Selected Procedures for Volumetric 

Calibrations

Georgia L Harris

NIST

Weights & Measures Division

NISTIR 7383

 

NISTIR 7383

Selected Procedures for Volumetric 

Calibrations

Georgia L Harris 

Weights and Measures Division 

Technology Services 

November 2006

U.S. DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez, Secretary 

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 

William Jeffrey, Director 

iii

Foreword 

This NIST IR of Selected Publications has been compiled as an interim update for a 

number of Good Laboratory Practices, Good Measurement Practices, and Standard 

Operating Procedures. 

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 updates have 

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 major changes incorporate 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. No substantive 

changes were made to core measurement processes or equations, with the exception of 

SOP 18, Standard Operating Procedure for Calibration of Graduated Neck-Type Metal 

Volumetric Field Standards, Volume Transfer Method. Temperature limits and equations 

have been added to SOP 18. 

The following Practices and Procedures are new in this interim publication: 

Standard Operating Procedures for: 

• Small Volume Prover, Water Draw (26) 

• Small Volume Prover, Gravimetric Calibration (SVP) 

Special thanks go to the following individuals for the critical editorial reviews needed to 

complete this interim publication: 

• Kelley Larson, AZ Department of Weights and Measures 

• Dan Newcombe, ME Department of Agriculture Metrology Laboratory 

• William Erickson, MI Department of Agriculture, E.C. Heffron Metrology 

Laboratory 

• Craig VanBuren, MI Department of Agriculture, E.C. Heffron Metrology 

Laboratory 

• Van Hyder, NC Department of Agriculture & Consumer Services, Standards 

Laboratory 

• L.F. Eason, NC Department of Agriculture & Consumer Services, Standards 

Laboratory 

• Val Miller, NIST, Weights and Measures Division 

• Carol Hockert, NIST, Weights and Measures Division 

• John Wright, NIST, Process Measurements Division 

• Dan Wright, WA State Department of Agriculture (WSDA), Metrology 

Laboratory 

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 
iv

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

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; therefore, some procedures in this publication will 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. 
v

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 

Liquid 

GMP 3-1 

6 Cleaning Metal Volumetric Measures GMP 6-1 

7 Cleaning Precision Glassware GMP 7-1 

Standard Operating Procedures 

13 Calibration of Volumetric Ware, Gravimetric Method SOP 13-1 

14 Gravimetric Calibration of Volumetric Ware Using an Electronic 

Balance 

SOP 24-1 

15 Calibration of Intermediate and Large Volume Standards 

Gravimetric Method Using an Equal-Arm Balance 

SOP 15-1 

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

17 Control Charts of Laboratory Owned Check Standards for 

Calibration of Measuring Flasks or Small Provers using Volume 

Transfer Methods 

SOP 17-1 

18 Calibration of Graduated Neck-Type Metal Volumetric Field 

Standards, Volumetric Transfer Method 

SOP 18-1 

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

Method 

SOP 19-1 

20 Control Charts for Calibration of Neck Type Provers, Volume 

Transfer Method 

SOP 20-1 

21 Calibration of LPG Provers SOP 21-1 

26 Calibration of Dynamic Small Volume Provers by the Water Draw 

Method 

SOP 26-1 

SVP Gravimetric Calibration of Dynamic Small Volume Provers SOP SVP-1 
vi

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11/15/2006 

GLP 10 Page 1 of 4 

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 or it 

may be used as a standard of volume for purposes of calibration. In each case, it must be clean; 

in the latter case it must be pure, as well. 

 

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. 

 

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

volumetric comparisons are involved. When a water density value is used in an equation for 

volume transfer, the density values for the standard and unknown are proportional to each other; 

therefore, deviations in the density values from pure water are insignificant. (This is not true for 

gravimetric calibrations.) The coefficient of expansion for distilled water and pure water are 

also essentially the same. It is obvious that dirty water could cause a number of problems, 

including depositing residues in a volumetric vessel that could cause volumetric errors or could 

soil its interior, as a minimum. When in doubt of the cleanliness of the water supply, filters 

should be attached to the supply lines used. 

 

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 requirements 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. 

 

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. In fact, most systems designed to meet these specifications actually 

provide quality better than required. 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, 

 

1

 ASTM D 1193, Standard Specification for REAGENT WATER, ASTM, http://www.astm.org, 1916 Race St., 

 Philadelphia, PA 19103. 
11/15/2006 

GLP 10 Page 2 of 4 

electrodialysis, or a combination thereof. 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. There are a number of commercial sources for such equipment. 

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 

rate through the cartridge. 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 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. 

Less accurate density meters are not suitable for evaluating the quality of water needed for 

gravimetric calibrations. These systems typically measure the density at a specific reference 

temperature (generally 20 oC). Density meters are generally not needed if an appropriate water 

purification system is used that includes a way to measure conductivity or resistivity. 

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. 

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). 
11/15/2006 

GLP 10 Page 3 of 4 

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 and 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. 

