reading. 

2.4.2.4 Repeat 2.4.2.3 by successive additions until water is near the top of 

the scale. Record scale readings after each addition. The last 

reading will be the final scale reading, srf. The closer the water is 

to the top of the neck, the harder it may be to "bounce" the liquid 

in the gauge. 

2.4.2.5 A plot	 of scale readings with respect to the total volume of water 

that is added Vw should be linear and will be a gross check of the 

validity of this calibratio n. 

2.4.2.6 Calculate	 and assess the accuracy of the neck scale for each 

interval. The error should be less than 0.5 % of the graduated neck 

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April 2013 

1 volume or /4 of a graduation (whichever is smaller) per NIST 

Handbook 105-3. If the error is greater than this, the scale should 

be replaced. Uncertainties associated with the neck scale 

calibration are primarily related to the setting of the meniscus on 

the flask used (with each drop), the reading of the meniscus on the 

unknown prover (at each volume reading), and the calibration 

uncertainty of the flask. These uncertainties must be considered 

when evaluating the acceptability of the neck scale. Alternatively, 

a Neck Scale Correction Value (NSCV) may be issued with 

instructions to the user if it is anticipated that this correction value 

will be used. 

2.4.2.7 Neck scale errors less than 0.5 % of the graduated neck volume 

should be included in the uncertainty estimate associated with the 

prover calibratio n. 

2.4.2.8 The neck scale correction value is calculated as follows: 

 if

w

srsr

V

NSCV





Eqn. 1 

Table 2. Variable s for neck scale correction value e quation. 

NSCV Neck scale correction value 

Vw Total volume of water added to neck 

Scale reading, final 

Scale reading, initial 

2.4.3 Body Calibratio n 

2.4.3.1 Fill	 the standard with water and then transfer the water into the 

unknown prover establishing a wet down of the standard. Wait 30 s 

after the cessation of the main flow before closing the drain valve 

on the standard. Level the unknown prover, and drain the water, 

again waiting 30 s after cessation of the main flow, before closing 

the drain valve. This establishes a "wetted-down" condition for 

provers with no bottom zero. If the unknown test vessel is a 5 gal 

(20 L) hand-held test measure, fill the unknown vessel with water 

to its nominal mark and empty it using a 30 s (± 5 s) pour followed 

by a 10 s drain after cessation of the main flow to establish the 

wetted-down condition. 

If a bottom zero is present, follow the guidance provided in SOP 

21 for LPG provers as follows: When the liquid reaches the top of 

the lower gauge glass, close the valve and allow the water to drain 

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April 2013 

from the interior of the prover into the lower neck for 30 s. Then 

bleed slowly with the bleed valve (4) until the bottom of the liquid 

meniscus reaches the zero graduation. (This step should be started 

during the 30 s drain period but should not be completed before the 

end of the drain period.) 

Alternatively, the prover may be completely drained with a 30 s 

drain time after the cessation of the main flow, and then refilled 

with a funnel and small volume of water to set the zero mark 

(which will add to the prover calibration uncertainty due to 

variable retention characteristics). 

2.4.3.2 Run 1. Fill the standard and measure and record the temperature. 

2.4.3.2.1	 Measure and record the temperature of the water in the 

standard, t1, then adjust the standard prover to its 

reference mark or record the neck reading, and then 

discharge into the unknown prover. Wait 30 s after 

cessation of the main flow to attain specified drainage, 

and then close the delivery valve. Remove any hoses or 

pipes to prevent additiona l water transfer. 

2.4.3.2.2	 Repeat step 2.4.3.2.1 as many times as necessary (note 

the 15-drop limit) to fill the unknown prover to its 

nominal volume. Verify the level condition and record 

the temperature of water in the standard for each drop, 

t1 to tN. 

2.4.3.2.3	 Level the filled unknown prover. Check the prover 

level by placing a precision spirit or electronic digital 

level vertically on the neck on at least two locations, 90 

degrees apart around the circumference of the neck and 

adjust the orientation of the unknown measure until the 

neck is as close to vertical (plumb or perpendicular to 

the horizontal plane) as possible. Verify and adjust any 

mounted levels that are on the prover to agree (when 

present and when possible). Read and record the scale 

plate (gauge) reading. 

2.4.3.2.4	 Measure the temperature of the water in the unknown 

prover, tx, and record. For test measures without 

thermometer wells, the temperature should be taken as 

close as possible to the center (vertically and 

horizontally) of the cylinder of the test measure main 

body (and not in the neck). For larger provers, and 

when thermometer wells are present, the average 

temperature, calculated from temperatures taken at 

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April 2013 

multiple locations from within the unknown prover 

should be used. (Alternatively, if a prover has mounted 

thermometers, the internal temperature from multiple 

locations within the prover may be used). 

2.4.3.2.5	 Perform the calculations described in section 3 to 

determine the prover volume at the appropriate 

reference temperature. 

2.4.3.4 Adjust the scale as needed. If adjusted, record the adjusted prover 

gauge reading for determining the “as left” value for Run 1. Run 2 

will validate the setting. Alternatively, the average of Run 1 and 

Run 2 may be used with the adjustment made after Run 2. In that 

case, a validation run is required to ensure correct setting of the 

scale plate. 

2.4.3.5 Run 2 - Repeat the process described in 2.4.3.2. Replicate runs of 

the test measure or prover must agree within ± 0.02 % of the test 

volume during calibration. (Agreement value is calculated as the 

difference between Run 1 and Run 2, divided by the nominal 

volume, and then multip lie d by 100.) 

NOTE: If excess disagreement between replicated measurements is 

observed, check all vessels for cleanliness, leaks, drain lines, 

additional valve, or damage, identifying and correcting any 

problems. Lack of measurement agreement may be due to 

contamination, lack of cleanliness, excessive temperature changes, 

poor laboratory conditions, or poor field conditions, such as when 

calibration is conducted in an unstable environment. Repeatability 

problems must be corrected before calibratio n can be completed. 

2.4.3.7 Seal the equipment as specified in the laboratory policy. 

3 Calculatio ns 

The following calculations assume that the standard was calibrated using a reference 

temperature of 60 °F (15.56 °C) and that you are calibrating a field standard to a 

reference temperature of 60 °F (15.56 °C). Equations for situations where different 

reference temperatures are involved follows in Sections 3.4 to 3.6. 

3.1	 Single Delivery 

3.1.1	 Calculate VX60, the volume of the unknown prover at 60 F, using the 

following equation: 

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   

   1 60 F 

 1 60 F 

 

1 6 0 1 1

6 0 









x x

S

X

t

V t

V



 

Eqn. 2 

April 2013 

3.2	 Multip le Deliveries 

3.2.1	 Calculate VX60, the volume of the unknown prover at 60 F, using the 

following equation: 

           

   1 60 F 

 1 60 1 F 60 F ... 1 60 F 

 

1 6 0 1 1 2 6 0 2 2 6 0

6 0 

  



  



x x

S S SN N N

X

t

V t V t V t

V



     

Eqn. 3 

Table 3. Variables for VX60 e quations. 

Symbols Used in Equations 

VX60 volume of the unknown vessel at 60 F 

VS60 volume of the standard vessel at 60 F 

 N, ,..., 21

density of the water in the standard prover where 1 is the density of the water 

for the first delivery, 2 is the density of the water for the second delivery, and 

so on until all N deliveries are completed 

1, 2,..., N 

volume difference between water level and the reference mark on the standard 

where the subscripts 1, 2,..., N, represent each delivery as above. If the water 

level is below the reference line,  is negative. If the water level is above the 

reference line,  is positive. If the water level is at the reference line,  is zero 

NOTE: units must match volume units for the standard. The  is zero for 

slicker-plate type standards. 

t1, t2, ..., tN temperature of water for each delivery with the subscripts as above 

 coeffic ient of cubical expansion for the standard in units / oF 

ß coeffic ient of cubical expansion for the prover in units / oF 

tx temperature of the water in the filled unknown vessel in units oF 

x density of the water in the unknown vessel in g/cm3 

Note: Values for the density of water may be calculated from the equations given in GLP 10. 

3.3	 Prover Error/Correction or Deviatio n From Nominal 

The total calculated volume of the prover at its reference temperature should be reported 

on the calibratio n report. The SI unit of volume is m3, so a conversio n factor is to be 

included on the report in the notes section when other volume units are used. 

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The prover volume for an open neck prover equals the Vx60 value minus the gauge 

reading that is the difference from the nominal volume (with matched units). 

 - V volume Prover gauge reading 

X 60 V - Nom

 volume Prover error Prover X V - Nom - V error Prover gauge reading  60

Eqn. 4 

Eqn. 5 

Eqn. 6 

where: 

VNom = Nominal Volume (taking care to match units) 

VX60 is the calculated volume of water that should be observed in the prover. A positive 

prover error means that the prover is larger than nominal. A negative prover error means 

that the prover is smaller than nomina l. 

Example 1:	 If VX60 is 100.02 gal and gauge reading is 0.02 gal (above nominal); 

then the prover volume at nominal is 100.00 gal; 

and the prover error and correction are 0; and 

no adjustment is needed. 

Example 2:	 If VX60 is 100.02 gal and gauge reading is -0.02 gal (below nominal); 

then the prover volume at nominal is 100.04 gal; 

the prover error is + 0.04 gal; and 

to adjust the prover, set the gauge to read 0.02 gal (the volume level will 

show a gauge reading of 0.02 gal, which is 4.62 in3 or about 5 in3

, above 

nomina l. ) 

3.4 Alternative Reference Temperatures 

3.4.1 Reference temperatures other than 60 oF (15.56 oC) may occasionally be 

used. Common reference temperatures for other liquids follow, however not all of 

them may be suitable for use with standards calibrated using this procedure: 

Commodity Reference 

Temperature 

Frozen food labeled by volume (e.g., fruit juice) -18 oC (0 oF) 

Beer 3.9 oC (39.1 oF) 

Food that must be kept refrigerated (e.g., milk) 4.4 oC (40 oF) 

Distilled spirits or petroleum 15.56 oC (60 oF) 

Petroleum (Internatio nal Reference) 15 oC (59 oF) 

Compressed Natural Gas (CNG) 15 °C (60 oF) 

Wine 20 oC (68 oF) 

Unrefrigerated liquids (e.g., sold unchilled, like soft drinks) 20 oC (68 oF) 

Hydrogen (H2) 21 oC (70 oF) 

Petroleum (Hawaii) 26.67 oC (80 oF) 

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Equations for calculatio ns when using alternative reference temperatures follow: 

3.5	 Single Delivery 

3.5.1	 Calculate VXt ref, the volume of the unknown prover at its designated 

reference temperature (F), using the following equation: 

    

   1 t 

 1 t 

 

X ref

1 1 S ref1







x x

S tref

Xtref t

V t

V



 

Eqn. 6 

3.6	 Multip le Deliveries 

3.5.1 Calculate VXt ref, the volume of the unknown prover at its designated 

reference temperature, using the following equation: 

              

   1 

 1 1 ... 1 

 

X r

S1 1 S ref11 2 2 22 S

X

x x ef

N ref SNN Sref S N tref S

trefS S tref

X tref tt

V tt V tt V tt

V



  





     

Eqn. 7 

Table 3A. Variable s for VXtrefX equations . 

Symbols Used in Equations 

VXtrefX 

volume of the unknown vessel, VX at its designated reference temperature, tref 

X 

VStrefS volume of the standard vessel, VS at its designated reference temperature, tref S 

 N, ,..., 21

density of the water in the standard where 1 is the density of the water for 

the first delivery, 2 is the density of the water for the second delivery, and so 

on until all N deliveries are completed 

1, 2,..., N 

volume difference between water level and the reference mark on the 

standard where the subscripts 1, 2,..., N, represent each delivery as above. If 

the water level is below the reference line,  is negative. If the water level is 

above the reference line,  is positive. If the water level is at the reference 

line,  is zero. NOTE: units must match volume units for the standard. The 

is zero for slicker-plate type standards. 

t1, t2, ..., tN temperature of water for each delivery with the subscripts as above 

 coeffic ient of cubical expansion for the standard in its designated units 

ß coeffic ient of cubical expansion for the prover in its designated units 

tx temperature of the water in the filled unknown vessel in designated units 

x density of the water in the prover in g/cm3 

Notes: Values for the density of water may be calculated from the equations given in GLP 

10. The cubical coefficient of the materials must match the unit assigned to the temperature 

measureme nt. 