Temperature equilibrium is another important factor in density stability of water. This is 

especially critical for large volumes. Water temperatures must be stable. 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. 

Water density tables (see Table 9.8 in NISTIR 6969 or Handbook 145) or calculations are used 

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

use of a calculation is often preferred to look-up tables. The following equation is recommended 

for use.2

[ ( )] 5

0

4

0

3

0

2

0 0 0 (T ) 1 A(T T ) B(T T ) C(T T ) D(T T ) E(T T ) ρ w = ρ − − + − + − + − + − Eqn. 1 

where: 

3.596 458 x 10 ( C) .

7.314 894 x 10 ( C)

7.575 677 x 10 ( C)

7.926 504 x 10 ( C)

7.013 4 x 10 ( C)

3.9818

 temperature of water in 

999.973 58 kg/m

density of water

12 5

10 4

8 3

6 2

8 1

0

3

0

− −

− −

− −

− −

− −

= −

=

= −

=

=

=

=

=

=

o

o

o

o

o

o

o

E

D

C

B

A

T C

Tw C

ρ

ρ

 

 

2

 Patterson, J. B., and Morris, E. C., Measurement of Absolute Water Density, 1 oC to 40 oC, Metrologia, 31, 277-

288, (1994). 
11/15/2006 

GLP 10 Page 4 of 4 

Equation 1 provides water density in kg/m3

. To convert the result to units of g/cm3 or g/mL, 

divide the result by 1000. 

Additional References: 

ASTM D 1125, Standard Test Method for Electrical Conductivity and Resistivity of Water, 

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

ISO 15212-1:1998, Oscillation-type density meters – Part 1: Laboratory instruments, ISO, 1998. 
11/15/2006 

GLP 13 Page 1 of 2 

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 pass 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 sucked through a tube connected to a vacuum pump 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. 

Solvent cleaning may be used with alcohol as 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. 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 denatured with 

oils to an extent that will leave residue on the standard. Care must also be taken to avoid mixing 

chemicals such as acetone and alcohols. The alcohol is allowed to drain as much as possible, 

followed by air drying as described above. 

 

Some metal containers have been 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 calibration is used. 

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. 

Calibration Tip: After the vessel is clean and dry, cover with glass or aluminum foil 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 
11/15/2006 

GLP 13 Page 2 of 2 

initial baseline “dry weight” of the clean container for use as a dry reference weight on 

subsequent weighing and drying cycles. 

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

should be reviewed to ensure safe handling of all chemicals noted in this procedure. 
11/15/2006 

GMP 3 Page 1 of 3

GMP 3 

Good Measurement Practice 

for 

Method of Reading A Meniscus Using Water or Other Wetting Liquid 

 

Two common methods are used for setting a meniscus. 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. 

In all apparatus where the volume is defined by a concave meniscus, the reading or setting 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 types of meniscus readers are available. These include black/white meniscus card 

readers or magnifying glasses with cross-hairs. The width of the graduation will affect the 

readability of the meniscus and should be estimated to the nearest 1/10 of a division. Black/ 

white meniscus card readers are simple to create as shown in the figure below. More elaborate 

card readers may be purchased that allow placement around the neck of a flask. 

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

meniscus. 

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 of reader is 

preferred for Option B. 

The meniscus of most liquids used in volumetric standards is concave with the lowest point in 

the center used to determine the reading. The meniscus formed by a non-wetting liquid, such as 

mercury (Hg), is convex with the highest point in the center. The highest point of such a 

meniscus is used to make the reading. The reading of a mercurial barometer is a classical 

example of this kind. In making the 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 curvature of a meniscus is related to the surface tension of the liquid and inversely related to 
11/15/2006 

GMP 3 Page 2 of 3

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. 

Option A – (Suitable only when graduation lines extend more than 75 percent of the 

circumference of the sight gage area.) 

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. 

Front Side of Index Line 

Meniscus Surface 

Rear Side of 

Index Line 

FRONT VIEW 

Observer’s View From Slightly Below the 

Horizontal Level of the Graduation Line. 

SIDE VIEW 

Exaggerated Curvature 

Meniscus Surface 

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 

Fraction of a Millimeter Below the 

Graduation Line (or a Card Reader with the 

Black Side on the Bottom.) 
11/15/2006 

GMP 3 Page 3 of 3

Option B 

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. 

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. 

When opaque liquids are used, an additional error or correction can be estimated based on the 

volume contained between the upper and lower edges of the meniscus. 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. 

Where possible, the method of reading the meniscus during calibrations should be performed in 

the same way in which the meniscus will be read during normal use. 

1) Top of the meniscus. 2) Mid-point of the meniscus. 

Graduation Line

Graduation Mid-point

Observer’s Eye Graduation Line 

11/15/2006 

GMP 6 Page 1 of 2 

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 adversely affected by greasy and oily 

surfaces. Corroded surfaces raise questions that impair future use, so corrosion-damaged containers 

may not be worth testing. 

Environmental requirements are becoming increasingly important. 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. 