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4 Measurement Assurance 

4.1.	 Duplicate the process with a suitable check standard or have a suitable range of check 

standards for the laboratory. See SOP 17, SOP 20 and SOP 30. Plot the check standard 

volume and verify it is within established limits OR a t-test may be incorporated to 

check the observed value against an accepted value. The mean of the check standard 

observations is used to evaluate bias and drift over time. Check standard observations 

can be used to calculate the standard deviation of the measurement process which 

contributes to the Type A uncertainty components. 

4.2.	 If a standard deviation chart is used for measurement assurance, the standard deviation 

of each combination of Run 1 and Run 2 is calculated and the pooled (or average) 

standard deviation is used as the estimate of variability in the measurement process. 

Note: the pooled or average standard deviation over time reflects varying conditions of 

test items that are submitted to the laboratory, but may not reflect potential meniscus 

reading errors (See GMP 3.) 

5 Assignme nt of Uncertainties 

5.1	 The limits of expanded uncertainty, U, include estimates of the standard uncertainty of 

the laboratory volumetric standards used, us, plus the standard deviation of the process, 

sp, at the 95 % level of confidence. See SOP 29 for the complete standard operating 

procedure for calculating the uncertainty. 

5.1.1	 The standard uncertainty for the standard, us, is obtained from the calibration 

report. The combined standard uncertainty, uc, is used and not the expanded 

uncertainty, U, therefore the reported uncertainty for the standard will usually 

need to be divided by the coverage factor k. See SOP 29 for the complete 

standard operating procedure for calculating the uncertainty when multiple 

deliveries or multiple standards are used to ensure correct handling of 

correlated uncertainties. Fifteen is the maximum recommended number of 

deliveries from a laboratory standard to a prover under test to minimize 

calibratio n uncertainties to the levels identified previously. 

5.2	 The standard deviation of the measurement process, sp, is taken from a control chart 

for a check standard or from standard deviation charts from provers of similar size 

(See SOP 17, SOP 20 and SOP 30). The larger of the value from the standard 

deviation over time for a check standard or from the standard deviation chart should be 

used in the uncertainty calculations. If a check standard is available, it is possible to 

evaluate the presence of bias in the measurement process. 

5.3	 Neck calibration uncertainty should be estimated based on the uncertainty of standards 

used, errors observed during calibration, ability to read the meniscus of all standards 

involved (see GMP 3) and the repeatability of the neck calibratio n. 

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5.4	 Other standard uncertainties usually included at this calibration level primarily 

include 1) uncertainties associated with the ability to read the meniscus, only part of 

which is included in the process variability due to parallax and visual capabilities, and 

2) uncertainties associated with temperature corrections that include values for the 

cubical coefficient of expansion for the prover under test, the accuracy and gradients 

associated with temperature measurements in test measures or provers. Additional 

factors that might be included are: round robin data showing reproducibility, 

environmental variations over time, and bias or drift of the standard as noted in control 

charts. 

5.5	 To properly evaluate uncertainties and user requirements (tolerances), assessment of 

additional user uncertainties may be required by laboratory staff. Through proper use 

of documented laboratory and field procedures, additional uncertainty factors may be 

minimized to a level that does not contribute significantly to the previously described 

factors. Additional standard uncertainties in the calibration of field standards and their 

use in meter verification may include: how the prover level is established, how 

delivery and drain times are determined, the use of a proper “wetted-down” prior to 

calibration or use, whether gravity drain is used during calibration or whether the 

volume of water is eliminated by pumping, the cleanliness of the prover and 

calibration medium, prover retention characteristics related to inside surface, 

contamination or corrosion, and total drain times, and possible air entrapment in the 

water, and connecting pipes. Systematic errors may be observed between laboratory 

calibration practices where a gravity drain is used and field use where the pumping 

system is used. 

5.6	 Example components to be considered for an uncertainty budget table are shown in 

Table 4. Multiple values of some items may need to be considered (e.g., multiple 

drops from the standard, multiple meniscus readings, and multiple temperature 

readings.) 

Table 4. Example Unce rtainty Budget Table . 

Unce rtainty Compone nt 

De s cription Symbol Source Typical Dis tribution 

Uncertainty of the standard (5.1) us 

Calibration report; may 

be multiplied or added 

based on dependencies 

Rectangular or 

Normal divided by 

coverage factor 

Accepted standard deviation of 

the process (5.2) sp 

Control chart, standard 

deviation chart Normal 

Uncertainty or uncorrected error 

associated with a neck 

calibration (5.3) 

un From experimental data Rectangular 

Ability to read the Meniscus in S 

(5.4) um 

None if using a slickerplate type standard; 

GMP 3 

Triangular 

Ability to read the Meniscus in 

X (5.4) um GMP 3 Triangular 

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April 2013 

Water temperature (S) (5.4) uts 

Consider accuracy, 

resolution, and gradients Rectangular 

Water temperature (X) (5.4) utx 

Consider accuracy, 

resolution, and gradients Rectangular 

Cubical Coefficient of 

Expansion on S (5.4) uCCE 

5 % to 10 % 

(EURAMET CG-21) Rectangular 

Cubical Coefficient of 

Expansion on X (5.4) uCCE 

5 % to 10 % 

(EURAMET CG-21) Rectangular 

Uncertainty of bias or drift of 

standards (5.2) ub From control chart Rectangular 

Uncertainty of drain time ud From experimental data Normal 

6 Report 

6.1	 Report results as described in SOP 1, Preparation of Calibration/Test Results, with the 

addition of the following: 

“To Contain” or “To Deliver” prover volume, reference temperature, uncertainty, 

material, thermal coefficient of expansion (assumed or measured), construction, any 

identifying markings, tolerances (if appropriate), laboratory temperature, water 

temperature(s) at time of test, barometric pressure, relative humidity, and any out–oftolerance conditions. Appendix B, Example Temperature Correction Chart may be 

provided as a supplement to the calibration report to encourage appropriate 

volumetric corrections of the provers during routine use. 

Additional Re fe rence s: 

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S. D., and Johnson, A. N., NIST 

Calibration Services for Liquid Volume, NIST Special Publication 250-72, National Institute of 

Standards and Technolo gy, Gaithersburg, MD, (2009). 

EURAMET Calibration Guide 21, Guidelines on the Calibration of Standard Capacity Measures 

Using the Volumetric Method (Version 1.0, 04/2013). 

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April 2013 

Appendix A 

Volume Transfer Data Sheet 

Laboratory data and conditions: 

Vessel Owner Op erator 

Vessel ID Date 

Nominal Volume Air Temp erature 

M aterial Relative Humidity 

Cubical Coefficient of Exp ansion Standard deviation of the p rocess, sp 

from Control Chart 

Reference temp erature of unknown 

p rover 

Standard deviation of the p rocess, sp 

from the Standard Deviation Chart 

Unknown p rover graduations Degrees of Freedom 

Ap p licable sp ecifications and 

tolerances 

Volume standard(s) data: 

ID (Not e ID of Standards) Nominal 

Volume Volume/Correction Exp anded Unc: From cal. rep ort 

Unc: 

k factor 

Cubical Coefficient 

of Exp ansion 

S 

S 

S 

S 

Run 1: Data for volumes delivere d from the standards: 

DROP 

# Rep ort ed Volume (gal) M aterial (M S/SS/BS/SL) Water Temp (°C) 

(Must be ≥ 0.5 °C and < 40 °C) 

Gauge Delta 

(in3) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

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April 2013 

Run 1: Data from the fille d unknown field standard: 

M aterial for the Unknown: M S, SS, TP, AL, PVLC 

Final Gauge Reading: in3 

Final Water Temp erature: °C 

Run 2: Data for volumes delivere d from the standards: 

DROP 

# Rep ort ed Volume (gal) M aterial (M S/SS/BS/SL) Water Temp (°C) 

(M ust be ≥ 0.5 °C and < 40 °C) 

Gauge Delta (in3) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

Run 2: Data from the filled unknown field standard: 

M aterial for the Unknown: M S, SS, TP, AL, PVLC 

Final Gauge Reading: in3 

Final Water Temp erature: °C 

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A pril 2013 

Appendix B 

Example Temperature Correction Table* 

Example for a 100 gallo n prover an d 60 °F reference temperature. 

CCE Mild Steel 

1.86 x 10-5/°F 

Stainles s Steel 

2.65 x 10-5/°F 

Temperatu re °F in3 gal in3 gal 

-20 -34 -0.149 -49 -0.212 

-15 -32 -0.139 -46 -0.199 

-10 -30 -0.130 -43 -0.186 

-5 -28 -0.121 -40 -0.172 

0 -26 -0.112 -37 -0.159 

5 -24 -0.102 -34 -0.146 

10 -21 -0.093 -31 -0.133 

15 -19 -0.084 -28 -0.119 

20 -17 -0.074 -24 -0.106 

25 -15 -0.065 -21 -0.093 

30 -13 -0.056 -18 -0.079 

35 -11 -0.047 -15 -0.066 

40 -9 -0.037 -12 -0.053 

45 -6 -0.028 -9 -0.040 

50 -4 -0.019 -6 -0.026 

55 -2 -0.009 -3 -0.013 

60 0 0.000 0 0.000 

65 2 0.009 3 0.013 

70 4 0.019 6 0.026 

75 6 0.028 9 0.040 

80 9 0.037 12 0.053 

85 11 0.046 15 0.066 

90 13 0.056 18 0.080 

95 15 0.065 21 0.093 

100 17 0.074 24 0.106 

105 19 0.084 28 0.119 

110 21 0.093 31 0.133 

115 24 0.102 34 0.146 

120 26 0.112 37 0.159 

CCE = coefficient of cubical expans ion 

*Provide only the applicable coefficient of cubical expans ion for the prover under tes t. 

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SOP 20 

Standard Operating Procedure 

for 

Standard Deviation and Range Charts 

1 Introduction 

1.1 Purpose 

This procedure describes a process to be followed to monitor the statistical control of a 

measurement process using standard deviation charts or range charts for any calibration 

method where replicate measurements are performed and where it is not practical or 

feasible to maintain laboratory check standards. Standard deviation charts are preferred 

to the use of range charts for monitoring and evaluation process standard deviations 

when replicate measurements are made. 

1.2 Prerequisites 

The procedure must match the calibration procedure that is being monitored. 

2 Summary 

Because of the size and cost of some laboratory standards, it is not always practical to have 

check standards remain in the laboratory for the purposes of measurement control. However, 

it is practical to maintain standard deviation (sp) charts or range (R) charts for each nominal 

size standard to evaluate the standard deviation of replicate runs. Directions for preparing and 

using an R control chart that monitors the precision of the test procedure are given. It is 

assumed that standards of the same nominal capacity and design will have similar 

characteristics with respect to the repeatability of tests. Since it is not practical to run a 

sufficient number of tests on each unknown standard to determine the repeatability, the 

absolute difference between replicate tests are graphed on the same sp or R chart to reflect the 

repeatability of measurement of the unknown standards tested in the laboratory. Note: 

Provers of similar readability may be grouped together on the same chart as long as results 

from different sized provers pass an F-test (e.g., provers greater than and equal to 500 gal 

generally have 20 in3

 graduations and equivalent repeatability.) 

3 Equipment 

All equipment is designated in the respective calibration SOP. 

4 Procedure 

4.1 Data Collection 

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4.2 

4.3 

4.4 

April 2013 

4.1.1 Conduct the required number of replicates per test on the unknown test item per 

the designated SOP. A minimum of 12 sets of data must be available before a 

reasonably adequate data base is established. Note: 25 to 30 replicate sets of 

data are recommended to determine valid uncertainties. 

4.1.2 Tabulate the measured errors as determined by each of the two trials using a 

form such as the one contained in the Appendix. The data may be maintained in 

a spreadsheet or other electronic program in lieu of a paper form. (If the 

unknown item is adjusted after the first run, the first trial reading is evaluated 

after the adjustment.) 

Calculate the standard deviation (preferred) 

4.2.1.	 A standard deviation of the replicate runs, sp, may be calculated for each set of 

runs according to the appropriate SOP. An accepted standard deviation over 

time can be calculated as the pooled standard deviation to represent the 

accepted standard deviation of the measurement process. 

Calculate the range (optional) 

4.3.1. Where the range is used, it represents is the absolute difference of two (or more) 

replicate runs. Be sure that only absolute values are used in the determination 

of the range and average range! 

R  x1  x2 Eqn. 1 

4.3.2. Calculate the average range of the trials, R , for the n tests as follows: 

R
   R Eqn. 2 

n 

4.3.3. The estimated standard deviation may be calculated using the average range 

as follows (obtain values for d2

* from NISTIR 6969, Table 9.1 and see 

NISTIR 6969, Section 8.3 for additional notes). For two runs, the d2

* value is 

1.414: 

R 

s 	 Eqn. 3 p d2 

* 

Construct Appropriate Charts 

4.4.1. Construct Standard Deviation Charts and Range Charts using the same 

approach. You should use 2 and 3 as the respective multipliers for the Upper 

Warning Limit and Upper Control Limits on standard deviation charts. Note 

that there will be no negative numbers when calculating standard deviations or 

ranges. 

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April 2013 

4.4.2. Construct an R control chart having the following limits: 

Central Line R 

Lower warning and control limits 0 

Upper warning limit (UWL) 2.512 R 

Upper control (or action) limit (UCL) 3.267 R 

These limits are for duplicate measurements. For triplicate measurements see 

Handbook 145, Section 7.4. 

4.2.3 The recommended format for construction of R control charts is given in NBS 

Handbook, Section 7.4. 

4.3 Use of Control Charts 

4.3.1 Replicate trials are run on each standard submitted to the laboratory for 

calibration according to the specific SOP. The values for standard deviation or 

range are plotted on the appropriate control chart, preferably in sequential order. 

The limits of the charts are such that 95 % of the values should fall within the 

warning limits and rarely should a value fall outside the control limits, provided 

that the system is in a state of statistical control. 

4.3.2 If the values plotted on the standard deviation or range chart fall outside of the 

control limits, a decrease in precision is indicated. Problems with the standards or 

process will need to be investigated. 

4.3.3 No calibration data should be accepted when the system is out of control. 

4.3.4 If a plotted value for standard deviation or range is outside of the warning limit 

but inside the control limit, a second set of replicate calibrations should be made. 

If the new value for the standard deviation or range is within the warning limit, 

the process may be considered in control. If it lies outside of the warning limit, 

lack of control is indicated. Investigation should be made, with suitable corrective 

action taken with demonstrated attainment of control before calibration 

measurements are considered to be acceptable. 

4.3.5 Even while the system is in an apparent state of control, incipient troubles may be 

indicated when the control data show short- or long-term trends, shifts, or runs. 

Interpretation of Control Chart Data 

5.1 Demonstration of "in control" indicates that the calibration process is consistent with 

the past experience of the laboratory. That is to say, there is no reason to believe that 

excessive changes in precision have occurred. 

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5 
 

 

April 2013 

5.2 The accuracy is inferred from a consideration of control of the sources of bias. 

5.3 To the extent appropriate, the precision of measurement of standards may be extended 

to the calibration of other standards of similar type, capacity and design. 

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April 2013 

Appendix 

Standard Deviation and Range Data 

Standard Capacity: Laboratory: 

Test 

Number Date Run 1 Run 2 Average 

of Runs Standard deviation* 

Range** 

|Run 1 - Run 2| 

(Max – Min) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

* Use of the standard deviation and pooled standard deviations are preferred to the use of Range as 

an estimate of the standard deviation. 

** This is the range, R, of the two trials and is actually the larger value minus the smaller value. 

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1 

April 2013 

SOP 21 

Standard Operating Proce dure for 

1 Calibration of LPG Provers 

Introductio n 

1.1	 Purpose of Test 

This procedure may be used to calibrate a volume standard used to test systems 

designed to measure and deliver liquefied petroleum gas (LPG) in the liquid state 

by definite volume, whether installed in a permanent location or mounted on a 

vehicle. A schematic diagram of such a prover is shown in Figure 1, together with 

numbers, e.g., 1, 2, 3, and 4 to clarify the various operations described in the 

procedure. The parts labeled A, B, and C are hose connections used in meter 

testing (versus prover calibrations). The prover being calibrated should be 

evaluated for conformance to appropriate specifications (using the checklist 

provided in NIST Handbook 105-4, Specifications and Tolerances for Liquefied 

Petroleum Gas and Anhydrous Ammonia Liquid Volumetric Provers, 2010) if 

being used for legal weights and measures applications. You should also review 

the schematic provided in Handbook 105-4. 

1.2	 Prerequisite s 

1.2.1	 Verify the unknown prover has been properly cleaned and vented with all 

petroleum products removed prior to submission for calibration to ensure 

laboratory safety. The prover and/or pressure gauge may be visually 

inspected to determine that residual products are not present. Smell is not 

necessarily an adequate indicator of cleanliness. 

NOTES: Many laboratories have a policy regarding cleanliness of submitted 

volumetric standards to minimize water contamination with flammable petroleum 

products. Be sure to follow laboratory safety policies for dealing with pressurized 

vessels. 

1.2.2	 Verify that valid current calibration certificates with measurement values 

and uncertainties are available for all of the standards used in the test. All 

calibration values must have demonstrated metrological traceability to the 

International System of Units (SI). Metrological traceability may be to the 

SI through a National Metrology Institute (for example, NIST.) 

Non-SI units are predominately in common us e in State legal metrology laboratories , and/or the petroleum indus try 

for many volumetric meas uremen ts , therefore non -SI units have been us ed to reflect the practical needs of the 

laboratories performing thes e meas urements as appropriate . The majority of LPG provers in us e are 20 gal, 25 gal, 

and 100 gal nominal s izes . The volume of LPG provers is es tablis hed at 60 oF and 100 ps ig. 

SOP 21	 Page 1 of 19 

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1.2.3	 Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of the calibratio n. 

1.2.4	 Verify the availability of an adequate supply of clean, preferably soft 

water (filtered and thermally equilibrated as appropriate) water (GLP 10). 

Water does not need to be distilled or deionized for use in this procedure. 

The equations used in GLP 10 for the calculation of water density (air 

saturated) may be used without a significant impact on the measurement 

results. 

1.2.5	 Verify that the operator has had specific training in SOP 19, SOP 20, SOP 

21, and GMP 3 and is familiar with the operating characteristics and 

conditioning of the standards and unknown test items being used and 

calibrated. 

1.2.6	 Cylinder of nitrogen or compressed air, or a regulated air source of at least 

200 psig, and a proper pressure regulator. 

1.2.7	 Verify that the laboratory facilities meet the following minimum 

conditions to make possible the expected uncertainty achievable with this 

procedure: 

Table 1. Laboratory environme ntal conditions . 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 C to 27 C 

Stable to ± 2.0 C / 1 h 

35 % to 65 % 

Stable to ± 20 % / 4 h 

1.3	 Field tests 

1.3.1	 A “field” calibration is considered one in which a calibration is conducted 

in an uncontrolled environment, such as out-of-doors. Calibrations 

conducted under field and laboratory conditions are not considered 

equivalent. 

1.3.2	 The care required for field calibrations includes proper safety, a clean and 

bubble-free water supply, measurement control programs, and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and clean test liquid (water) to reach an equilibrium 

temperature with minimal evaporation. Environmental conditions must be 

selected to be within stated laboratory conditions during the 

measurements. All data and appropriate environmental conditions must be 

documented regardless of test location. 

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2 

April 2013 

Methodology 

2.1	 Scope, Precision, Accuracy 

This procedure is applicable for the calibration of LPG provers with capacities of 

100 L to 500 L (20 gal to 100 gal) or larger when appropriate. Provers of 20 gal, 

25 gal, and 100 gal (with gal and in3 units) are encountered most frequently, 

hence the procedure is written with that in mind. The changes necessary for 

testing provers of other capacities will be obvious and are not described in this 

document. The agreement of duplicate measurements made within a short period 

of time on a given 100 gal LPG prover must be within 5 in3 (0.02 gal). For any 

nominal volume, replicate values must agree within 0.02 % of the volume. The 

accuracy will depend on the uncertainty in the volume of the standard, on the care 

exercised in making the various measurements and temperature readings, and on 

correct applicatio n of the corresponding corrections. 

2.2	 Summary 

The procedure is a modification of one described by M.W. Jensen in NBS 

Handbook 99, "Examination of Liquefied Petroleum Gas Liquid- Measuring 

Devices." The LPG prover is calibrated with a known volume of water delivered 

into it from a standard prover of calibrated volume. Depending on the respective 

volumes, multiple transfers may be required. While multiple transfers should be 

minimized, a maximum number of 15 transfers are permitted to ensure that final 

calibration uncertainties are sufficiently small to meet user applications. The 

temperature of the calibration medium (water) cannot be considered to be 

constant during transfers; hence, the temperature of the water for each transfer 

must be measured. Because of the large volumes, the difference in thermal 

expansion of the respective vessels must be considered. The LPG prover is 

pressurized and the liquid level is measured at each of several values of applied 

pressure. The calibration thus defines the capacity of the prover over its expected 

range of operational pressures. 

2.3	 Standards and Equipment 

2.3.1	 Calibrated standard prover of minimum volume of 5 gal for 20 gal and 25 

gal LPG provers is acceptable. A 10 gal standard is acceptable for 

calibrating a 100 gal LPG prover, but a standard that is of the same 

volume as the LPG prover is preferable. NOTE: standard provers used for 

calibration may need to have an alternative calibration value based on 

restricted flow delivery as the opening for many LPG provers may not be 

adequate to receive the full flow delivery from the reference standard. 

2.3.2	 A funnel for transferring water from calibrated flasks into the unknown 

prover. 

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2.3.3	 Calibrated flasks of suitable sizes to calibrate the neck of prover. 

2.3.4	 Thermometers (2) with resolutio n and uncertainty less than 0.1 C. 

2.3.5	 Meniscus reading device (See GMP 3). 

2.3.6	 Timing device (calibration is not required; uncertainty of the measurement 

only needs to be less than 5 s for a 30 s pour time.) 

2.3.7	 Sturdy platform, with appropriate safety conditions, with sufficient height 

to hold standard and to permit transfer of water from it to the prover by 

gravity flow. 

2.3.8	 Clean the pipe or tubing (hoses) to facilitate transfer of water from the 

laboratory standard to prover. Nearly all LPG provers require reducers to 

be used between normal laboratory piping and the top hole on the prover. 

Pipe and hose lengths must be minimized to reduce water retention errors. 

Care must be taken during wet-downs and runs to ensure complete 

drainage and consistent retention in all hoses or pipes. Arrange all hoses 

so that there are no loops or low spots that can hold water. 

2.3.9	 Compressed nitrogen cylinder or air, suitable regulator, and an appropriate 

pressure gauge. The calibration relies on the accuracy of the pressure 

gauge on the prover. It assumes that systematic errors in the prover 

pressure gauge will be present in field applications as well, thus 

calibration of the laboratory pressure gauge is not essential. However, the 

prover must be recalibrated if pressure gauges are changed in the field . 

When a laboratory pressure gauge is used during the calibration, the 

unknown pressure gauge and laboratory gauge must both have current 

calibratio n reports. 

2.4	 Procedure 

2.4.1	 Preliminary Operations 

2.4.1.1 Install	 and level the standard(s) on a raised platform with 

appropriate security and safety ensured for the prover(s) and 

operator(s). Provide pipe or tubing for delivery of water by most 

direct route to prover. 

2.4.1.2 Position	 and level the unknown prover where it can be reached 

from the elevated standard by the shortest feasible delivery system. 

2.4.1.3 It	 is recommended that all valves, hoses, and piping be removed 

from ports below the nominal volume line to eliminate errors that 

may result from leakage or expansion while the prover is under 

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2.4.2 

2.4.3 

April 2013 

pressure. These potential errors typically only affect the calibration 

but not during normal use. Plug one port with a fitting and valve of 

suitable pressure rating for draining the prover. Plug all other ports 

with sealed plugs of suitable pressure ratings. 

2.4.1.4 Remove	 the plug and relief valve (1) from the top, and extend the 

pipe into the hole. This may require the use of a reducer and a 

short length of hose (about 1 inch in diameter). If this is a tight fit, 

open the vapor return line valve (2) to provide an air bleed. 

Use the prover inlet line (3) as a gravity drain. If necessary, 

remove the fitting on the end and connect a hose or pipe to make 

the necessary drain line. 

Warning: ensure that a check valve is not plumbed into the prover 

inlet line. If it is, remove the check valve, otherwise the prover will 

need to be drained via the plug in the bottom of the lower neck. 

Cleanliness Check 

Both the standard and the unknown prover must be internally clean. This 

should be verified by checking that water drains properly from them. If 

necessary, either or both should be cleaned with water and non-foaming 

detergent (see GMP No. 6) to attain good drainage characteristics. 

Additional effort may be required to eliminate scaling and contamination 

build-up from the inside of LPG provers. 

Neck scale plate verification (This is generally only conducted for new or 

damaged measures or those that have not been calibrated by the 

laboratory in the past.) 

2.4.3.1 Fill the	 unknown prover with water from the standard. Check the 

prover level condition in the same way in which it will be used and 

adjust if necessary by placing a precision spirit or electronic digital 

level vertically on the neck on at least two locations, 90 degrees 

apart around the circumference of the neck and adjust the 

orientation of the standard until the neck is as close to vertical 

(plumb or perpendicular to the horizontal plane) as possible. Verify 

and adjust any mounted levels that are on the prover to agree 

(when present and when possible). Check the prover system for 

leaks. This is a wet-down run. 

2.4.3.2 Bleed the liquid level down to a graduation near the bottom of the 

upper neck. "Rock" the prover to "bounce" the liquid level, 

momentarily, to ensure that it has reached an equilibrium level. 

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April 2013 

Read and record this setting to be used as the initial scale reading 

sri. This is in preparation for calibratio n of the neck scale. 

2.4.3.3 Remove the fill hose or pipe from the top and insert a funne l. 

2.4.3.4 Recheck the scale reading, then add water in a quantity equal to 

1 approximately 1⁄4 or /5 of the graduated neck volume from a 

suitable standard; record the scale reading. 

2.4.3.5 Repeat 2.4.3.4 by successive additions until water is near the top of 

the scale (the neck capacity is usually about 5 gal on a 100 gal 

LPG prover). Record scale readings after each addition. The last 

reading will be the final scale reading, srf. The closer the water is 

to the top of the neck, the harder it may be to "bounce" the liquid 

in the gauge. 

A plot of scale readings with respect to the total volume of water 

that is added Vw should be linear and will be a gross check of the 

validity of this calibratio n. 

2.4.3.6 Calculate	 and assess the accuracy of the neck scale for each 

interval. The error should be less than 0.5 % of the graduated neck 

volume. If more than this, the scale should ideally be replaced. 

Alternatively, a Neck Scale Correction Value (NSCV) may be 

issued with instructions to the user if it is anticipated that this 

correction value will be used. 

2.4.3.7 Neck scale errors less than 0.5 % of the graduated neck volume 

should be included in the uncertainty estimate associated with the 

prover calibration. Uncertainties associated with the neck scale 

calibration are primarily related to the setting of the meniscus on 

the flask used (with each drop), the reading of the meniscus on the 

unknown prover (at each volume reading), and the calibration 

uncertainty of the flask. These uncertainties must be considered 

when evaluating the acceptability of the neck scale. 

2.4.3.8 The neck scale correction value is calculated as follows: 

 if

w

srsr

V

NSCV





Eqn. 1 

Table 2. Variables for neck scale corre ction value equation. 

NSCV Neck scale correction value 

Vw Total volume of water added to neck 

Scale reading, final 

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2.4.4
 

April 2013 

i

sr

Scale reading, initial 

Body Calibratio n 

2.4.4.1 Drain	 the unknown LPG prover through its inlet valve and the 

liquid bleeder valve. When the liquid reaches the top of the lower 

gauge glass, close the inlet valve and allow the water to drain from 

the interior of the prover into the lower neck for 30 s, while 

controlling the water flow and level with the bleeder valve until the 

liquid meniscus reaches the zero graduation. The liquid level 

should be exactly at the zero graduation and the bleeder valve 

closed simultaneously at the 30 s drain time. (Draining with the 

bleeder valve close to the zero mark should be started during the 

30 s drain period but should not be completed before the end of the 

drain period.) 

Alternatively, though not recommended, the prover may be 

completely drained with a 30 s drain time and then refilled with a 

funnel that has been wet down, and adding a small volume of 

water to set the zero mark. Errors from this process will result due 

to the additional drain and retention time and other factors 

associated with the process and should be considered in the 

uncertainty assessment. 

2.4.4.2 Run	 1. Transfer the volume from the standard in the usual manner, 

and record the standard and prover temperature readings. If 

multiple transfers are required, record temperature of the standard 

at the time of each transfer, but that of the prover only after the 

final transfer. Check the prover level by placing a precision spirit 

or electronic digital level vertically on the neck on at least two 

locations, 90 degrees apart around the circumference of the neck 

and adjust the orientation of the standard until the neck is as close 

to vertical (plumb or perpendicular to the horizontal plane) as 

possible. Verify and adjust any mounted levels that are on the 

prover to agree (when present and when possible). "Rock" the 

prover to "bounce" the liquid in the upper gauge glass before 

reading. Record the final scale reading after the nominal volume 

has been transferred into the unknown LPG prover with no 

pressure applied. 

Note regarding temperature measurements: A digital temperature 

sensing device with a long cable can allow insertion of the probe 

into the standard and the unknown to enable direct liquid 

temperature measurements at the bottom, middle, and top of the 

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provers. If the prover thermometer wells are used, ensure that the 

prover has equalized with the temperature of the water. 

2.4.4.3	 Run 2. Drain the LPG prover as described in 2.4.4.1 and make 

another test run. Record the temperatures of the standard(s) and 

the unknown and final scale reading. Calculate the prover error 

at 0 psig (no pressure applied) for each run using the appropriate 

equations in Section 3; these values are used to evaluate 

repeatability of the test only. The error at 0 psig for the test runs 

must agree within 0.02 % of the prover volume or 

approximately one-half the prover tolerance (i.e., 5 in3 on a 100 

gal LPG prover). If the two runs fail to agree within 0.02 % of 

the prover volume, identify and correct problems with the 

prover or set-up. Then, continue until replicates agree within 

these limits, taking care to ensure that poor cleanliness, 

contamination, bubbles in hoses, leaking valves or seals are not 

contributing to poor repeatability. Lack of measurement 

agreement may also be due to poor field conditions, such as 

when calibration is conducted in unstable environments. Poor 

agreement must be corrected before calibration can be 

completed. 

2.4.4.4	 While the LPG prover remains full from Run 2, replace the 

relief valve and plug in the top of the prover using suitable pipe 

joint compound or tape. 

2.4.5 Prover Adjustments 

2.4.5.1	 The internal pressure and hence the volume of the prover may 

vary during use. Accordingly, a pressure correction must be 

made using the data of steps 2.4.6. 

To minimize the amount of correction needed when the prover 

is in use, the prover should be adjusted to indicate its nominal 

capacity when 100 psig is applied. (An internal pressure of 

100 psig is suggested as being convenient.) If the actual volume 

of the prover is not near a convenient whole gallon value and 

cannot easily be adjusted to a whole gallon value, a prover 

correction value can be computed (see 3.3) and added to the 

pressure correction values to obtain a set of combined prover 

and pressure correction values to be computed. The pressure 

correction is computed in 3.3. The pressure gauge that is 

mounted to the LPG prover may be used for setting calibration 

pressures, but, if following NIST Handbook 105-4, it is required 

to be calibrated. Since the correction values assigned to the 

prover during calibration will match those during use, the 

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April 2013 

2.4.5.2 

2.4.5.3 

prover corrections obtained using a mounted pressure gauge are 

generally acceptable. Calibration status of the pressure gauge 

mounted on the prover should be assessed and included on the 

calibratio n report. 

Use a cylinder of nitrogen or compressed air and a proper 

pressure regulator with an integrated pressure gauge. 

Connect the cylinder regulator output to the vapor return fitting 

(2) near the top of the neck. This may require fashioning a 

connection with steel pipe nipples or other appropriate materials 

and the existing fittings. 

Caution: Ensure that all piping and fittings are rated for the 

pressures to which they will be exposed. 

Make sure all valves are closed except the vapor return valve. 

Verify that the final scale reading has not changed since it was 

recorded (if it has changed it may signal a leak in one of the 

valves or fittings), and then slowly introduce pressure until the 

installed prover gauge reads 100 psig. Lightly tap the gauge to 

ensure that the gauge needle is not sticking. "Bounce" the liquid 

in the neck, then read and record the liquid level at this applied 

pressure. 

Return pressure to 0 psig and reapply pressure as above. This 

reading at 100 psig should agree with the above recorded 

reading within 0.02 % of the nominal volume of the prover. 

Leaking seals or valves may cause problems with repeatability 

of the gauge readings under pressure. 

With the pressure in the prover at 100 psig, adjust the upper 

scale to read the nominal volume. This is accomplished by 

adjusting the upper scale so that the water level reading is: 

Desired scale reading = VX60 – (VNOM * 1.00032) Eqn. 2 

Take care to use like units in the calculation. The calculation for 

VX60 is given in 3.1, Eqn. 5 or Eqn. 6. 

Note: The correction factor 1.00032 corrects for the compressibility of the water at 60 °F and 100 psig. If the upper scale is 

not adjustable, see 2.4.5.4. 

SOP 21 Page 9 of 19 
 

 

 

 

 

 

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April 2013 

2.4.5.4	 For provers with only an adjustable lower scale (or one in which 

the upper scale is not adjustable), a prover correction, LC, may 

be calculated at 100 psig as follows: 

  XC NOM u VVL .1* 00032 rs 60   Eqn. 3 

where: 

Prover correction at 100 psig 

VX60 Volume of unknown prover at 60 F 

Nominal volume of prover 

Upper scale reading at 100 psig 

1.00032 Correction factor for the compressibility of 

water at 100 psig 

Take care to use like units in the calculatio n. 

If the prover correction is negative, move the bottom scale down 

to increase the prover volume. If the prover correction is 

positive, move the bottom scale up to decrease the prover 

volume. The distance h that the bottom scale is to be moved is: 

2

 4

 

d

L

h

C





Eqn. 4 

where: 

h Distance in inches the bottom scale is to be 

moved, up or down 

Prover correction at 100 psig in cubic inches 

d Inside diameter of the lower neck of the 

prover in inches (as noted on identificatio n 

plate) 

2.4.6 Pressure Correction 

2.4.6.1	 Return pressure to 0 psig. Record the reading. Slowly introduce 

pressure until the installed prover gauge reads 50 psig. Lightly 

tap the gauge to ensure that the gauge needle is not sticking. 

"Bounce" the liquid in the neck, then read and record the liquid 

level at this applied pressure. 

2.4.6.2	 Repeat step 2.4.6.1 at 100, 150, and 200 psig. Other pressure 

points in between those listed may be tested if so desired. (The 

water level should decrease 10 in3 to 15 in3 for each 50 psig 

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April 2013 

increase in pressure on a 100 gal prover, although this varies 

depending on the geometry and age of the LPG prover. Water 

level changes significantly greater than indicated may be due to 

leaking seals and/or valves.) Erratic pressure readings may also 

be due to air entrapment based on prover design; repeated 

pressurizing of the prover should eliminate entrapped air. Air 

entrapment problems due to design may need to be investigated 

and corrected. 

2.4.6.3	 Repeat step 2.4.6.1 as the pressure is bled down to 150, 100, 50, 

and 0 psig (atmospheric pressure). The readings must agree with 

those previously obtained within approximately 0.02 % of the 

nominal prover volume. If the data are not linear with respect to 

pressure, repeat the series of measurements above to verify the 

nonlinearity of the readings. Leaking seals or valves may cause 

problems with repeatability of the gauge readings under 

pressure. The cause of poor agreement must be identified and 

corrected before continuing the calibratio n. 

2.4.7	 Final Operations 

2.4.7.1	 Seal the bottom and top scales as specified by laboratory 

policy and as appropriate. 

2.4.7.2	 Drain prover, then remove plug (5) at the lower neck to 

facilitate drainage below the lower gauge. If time permits, 

let the prover drain overnight. 

2.4.7.3	 With the nitrogen cylinder or compressed air connected, 

blow nitrogen or air through the prover to remove 

remaining moisture. Be sure to blow out the drain line and 

any other portions of the system that may have become 

contaminated with water. 

2.4.7.4	 If water has entered the pump-off system, pour several 

gallons of alcohol into the prover and pump the alcohol 

through the system to remove the water to prevent it from 

freezing in the pump when LP gas is used. 

Calculatio ns 

3.1 Single	 Delivery 

3.1.1	 Calculate VX60, the volume of the unknown prover at 60 F, using the 

following equation: 

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3 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

   1 60 F 

 1 60 F 

 

1 6 0 1 1

6 0 









x x

S

X

t

V t

V



 

Eqn. 5 

April 2013 

3.2	 Multip le Deliveries 

3.2.1	 Calculate VX60, the volume of the unknown prover at 60 F, using the 

following equation: 

           

   1 60 F 

 1 60 1 F 60 F ... 1 60 F 

 

1 6 0 1 1 2 6 0 2 2 6 0

6 0 

  



  



x x

S S SN N N

X

t

V t V t V t

V



     

Eqn. 6 

Table 3. Variables for VX60 equations. 

Symbols Us ed in Equations 

VX60 volume of the unknown ves s el at 60 F 

VS60 volume of the s tandard ves s el at 60 F 

 N, ,..., 21

dens ity of the water in the s tandard prover where 1 is the dens ity of the water for the firs t 

delivery, 2 is the dens ity of the water for the s econd delivery, and s o on until all N deliveries are 

completed 

1, 2,..., N 

volume difference between water level and the refe rence mark on the s tandard where the 

s ubs cripts 1, 2,..., N, repres ent each delivery as above. If the water level is below the reference 

line,  is negative. If the water level is above the reference line,  is pos itive. If the water level is 

at the reference line,  is zero 

NOTE: units mus t match volume units for the s tandard . For s licker-plate type s tandards , the  is 

zero. 

t1, t2, ..., tN temperature of water for each delivery with the s ubs cripts as above 

 coefficient of cubical expans ion for the s tan dard in units / oF 

ß coefficient of cubical expans ion for the prover in units / oF 

tx temperature of the water in the filled unknown ves s el in units oF 

x dens ity of the water in the unknown ves s el in g/cm3 

Note: Values for the dens ity of water at the res pective temperatures may be calculated us ing the equations given in 

GLP 10 for air-s aturated water. 

3.3 Pressure Corrections 

Compute the pressure correction, Pcorr, at each pressure that the prover was 

read, after any adjustments, by correcting for the compressibility of the water. 

The equation is: 

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April 2013 

  









 



 

100

100

@100 @

psigXpsig

water compressiblity factor

corr ScaleP reading scalepsig reading psigX

Eqn. 7 

where the water correction factor due to compressibility is 7.4 in3 or 0.032 gal 

for a 100 gallon prover (1.8 in3 (0.008 gal) for a 25 gallon prover; 1.5 in3 

(0.006 gal) for a 20 gal prover). The compressibility value is 0.00032 gal/al at 

100 psig. The compressibility factor is given in both cubic inches and gallons 

so the proper unit can be selected depending upon the unit used for the scale 

readings. 

Plot the pressure corrections. If the corrections versus the pressure are linear, 

make a straight line best fit of the data and interpolate to obtain the pressure 

corrections for any desired pressure. If the data is nonlinear, then perform a 

straight line interpolation between adjacent pressure readings to obtain 

pressure corrections at any desired intermediate pressures. Alternatively, a 

best fit curve can be drawn for the nonlinear data and the pressure corrections 

interpolated from the graph for intermediate pressures. See Appendix A for an 

example of the pressure corrections. 

3.4 Prover Volume 

LPG provers are generally adjusted to the nominal value using 100 psig as the 

reference pressure and a 60 °F reference temperature. A gauge reading on a 

prover that indicates a nominal volume at 0 psig will be lower when pressurized 

to 100 psig due to both the compressibility of water under pressure and the 

expansion of the prover. The expansion of the prover is consistent whether there 

is water in the prover or LPG. However, a correction must be made for the 

compressibility of water as noted in 3.3. Thus, to adjust a 100 gal prover to its 

nominal volume at 100 psig, the gauge reading should be set to the VX60 value 

minus 7.4 in3 . (The water level on the prover’s upper scale will be below a 

calculated VX60 value by 7.4 in3 when pressurized to 100 psig.) 

Another possible way to handle the compressibility of water is to add the volume 

of water (e.g., 7.4 in3 for a 100 gal prover) to the volume of water in the prover so 

that it can be set to the VX60 value at 100 psig. 

The total calculated volume of the prover at its reference temperature and 

pressures at 0 psig, 50 psig, 100 psig, and 150 psig and 200 psig, should be 

reported on the calibratio n report. 

Measurement Assurance 

4.1	 Duplicate the process with a suitable check standard or have a suitable range of 

check standards for the laboratory. See SOP 17, SOP 20 and SOP 30. Plot the 

SOP 21	 Page 13 of 19 

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5 

April 2013 

check standard volume and verify it is within established limits OR a 

t-test may be incorporated to check the observed value against an accepted value. 

The mean of the check standard observations is used to evaluate bias and drift 

over time. Check standard observations are used to calculate the standard 

deviation of the measurement process which contributes to the Type A 

uncertainty components. 

4.2	 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of Run 1 and Run 2 is calculated and the pooled 

(or average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of LPG provers that are submitted to the laboratory 

but do not reflect potential meniscus reading errors (See GMP 3.) 

. 

Assignme nt of Uncertainties 

5.1	 The limits of expanded uncertainty, U, include estimates of the standard 

uncertainty of the laboratory volumetric standards used, us, plus the uncertainty of 

measurement, um, at the 95 % level of confidence. See SOP 29 for the complete 

standard operating procedure for calculating the uncertainty. 

5.1.1	 The standard uncertainty for the standard, us, is obtained from the 

calibration report. The combined standard uncertainty, uc, is used and not 

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. 

Note: See SOP 29 for the complete standard operating procedure for 

calculating the uncertainty when multiple deliveries or multiple standards 

are used to correctly calculate correlated uncertainties. Fifteen is the 

maximum recommended number of deliveries from a laboratory standard 

to a prover under test to minimize calibration uncertainties to the levels 

identified previously. 

5.2	 The standard deviation of the measurement process sp, is taken from a control 

chart for an LPG check standard (not from charts for a refined fuel check 

standard) or standard deviation charts for LPG calibrations (See SOP 17, SOP 20 

and SOP 30). Check standards are not normally availab le. 

5.3	 Neck calibration uncertainty should be estimated based on the uncertainty of 

standards used, errors observed during calibration, ability to read the meniscus of 

all standards involved (see GMP 3), and the repeatability of the neck calibratio n. 

5.4	 Other standard uncertainties usually included at this calibration level are 1) 

uncertainties associated with the ability to read the meniscus, only part of which is 

included in the process variability due to parallax and visual capabilities, and 2) 

uncertainties associated with temperature corrections that include values for the 

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April 2013 

cubical coefficient of expansion for the prover under test, the accuracy and 

gradients associated with temperature measurements in the provers. Additional 

factors that might be included are: data showing reproducibility, environmental 

variatio ns over time, and bias or drift of the standard as noted in control charts. 

5.5	 To properly evaluate uncertainties and user requirements (tolerances), assessment 

of additional user uncertainties may be required by laboratory staff. Through 

proper use of documented laboratory and field procedures, additional uncertainty 

factors may be minimized to a level that does not contribute significantly to the 

previously described factors. Additional standard uncertainties in the calibration 

of field standards and their use in meter verification may include: how the prover 

level is established, how delivery and drain times are determined, the use of a 

proper “wet-down” prior to calibration or use, whether gravity drain is used 

during calibration or whether the volume of water is eliminated by pumping, the 

cleanliness of the prover and calibration medium, prover retention characteristics 

related to inside surface, contamination or corrosion, and total drain times, and 

possible air entrapment in the water. Systematic errors may be observed between 

laboratory calibration practices where a gravity drain is used and field use where 

the pumping system is used. 

5.1	 Example components to be considered for an uncertainty budget table are shown in 

Table 4. Multiple values of some items may need to be considered (e.g., multiple 

drops from the standard, multiple meniscus readings, and multiple temperature 

readings.) 

Table 4. Example Unce rtainty Budget Table. 

Unce rtainty Compone nt 

De s cription Symbol Source Typical Dis tribution 

Uncertainty of the standard (5.1) us 

Calibration report; may 

be multiplied or added 

based on dependencies 

Rectangular or 

Normal divided by 

coverage factor 

Accepted standard deviation of 

the process (5.2) sp 

Control chart, standard 

deviation chart Normal 

Uncertainty or uncorrected error 

associated with a neck 

calibration (5.3) 

un From experimental data Rectangular 

Ability to read the Meniscus in S 

(5.4) um 

None if using a slickerplate type standard; 

GMP 3 

Triangular 

Ability to read the Meniscus in 

X (5.4) um GMP 3 Triangular 

Water temperature (S) (5.4) uts 

Consider accuracy, 

resolution, and gradients Rectangular 

Water temperature (X) (5.4) utx 

Consider accuracy, 

resolution, and gradients Rectangular 

Cubical Coefficient of uCCE 5 % to 10 % Rectangular 

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6 

April 2013 

Expansion on S (5.4) (EURAMET CG-21) 

Cubical Coefficient of 

Expansion on X (5.4) uCCE 

5 % to 10 % 

(EURAMET CG-21) Rectangular 

Uncertainty associated with the 

pressure gauge 

upsig 

Handbook 105-4, 5 psig 

increments; use 2.5 psig Rectangular 

Uncertainty of bias or drift of 

standards (5.2) ub From control chart Rectangular 

Uncertainty of drain time ud From experimental data Normal 

Report 

6.1	 Report results as described in SOP No. 1, Preparation of Calibration/Test Results, 

with the addition of the following: 

For LPG provers, the total prover volume and uncertainty, reference temperature, 

material, coefficient of expansion (assumed or measured), any identifying 

markings, tolerances (if appropriate), laboratory temperature, water temperature, 

barometric pressure, relative humid ity, out-of-tolerance conditions, and the total 

drain time from opening of the valve, includ ing the 30 s drain after cessation of 

flow. 

The report should also include temperature and pressure correction tables or chart, 

along with a note regarding possible differences in retention characteristic s 

between water, the calibratio n medium, and LPG products. 

The SI unit of volume is m3

, so a conversion factor is to be included on the report 

in the notes section when other volumes are used. 

SOP 21	 Page 16 of 19 
 

 

 

A pril 2013 

Figure 1. LPG Prover Schematic. 

SOP 21 Page 17 of 19
 
 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

Appendix A 

Volume Transfer Data Sheet for LPG Provers 

Laboratory data and conditions: 

Vessel Owner Op erator 

Vessel ID Date 

Nominal Volume Air T emp erature 

M aterial Relative Humidity 

Cubical Coefficient of Exp ansion 

Standard deviation of the 

p rocess, sp from the Standard 

Deviation Chart 

Reference temp erature of unknown 

p rover Degrees of Freedom 

Unknown p rover graduations Ap p licable sp ecifications and 

tolerances 

Volume standard(s) data: 

ID (Not e ID of Standards) Nominal 

Volume Volume/Correction Exp anded Unc: From cal. rep ort 

Unc: 

k factor 

Cubical Coefficient 

of Exp ansion 

S 

S 

Run 1: Measurement Observations 

DROP 

# Rep ort ed Volume (gal) M aterial (M S/SS/BS/SL) Water Temp (°C) (Must be ≥ 0.5 °C and < 40 °C) 

Gauge Delta 

(in3) 

1 

M aterial for the Unknown: M S, SS, TP, AL, PVLC 

Final Gauge Reading at 0 p sig: in3 

Final Water Temp erature: °C 

Run 2: Measurement O bservations 

DROP 

# Rep ort ed Volume (gal) M aterial (M S/SS/BS/SL) Water Temp (°C) 

(Must be ≥ 0.5 °C and < 40 °C) 

Gauge Delta 

(in3) 

1 

M aterial for the Unknown: M S, SS, TP, AL, PVLC 

Final Gauge Reading at 0 p sig: in3 

Final Water Temp erature: °C 

Run 2: Pressure Observations 

Gauge Reading at 100 p sig in3 

Accep table p ressure 

rep eatability ? Y/N 

Gauge Reading at 0 p sig: in3 

Rep eated Gauge Reading at 100 p sig in3 

Increasing Pressure Readings, 0 p sig Decreasing Pressure Readings, 150 p sig in3 

Increasing Pressure Readings, 50 p sig Decreasing Pressure Readings, 100 p sig in3 

Increasing Pressure Readings, 100 p sig Decreasing Pressure Readings, 50 p sig in3 

Increasing Pressure Readings, 150 p sig Decreasing Pressure Readings, 0 p sig in3 

Increasing Pressure Readings, 200 p sig in3 

SOP 21 Page 18 of 19 
 

 

 

 

 

 

 

A pril 2013 

Appendix B 

Example Temperature Correction Table* 

Example for a 100 gallon prover an d 60 °F reference temperature. 

CCE Mild Steel 

1.86 x 10-5/°F 

Stainles s Steel 

2.65 x 10-5/°F 

Temperatu re °F in3 gal in3 gal 

-20 -34 -0.149 -49 -0.212 

-15 -32 -0.139 -46 -0.199 

-10 -30 -0.130 -43 -0.186 

-5 -28 -0.121 -40 -0.172 

0 -26 -0.112 -37 -0.159 

5 -24 -0.102 -34 -0.146 

10 -21 -0.093 -31 -0.133 

15 -19 -0.084 -28 -0.119 

20 -17 -0.074 -24 -0.106 

25 -15 -0.065 -21 -0.093 

30 -13 -0.056 -18 -0.079 

35 -11 -0.047 -15 -0.066 

40 -9 -0.037 -12 -0.053 

45 -6 -0.028 -9 -0.040 

50 -4 -0.019 -6 -0.026 

55 -2 -0.009 -3 -0.013 

60 0 0.000 0 0.000 

65 2 0.009 3 0.013 

70 4 0.019 6 0.026 

75 6 0.028 9 0.040 

80 9 0.037 12 0.053 

85 11 0.046 15 0.066 

90 13 0.056 18 0.080 

95 15 0.065 21 0.093 

100 17 0.074 24 0.106 

105 19 0.084 28 0.119 

110 21 0.093 31 0.133 

115 24 0.102 34 0.146 

120 26 0.112 37 0.159 

CCE = coefficient of cubical expans ion 

*Provide only the applicable coefficient of cubical expans ion for the prover under tes t. 

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April 2013 

SOP 26
 

Standard Ope rating Proce dure
 

For
 1 Gravime tric Calibratio n of Dynamic Volume tric Systems use d as Standards 

1	 Introductio n 

1.1	 Purpose of Test 

This procedure describes the gravimetric calibration of volumetric systems that 

may be used as volumetric measuring standards. (Gravimetric calibration of fixed 

volume graduated-neck or slicker-plate type standards should be completed using 

SOP 14.) This procedure uses gravimetric calibration principles with mass values 

and pure water sources to obtain calibration uncertainties that are generally less 

than those obtained during volume transfer procedures of similar standards. 

Alternative test liquids are not considered in this procedure. Accordingly, the 

procedure is especially useful for high accuracy calibrations. The procedure uses 

replicate testing to incorporate measurement assurance steps to ensure the validity 

of the measurement process; additional analyses must be performed to assess for 

bias (e.g., gravimetric calibration of other similar sized standards using the same 

methods, or interlaboratory comparisons with similar standards or provers). The 

procedure makes use of an electronic balance and is suitable for all sizes of 

gravimetric calibrations as limited by the capacity and resolution of the balance, 

availab le water source, mass standards, and handling capacity of the laboratory. 

This procedure can be used for single direction and bi-directional calibration of 

small volume provers, for calibration of volumes delivered through a master 

meter, for fixed volume delivery from alternative volumetric measuring systems, 

or other alternative test methods and standards where the gravimetric calibration 

provides a useful calibration result and measurement uncertainty. All steps in the 

procedure and calculations must be thoroughly reviewed and evaluated for 

appropriateness for the specific standards under test to ensure accurate 

measurement results are reported to the user. 

1.2	 Prerequisites 

1.2.1	 Verify that valid calibration certificates with appropriate values and 

uncertainties are available for all standards, instruments and sensors used 

in this procedure. Calibration values must have demonstrated metrological 

traceability to the International System of Units (SI), which may be to the 

SI, through a National Metrology Institute (for example, NIST.) 

1.2.2	 Verify that all standards and instruments (e.g., mass standards, 

thermometer, barometer, and hygrometer) have sufficiently small standard 

uncertainties for the level of calibration. Reference standards that need 

special care and protection should not be used for gravimetric calibration 

where there is risk for contamina tio n or damage from water. 

1 Non-SI units are predominately in common us e in State legal metrology laboratories , and/or the petroleum indus try 

for many volumetric meas urements , therefore non -SI units are us ed to reflect the practical needs of the laboratories 

performing thes e meas urements when appropriate. 

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April 2013 

1.2.3	 Verify that the balance has suffic ie nt capacity and is in good operating 

condition with suffic ie ntly small process standard deviation. Process 

standard deviatio ns need to be verified by a valid control chart or 

preliminary experiments to ascertain performance quality. The accuracy of 

the balance and weighing procedures should also be evaluated to minimize 

potential bias in the measurement process. 

1.2.4	 Verify that the operator is experienced and has demonstrated proficiency 

in precision weighing techniques and volumetric measurements and has 

had specific training in SOP 2, SOP 4, SOP 19, SOP 29, GMP 10, and 

especially in gravimetric calibratio ns such as those used in SOP 14. 

1.2.5	 Verify that an adequate quality and supply of distilled or de-ionized water 

(see GLP 10) is available. Do not use tap or other impure water sources 

for this procedure! The laboratory must have a continuous flow of water 

available and may thermally equilibrate water in a large volumetric prover 

or a water tank provided purity is ensured. Note: Calibration of some 

systems may require other liquids due to viscosity or lubricity 

requirements and alternative procedures should be considered. Use of 

calibratio n liquids other than water is not considered in this SOP. 

1.2.6	 Verify that the laboratory facility is free of air currents and/or temperature 

fluctuations where the mass measurements will be performed. The 

volumetric proving system must also be calibrated in a thermally stable 

environment. Where the volume and weighing areas are not the same, 

movement of standards and transfer vessels must not negatively affect 

environmental stability. Stable temperatures, and thermal equilibration of 

water, are especially important to minimize possible convection currents 

on precision balances. Humidity control is essential for minimizing 

possible evaporation and/or condensation during the measureme nt process. 

1.2.7	 Verify that the laboratory facilities meet the following minimum 

conditions to meet the expected uncertainty possible with this procedure: 

Table 1. Laboratory environme ntal conditions . 

Procedure Temperature Relative 

Humid ity 

Gravimetric 

20 C to 23 C 

Stable to ± 1 C / 1 h during the 

calibratio n. 

40 % to 60 % 

Stable to ± 10 % / 4 h 

1.2.8	 All necessary maintenance to the unknown volumetric standard must be 

completed by the device owner prior to starting the gravimetric 

calibration. It is advisable to perform a static leak test prior to performing 

the test on systems that allow such testing. Replace any seals that are 

present on the prover if there is any doubt as to their integrity. If “as 

found” data is required, it must be obtained before any seal replacements. 

A second calibration will be required after any maintenance is completed 

to obtain an “as left” calibration value. Note: “as found” data is essential 

for setting, monitoring, or adjusting calibratio n intervals. 

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April 2013 

1.2.9	 Any standard inlet(s) and outlet(s) that are not used in the calibration 

process must be blocked by the device owner before calibration by using a 

blind flange, double-block and bleed valve, or other appropriate hardware. 

All extra valves, piping must be evaluated to ensure that air is not 

entrapped in the system. 

1.2.10 The	 device owner must provide all necessary manufacturers’ manuals and 

hardware (e.g., including pipe fittings, valves, solenoids, wiring, etc.) as 

well as trained personnel to operate the device during the calibration to 

ensure that the device is calibrated in the same manner in which it will be 

used. 

Methodology 

2.1	 Scope, Precision, Accuracy 

The procedure is applicable for the calibration of any size of volumetric 

measuring system that, when filled with water, will not overload the electronic 

balance used. Typical volumetric proving systems ranging in capacity from 5 gal 

to 120 gal may be calibrated. Continuous systems that measure these quantities 

that are controllable in the laboratory may be considered as well (e.g., a metering 

system delivering 40 gallons per minute to 100 gallons per minute may be 

possible.) Flow rates that will be assessed need to be determined between the 

laboratory and the standard owner prior to calibration and should consider the 

practical range of use, the laboratory capability, and any documentary or legal 

requirements of applicable specificatio ns and tolerances. 

The precision of this calibration depends on strict adherence to the various steps 

of the procedure. The accuracy attainable will depend on the uncertainties of the 

standard weights, the uncertainties associated with the air buoyancy corrections, 

the accuracy of temperature measurements, the purity and density of the water, 

and the thermal expansion corrections that are made. Another important factor to 

consider is the repeatability of the procedure and the repeatability of the standard 

under test. 

2.2	 Summary 

The mass of the water delivered by the volumetric proving system is determined 

by weighing the water on an electronic balance and comparing it to mass 

standards. Volume is derived from the mass of the mass standards, the density of 

pure water, appropriate air buoyancy corrections, and thermal and pressure 

expansion corrections, using the equations provided in Section 3. 

2.3	 Standards, Equipment, and Calibratio n Notes 

2.3.1	 An electronic balance having sufficie nt capacity to weigh the loaded 

vessel is required. The repeatability of the balance, measureme nt process, 

and standard under test are limiting factors in the accuracy of the 

measureme nt. The resolutio n of the balance and repeatability of the 

measureme nt process must be smaller than the expected uncertainty of the 

calibratio n. NOTE: standard deviations obtained from precision mass 

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2.3.2
 

2.3.3 

2.3.4 

2.3.5 

2.3.6 

2.3.7 

2.3.8 

April 2013 

calibratio ns generally do not reflect the process repeatability of this 

procedure; therefore repeatability must be assessed using this procedure. 

Mass standards of suffic ient quantity and capacity are required. 

Ordinarily, standards of ASTM Class 2 or 3 or OIML Class F1 or F2 

weight specificatio ns are required. Working standards of other classes are 

generally not designed to maintain adequate stability needed; however, 

corrections obtained within a few days of the volume calibratio n may be 

used if the uncertainty is suffic iently small. Mass standards are selected so 

that they are slightly larger than the volume of water and container or 

transfer vessel to be weighed. Linearity errors or additional uncertainties 

may need to be considered when the mass standards are slightly less than 

the volume or container being measured. When summatio ns of masses are 

used, the summatio n mass is used, and the “effective density” must be 

calculated, taking care not to use “average” density values. 

Filter paper and padding for protection of mass standards when placed on 

the balance pan, stacked, or placed on the calibratio n item may be used. 

When all such materials are used, care must be taken to determine when 

and how the mass of these items are incorporated into the process (as tare 

weight, or as tared/zeroed off the balance readings). 

A transfer vessel is required that is made of some inert and stable material 

with a volumetric capacity larger than the volume to be measured and a 

port large enough to fill the vessel on the top surface. The transfer vessel 

should be as small as possible to minimize its influe nce on the balance, but 

approximate ly 25 % larger than the volume to be measured in order to 

prevent water loss due to splashing out of the top fill port. The transfer 

vessel may need to be suspended with a hoist or mounted to a pallet to be 

moved with a forklift or pallet jack. 

Weight handling equipment is required for this procedure that has 

adequate capacity for handling the filled and empty transfer vessel. It must 

have the ability to be moved slowly and gently to minimize water sloshing 

and to gently set the empty or filled vessel on the balance pan. 

Thermometers, with resolution and uncertainty less than 0.1 °C to 

determine water and volumetric proving system temperatures. 

Submersible thermometer probes and cables must be long enough to 

measure the temperature of the water near the center of the transfer vessel. 

Therefore, liquid-in-glass thermometers are not adequate. 

Barometer with resolution and uncertainty less than 135 Pa (1 mm Hg to 

determine barometric pressure (absolute). 

Hygrometer with resolution and uncertainty less than 10 % to determine 

relative humid ity. 

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April 2013 

2.3.9	 Pressure gauge(s) with resolution and uncertainty less than 1 psig for 

determining the volumetric proving system pressure (where applicable). 

2.3.10 If	 a proving system does not have operational temperature sensors and 

pressure gauges installed, the initial inspection should reveal that the 

proving system is not adequately prepared for calibration. If the 

calibration relies on the accuracy of the temperature sensors and pre ssure 

gauges installed on the prover, they must be installed prior to the volume 

calibration and have current calibration reports from an accredited 

calibration laboratory that are readily available for inspection. When 

laboratory pressure and temperature sensors are used during the 

calibratio n all laboratory sensors must all have current calibratio n reports. 

2.3.11 Mechanica l problems and sources of errors that may be encountered 

during a calibratio n and affect the ability of the system to repeat may 

include many possibilities, several of which are listed below. Mechanica l 

problems with the volumetric standard must be corrected before 

calibratio n. Quantificatio n of errors that cannot be eliminated must be 

evaluated and includ ed in the uncertainty budget table. 

- Proper operation of the system; 

- Air in the system; 

- Instability of the temperature of water or ambient conditio ns 

- Pressure fluctuatio ns in the system; 

- Error in reading the test measure(s); 

- Incorrect drain time for reading test measure(s); 

- Contamina tio n of the systems; 

- Damaged measures/system; 

- Error in reading temperature or pressure; 

- Displacer problems (when present); 

- Malfunctio n of switches (when present); 

- Damage, worn, or badly fitted seals; 

- Damage, scoring, or pitting on the inside of the proving system; 

- Damaged or misaligned detector switches (when present); 

- Light interference in optical switches (when present); 

- Malfunctio n of solenoid valve (when present); 

- Leaks in prover/system or bypass valves. 

2.3.12 Errors that may be encountered in weighing steps of the calibratio n may 

include any of the items listed below. Quantificatio n of errors that cannot 

be elimina ted must be evaluated and included in the uncertainty budget 

table. 

- Balance drift; 

- Off center loading of the balance; 

- Non-linearity of the balance and improper selection of the mass 

standards to calibrate the weighing instrume nt in the range of use; 

- Air currents or convection currents when weighing is performed in a 

large mass laboratory or when the temperature of the water, system, or 

laboratory are not adequately equilibrated; 

- Care in placing items on the weighing instrume nt; 

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April 2013 

- Inadequate water quality. 

2.4	 Procedure 

2.4.1	 Inspect the volumetric proving system to verify that it and associated 

piping are drained, clean, and safe for placement in the laboratory. For 

large volumetric proving systems, ensure that there is adequate space in 

the laboratory to safely position the system near the pure water source and 

that a drain is accessible and that the proximity of the mass calibration 

area is convenient. Direct the driver to position to system appropriately, 

taking appropriate precautions to prevent injury to anyone or damage to 

the laboratory and/or equipment and standards. Allow adequate time for 

the system under test to equilibrate with the laboratory environment. The 

time required will be dependent on the difference between inside and 

outside temperature and relative humid ity. 

2.4.2	 Initial inspection. Record the data about the system being calibrated, 

taking care to record all applicable serial numbers, coefficients of cubical 

expansion, reference temperatures, flow rates, presence or lack of the 

calibration status of all auxiliary standards associated with the standard 

(such as pressure gauges and temperature sensors), and means for sealing 

the system after calibratio n. 

2.4.3	 Install, or have the owner install, volumetric proving system hardware per 

manufacturer’s instructions or have the owner provide this service. 

(Hardware must be provided by device owner.) 

2.4.4	 Connect the water supply to the volume tric proving system. 

2.4.4.1 In	 general, ensure that all air is bled from the system, suitable 

water supply is provided and the device temperature is in 

equilibrium with that of the water supply (several runs are 

generally required prior to the calibration to ensure that all air is 

out of the system and that all components are in thermal 

equilibrium with the water.) Set device valves as appropriate for 

the test to be conducted. 

2.4.4.2 Follow	 the operator’s guidance (and per manufacturer’s 

instructions) to become familiar with and to establish correct valve 

positions for each step of the calibratio n when applicable. 

2.4.5	 Install and/or use calibrated thermometers with evidence of current 

metrological traceability to record air temperature, water temperature, 

detector bar temperature (Td) (where present), volumetric proving system 

temperatures (Tp). 

2.4.6	 Install and/or use calibrated pressure gauge(s) to record prover pressure(s) 

(Pp) when present and appropriate. 

2.4.7	 Analyze the piping and valves to determine if the configuration needs to 

be changed to deliver water into the transfer vessel. 

2.4.8	 Record all of the prover-specific variables on the data entry form. 

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2.4.9
 

April 2013 

Note: All references in the following weighing options to the empty 

transfer vessel assume that the empty transfer vessel has been placed in a 

“wetted-down” condition. This wet down condition is achieved when the 

vessel has been filled with water and then drained using the same process 

that will be used throughout this calibration. Several runs may be needed 

on the volumetric proving system to ensure proper wetting of all lines and 

drains before the measurement data is recorded. 

Weighings (Option A) 

2.4.9.1 Zero the balance. Place a standard mass, Ms1, on the balance 

platform (Ms1 should be slightly larger than the mass of the empty 

transfer vessel.) Record the balance indicatio n as O1. 

2.4.9.2 Zero the balance and then place the empty transfer vessel on 

balance platform and record the balance indication as O2. Caution: 

the transfer vessel must be dry on the outside for all weighings. 

2.4.9.3 Record air temperature, barometric pressure and relative humidity 

at the time of these measurements. Due to timing of this type of 

calibration, environmental conditions must be recorded for both 

the empty and full transfer vessel. 

2.4.9.4 Zero the balance and then place a standard mass, Ms2, on the 

balance platform (Ms2 should be slightly larger than the mass of the 

filled vessel.) Record the balance indication as O3. (This 

observation may be made before or after the weighing of the filled 

transfer vessel, depending on laboratory configurations and 

convenience.) 

2.4.9.5 Fill the	 transfer vessel through the volumetric proving system. Do 

not fill the transfer vessel while it is on a laboratory balance. 

Ensure that all of the water from the volumetric standard or 

registered on a meter is captured in the transfer vessel. Verify that 

the water temperature in the system is uniform and stable 

throughout the filling process (± 0.2 °C). Read and record all 

pertinent volumetric standard temperatures and pressures during 

the calibration sequence. Place the lid on the transfer vessel to limit 

evaporation. 

2.4.9.6 Zero the balance and then place the filled transfer vessel on the 

balance and record the balance indicatio n as O4. 

2.4.9.7 Read and record the temperature of the water in the transfer vessel 

immediately after weighing. It is critical to measure the 

temperature after weighing to ensure that water is not removed 

from the transfer vessel prior to obtaining the mass value. 

2.4.9.8 Record the air temperature, barometric pressure and relative 

humid ity at the time of these measurements. 

2.4.9.9 Make	 at least five replicate runs with at least two runs at a flow 

rate differing from the others by at least 25 % The measured 

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April 2013 

result (V60) of each of these calibration runs must agree within 

0.02 % of the average volume of all volume calibration runs (i.e., 

the maximum result minus the minimum result must be less than 

0.02 % of the average measured volume ). 

2.4.9.10	 Calculate the volume using Equation 1 in Section 3.1.1., 

(Option A). 

2.4.10 Weighings (Option B) 

2.4.10.1	 Place mass standards that approximate the mass of the 

empty transfer vessel (with a lid) and adequate filter paper or other 

clean, lint-free padding material (to protect the standards being 

used) on the electronic balance. With these items on the balance, 

zero the balance. Note: the padding materials must be included on 

all measurements or their mass treated as tare. 

2.4.10.2	 Place additiona l mass standards approximating the nomina l 

mass of the water volume to be measured on the balance. Take 

care to place the weights on filter paper or other appropriate 

protective padding. Record this balance indicatio n as O1. 

2.4.10.3	 Remove all mass standards. Record the air temperature, 

barometric pressure, and relative humid ity readings. 

2.4.10.4	 Place the empty transfer vessel on the balance, with the 

padding material and zero the balance indicatio n. Remove the 

transfer vessel, lid, and padding material and record the base empty 

vessel reading (B). 

2.4.10.5	 Fill the transfer vessel from the volumetric proving system. 

Read and record all pertinent volumetric standard temperatures and 

pressures during the calibration sequence. Place the lid on the 

transfer vessel to limit evaporation. 

2.4.10.6	 Immediately prior to weighing full vessel record balance 

reading as (d1). This reading will be used to calculate any balance 

drift that occurred while the transfer vessel was being filled. 

2.4.10.7	 Place the filled vessel and all padding material on the 

balance. If needed, add known mass standards as tare weights to 

bring the water mass up to the mass of the standards used for O1. 

This balance reading is recorded as O2. Record the mass of all tare 

weights. 

2.4.10.8	 Remove the filled transfer vessel and record the balance 

indicatio n as (d2). This reading is used to calculate balance drift 

over the entire calibratio n process. 

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3 

April 2013 

2.4.10.9	 Immediately after removing the filled transfer vessel from 

the balance, record the temperature of water in the vessel. 

2.4.10.10	 Make at least five replicate runs with at least two runs at a 

flow rate differing from the others by at least 25 % when the 

system allows for varying flow rates. The range measured result 

(V60) of each of these calibratio n runs must agree within 0.02 % of 

the volume (i.e., the maximum result minus the minimum result 

must be less than 0.02 % of the volume being measured). 

2.4.10.11	 Calculate the volume using Equations 2 and 3 in Section 

3.1.1., (Option B). 

Calculatio ns 

3.1 Compute	 the volume at the temperature of the measurement, Vt, for each 

determinatio n using the equation: 

3.1.1	 Option A. 















































  















 

 

1

1 

O

O

1 

O

O

 

1

1

1

2

2

2

3

4

s aw

a

s

s

a Vt Ms M









Eqn. 1 

Table 2. Variable s for volume e quation. 

Variable Descriptio n 

Ms, Ms1, Ms2 

mass of standards 

Ms1, is the mass of the standards used with the empty transfer 

vessel 

Ms2, is the mass of the standards used with the transfer vessel after 

filling with delivered water 

s density of MS standards 

w density of water at the temperature of measurement 

a density of air at the conditions of calibratio n – may be different 

for empty and filled weighing of the transfer vessel 

Vt Volume at the temperature of the test for the unknown under test 

SOP 26	 Page 9 of 16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

3.1.1 Option B. 









































































































t aw

a

t

s

s a

t 2 c

 - 

1

 - - 1 M - 1 

O

M V = O

1

Eqn. 2 

 























 

 B

dd

c OO

2

21

22

Eqn. 3 

Table 3. Variables for volume equations . 

Variable Description 

O1 Observation 1, balance reading for mass standard 

O2 Observation 2, balance reading for water delivered from prover 

O2c Drift-compensated O2 reading 

d1 Drift while filling the vessel 

d2 Drift over entire process 

B Base balance reading drift is based on 

MS Mass of mass standards (true mass, vacuum mass) 

Mt Mass of tare weights 

a Air density 

s Density of MS 

t Density of Mt 

w Water density (calculated using GLP 10 equations) 

3.2 Compute V60, the volume at 60 F, for each run, using the equations noted below: 

  

       

   

 

p p p

p

p

p cbp

p abp lbd

p

p

t

CCF CPSCTSCPL

E WT

P ID

CPS

CTS GTT

CTS GTT GTT

P

CPL

CCF

V

V

**

*

*

1

1 *

1 1** *

.0(1 0000032*

1

where

2

1

6 0























 







SOP 26 Page 10 of 16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

Table 4. Additional Variables for Volume Equations. 

Variable Descriptio n 

Tb Reference (Base) temperature 

Td Detector bar temperature (Temperature, detector) – where present 

Tp Prover temperature (Temperature, prover) 

Pp Prover pressure (Pressure, prover) in psig 

E Modulus of elasticity (flow tube) 

WT Wall Thickness of flow tube 

ID Inside Diameter of flow tube 

Gl 

Coefficient of linear thermal expansion (switch bar) – where present 

(either linear and area values are used in combinatio n or the cubical 

value is used) 

Ga 

Coefficient of flow tube area thermal expansion (either linear and 

area values are used in combinatio n or the cubical value is used) 

Gc 

Coefficient of cubical thermal expansion (either linear and area 

values are used in combinatio n or the cubical value is used) 

CPL Correction for the pressure on the liquid 

CTS 

Correction for the temperature on the standard prover CTSp1, based 

on linear and area coefficients of expansion or CTSp2, based on 

cubical coeffic ie nts of expansion 

CPS Correction for the pressure on the standard prover 

CCF Combined correction factor 

3.3 Calculate water density for air-saturated water, using the equations provided in GLP 

10. 

3.4 Calculate	 the air density per NISTIR 6969, Selected Mass Calibratio n Procedures, 

SOP 2, Option B. 

3.5 Calculate the uncertainty for the calibratio n using Section 5. 

Measurement Assurance
 

4.1 Record and plot standard deviations of each five run calibration to determine shortterm repeatability of the measurement process. 

4.2 Perform applicable calibratio ns of check standards where availab le. 

SOP 26	 Page 11 of 16 

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5 

April 2013 

Assignme nt of Uncertainties 

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of 

the mass standards used, us, plus the uncertainty of measurement, sp, at the 95 % level of 

confidence. See SOP 29 for the complete standard operating procedure for calculating the 

uncertainty. 

5.1	 The standard uncertainty for the mass standards, us, is obtained from the 

calibration reports for the standards used. The combined standard uncertainty, uc, is used and not the expanded uncertainty, U, therefore the reported uncertainty for 

the standard will usually need to be divided by the coverage factor k. 

5.2	 The standard deviation of the measurement process is obtained from replicate 

measurements and standard deviation chart performance data (See SOP 17 or 20.) 

The value for sp is obtained from the standard deviation chart data and results for 

the current run must be compared to the standard deviations observed from 

replicate measurements over time. The standard deviation of the process, 

determined from this approach incorporates a repeatability factor related to the 

precision of all weighings and need not be duplicated. An F-test may be 

incorporated to compare observed standard deviations from the current calibration 

with the accepted standard deviations of the process for similar type proving 

systems used as standards. 

5.3	 Other standard uncertainties usually included for this type of calibration level 

include uncertainties associated with water temperature measurements, 

thermometer accuracy, calculation of air density, and standard uncertainties 

associated with the density of the standards used or the lack of internal 

cleanliness. 

5.4	 An example uncertainty budget table is shown in Table 4. Additional components 

may need to be considered depending on the technology being calibrated. 

Table 4. Example uncertainty budge t table . 

Uncertainty Compone nt 

Des cription S ymbol S ource Typical Dis tribution 

Mas s Standards (filled; empty ) us Calibration Report Normal, 1s 

Mas s Dens ity uρs NIST Rectangular 

Standard deviation of the proces s sp Control chart, s tandard deviation chart Normal, 1s 

Prover Temperature utp 

Ability to meas ure and pos s ibility of 

gradients Rectangular 

W ater Temperature utw 

Ability to meas ure and pos s ibility of 

gradients Rectangular 

W ater Dens ity Equation uρw GLP 10, CIPM Reference Rectangular 

W ater Compres s ibility uK Kell, CIPM Reference Rectangular 

Cubical Coefficient of Thermal 

Expans ion uGc 

5 % to 10 % 

(EURAMET CG-19) Rectangular 

Area Coefficient of Thermal 

Expans ion uGa 

5 % to 10 % 

(EURAMET CG-19) Rectangular 

Linear Coefficient of Thermal 

Expans ion uGl 

5 % to 10 % 

(EURAMET CG-19) Rectangular 

SOP 26	 Page 12 of 16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

Modulus of Elas ticity (E) uE Es timate 1 % Rectangular 

Prover Pres s ure upsig Calibration report Rectangular 

Flow Tube Diameter (ID) uID 

Es timate by one divis ion in las t 

decimal place Rectangular 

Tube W all Thick (WT) uWT 

Es timate by one divis ion in las t 

decimal place Rectangular 

Air Temperature uta 

NISTIR 6969, SOP 2, CIPM 

Reference, Calibration report Rectangular 

Barometric pres s ure (abs olute) up 

NISTIR 6969, SOP 2, CIPM 

Reference, Calibration report Rectangular 

Relative Humidity uRH 

NISTIR 6969, SOP 2, CIPM 

Reference, Calibration report Rectangular 

Air Dens ity Equation uρa eqn

NISTIR 6969, SOP 2, CIPM 

Reference, Calibration report Rectangular 

Vis cos ity uV NIST SP 250-72 Rectangular 

6 Report 

6.1 Report results as described in SOP 1, Preparation of Calibratio n/Te st	 Results, with 

the addition of the following: 

6.1.1 Volume, reference temperature, uncertainty, material, thermal coeffic ie nt of 

expansion (assumed or measured), constructio n, any identifying markings, 

tolerances (if appropriate), laboratory temperature, water temperature(s) at 

time of test, barometric pressure, relative humid ity, and any out–oftolerance conditions. Volume may need to be reported as “up-stream” and 

“down-stream” volumes for bi-directional provers. 

6.1.2 The status of items that are not calibrated by the laboratory but that may be 

used to perform measureme nts must be noted on the calibratio n report 

(e.g., temperature sensors, pressure gauges, or full flow rates that may be 

used in the field but that are not calibrated by the laboratory.) A statement 

such as the following must be included on calibratio n reports: “Only items 

presented on this calibratio n report were tested under the conditions 

shown”. Any sensors or gauges that were not calibrated by the laboratory 

should be clearly identified on the report (e.g., “Calibratio n reports for the 

system includ ed temperature sensors and pressure gauges that were 

provided to the laboratory for evaluatio n prior to calibratio n and were 

found to be acceptable.”) 

6.1.3 The volumetric	 proving system being calibrated as a standard should be 

evaluated for conformance to applicable specificatio ns and tolerances if 

being used for legal weights and measures applicatio ns; if no specific 

standards apply, or a laboratory does not perform an assessment, a notice 

should be included on the calibratio n report to the effect that a legal 

metrology assessment was not performed. (For example, “Conformity 

assessment was not completed as a part of this calibratio n. Accurate use in 

field testing requires assessment of repeatability in field applicatio ns as 

well as proper training of the operator, maintenanc e of the proving system, 

integrity of all seals and sensors, and any other auxiliary mechanica l or 

electronic components. The entire system has not been assessed for 

suitability as a field standard for weights and measures applicatio ns. ”) 

SOP 26	 Page 13 of 16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

Additional Refere nces 

Chapter 4, Manual of Petroleum Measurement Standards, and the following Sections as 

applicable: 

Section 1 – Introductio n 

Section 2 – Conventio nal Pipe Provers 

Section 3 – Small Volume Provers 

Section 4 – Tank Provers 

Section 5 – Master-Meter Provers 

Section 6 – Pulse Interpolatio n 

Section 7 – Field Standard Test Measures 

Section 8 – Operation of Proving Systems 

NIST Handbook 105-7: Specificatio ns and Tolerances for Reference Standards and Field 

Standard Weights and Measures, 7. Specificatio ns and Tolerances for Dynamic Small Volume 

Provers, 1996. 

Bean, V. E., Espina, P. I., Wright, J. D., Houser, J. F., Sheckels, S. D., and Johnson, A. N., NIST 

Calibration Services for Liquid Volume, NIST Special Publication 250-72, National Institute of 

Standards and Technolo gy, Gaithersburg, MD, (2009). 

EURAMET Calibration Guide 19, Guidelines on the Determination of Uncertainty in 

Gravimetric Volume Calibratio n, (Version 2.1, 03/2012). 

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April 2013 

Appendix A – Gravimetric Calibration Data Sheet 

Company Name: ________________________________________ T est No: __________________ 

Address: ________________________________________ P urchase Order No: __________________ 

Cit y, St at e, Zip: ________________________________________ Dat e Scheduled: __________________ 

Represent ative: ________________________________________ Dat e Received: __________________ 

P hone: __________________ Fax: ________________ Dat e T ested: __________________ 

Email: ________________________________________ Dat e Ret urned: __________________ 

Company URL: ________________________________________ Next Appointment: __________________ 

General Descript ion ________________________________________ 

Manufact urer: ________________________________________ 

Model Number: _______________ Serial Number: ___________ 

Con dit ion: ________________________________________ 

Comp ressibility factor for water 3.2000E-06 Cubical Thermal Exp ansion Coefficient (Gc) 

Reference Temp erature(Tb) (oF) Area T hermal Exp ansion Coefficient (Ga) 

Reference Temp erature (oC) Det ector Thermal Exp ansion Coefficient (Gl) 

Reference Pressure (p sig) M odulus of Elasticity (flow tube) (E) 

Flow Tube Inside Diameter (inches) (ID) 

Flow Tube Wall Thickness (inches) (WT) 

Mass standard(s) data: 

ID (Note ID and whether 

for Filled or Emp ty 

Transfer Vessel) 

Nominal M ass M ass Correction* Exp anded Unc: 

From cal. rep ort 

Unc: 

k factor 

Density 

g/cm3 

S 

S 

S 

S 

S 

S 

S 

S 

*M ass Correction = Mass values are required for this p rocedure (i.e., Conventional M ass must not be used). 

SOP 26 Page 15 of 16 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

April 2013 

Observations (Option A): 

Fill Number Fill # 1 Fill # 2 Fill # 3 Fill # 4 Fill # 5 

Flow Rate Fast Fast Fast Slow Slow 

Run T ime (sec) 

Balance Reading O1 (St andards for Empty 

T ransfer Vessel) 

Balance Reading O2 (Empty Transfer Vessel) 

Balance Reading O3 (St andards for Filled 

T ransfer Vessel) 

Balance Reading O4 (Filled T ransfer Vessel) 

Air T emperature (oC) 

Baromet ric P ressure (mm Hg) 

Relat ive Humidit y (% RH) 

W at er Temperature ( oC) – record all values 

Det ect or Bar (where present) 

T emperature (Td) (oC) 

P ro ver T emperature (Tp) (oC) 

P rover pressure (Pp) (psig) 

Observations (Option B): 

Fill Number Fill # 1 Fill # 2 Fill # 3 Fill # 4 Fill # 5 

Flow Rate Fast Fast Fast Slow Slow 

Run T ime (sec) 

Balance Reading O1 (st andards) 

Balance Reading Empty Transfer Vessel T ared 

& Removed (B)) 

Balance Reading Immediately Before O2 

Reading (d1) 

Balance Reading O2 (wat er) 

Balance Reading Full T ransfer Vessel 

Removed (d2) 

Validit y Check (Compares d1 -B, and d2 -d1) 

Drift Comp ensated O2 (O2c) 

Air T emperature (°C) 

Baromet ric P ressure (mm Hg) 

Relat ive Humidit y (% RH) 

W at er Temperature (oC) – record all values 

W at er Temperature (°F) 

Det ect or Bar (where present) 

T emperature (Td) (°C) 

Det ect or Bar (where present) 

T emperature (Td) (°F) 

P rover T emperature (Tp) (°C) 

P rover T emperature ( Tp) (°F) 

P rover pressure ( Pp) (psig) 

SOP 26 Page 16 of 16