 

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 

is difficult to ascertain whether additional changes have occurred. Even when dents have been 
11/15/2006 

GMP 6 Page 2 of 2 

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. 
11/15/2006 

GMP 7 Page 1 of 3 

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 EC) sodium dichromatesulfuric acid cleaning solution. However, use of this hot solution is hazardous 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, not 

methanol) before drying or rinsing with water. Acetone, if allowed to dry, also leaves a film 

deposit. 

 

The above solvents need not be used if the glass does not have an 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. 

See GLP 13, Good Laboratory Practice for Drying Containers for appropriate drying techniques. 
11/15/2006 

GMP 7 Page 2 of 3 

 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 sulphuric 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 sulphuric 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 sulphuric 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 all of the 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 

sulphuric 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 

acetone, followed by a water rinse. 

 

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. 
11/15/2006 

GMP 7 Page 3 of 3 

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 sucking the air through the 

vessel). 

 

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

used for drying purposes. 

11/15/2006 

SOP 13 Page 1 of 7 

SOP 13 

Standard Operating Procedure 

for 

Calibration of Volumetric Ware, Gravimetric Method1

1 Introduction 

 1.1 Purpose of Test 

Volumetric flasks, pipets, graduated cylinders, burets, and similar glass and 

plastic volumetric ware, such as those used in chemical and clinical laboratories, 

need to be calibrated to ensure accuracy of measurement. This SOP describes 

procedures for calibration of such ware with capacities ranging from 0.1 cm3 to 

2000 cm3. The method is extendable, in principle, to larger volumes, limited only 

by the capacity and physical dimensions of the weighing apparatus. It is not 

recommended for volumetric ware with capacities less than 0.1 cm3. This 

procedure makes use of a single pan mechanical balance. For calibrations with an 

electronic balance see SOP 14. 

1.2 Prerequisites 

1.2.1 Verify that valid calibration certificates are available for the standards 

used in the test. 

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

uncertainties for the intended level of calibration. Reference standards 

should not be used for gravimetric calibration. 

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

sufficiently small process standard deviation, as verified by a valid control 

chart or preliminary experiments, to ascertain its performance quality 

when a new balance is put into service. 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 the laboratory facilities meet the minimum conditions shown 

in Table 1 to meet the expected uncertainty that is achievable with this 

procedure. 

1.2.6 Verify that an adequate supply of distilled or deionized water (see GLP 

10) is available. 

 

1 Based on the work of J. Lembeck "The Calibration of Small Volumetric Glassware," NISTIR 74-461 (1974). 
11/15/2006 

SOP 13 Page 2 of 7 

Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Gravimetric 20 °C to 23 °C, a set point ± 2 °C, 

maximum change 1 °C/h 

40 % to 60 % 

± 10 % max change / 4 h 

 

2 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 balance used. The precision of 

calibration will depend on the care exercised in adjusting the various volumes and 

strict adherence to the various steps of the procedure. The accuracy attainable 

will depend on the uncertainties of the standard weights and the air buoyancy and 

thermal expansion corrections that are made. 

2.2 Summary 

This procedure is based on a determination of the mass of water contained in or 

delivered from the vessel that is calibrated. The volumetric determination is 

calculated from the above measurements and a knowledge of the temperature, 

pressure, and relative humidity of the air, and the temperature of the water that is 

weighed. 2.3 Equipment and Standards 

2.3.1 Balance having sufficient capacity to weigh the loaded vessel. The 

sensitivity of the balance will be a limiting factor in the accuracy of the 

measurement. 

2.3.2 Mass standards or built-in weights calibrated with adequate accuracy and 

valid calibration certificates traceable to NIST. Ordinarily, meeting 

ASTM Class 2 or 3 weight specifications are required. 

2.3.3 Calibrated thermometer accurate to ± 0.1 °C with recent calibration values 

that are traceable to NIST to determine water temperature. 

2.3.4 Calibrated thermometer accurate to ± 0.5 °C with recent calibration values 

that are traceable to NIST to determine air temperature.2

2.3.5 Calibrated barometer accurate to ±135 Pa (1 mm Hg) with recent 

calibration values that are traceable to NIST to determine the air pressure. 

2.3.6 Calibrated hygrometer accurate to ± 10 % with recent calibration values 

that are traceable to NIST to determine relative humidity. 

 

2 Values from the thermometer, barometer and hygrometer are used to calculate the air density at the time of the 

measurement. The air density is used to make an air buoyancy correction. The accuracies specified are 

recommended for high precision calibration. Less accurate equipment can be used with only a small degradation in 

the overall accuracy of the measurement. 
11/15/2006 

SOP 13 Page 3 of 7 

2.3.7 Distilled or deionized water (See GLP 10). 

2.3.8 Stopwatch or other suitable timing device (does not require calibration). 

2.4 General Considerations 

2.4.1 All glassware must be meticulously cleaned, prior to calibration. When 

clean, the walls will be uniformly wetted. Instructions for cleaning are 

given in 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 Volumetric calibrations are critically dependent on the setting of a 

meniscus. See GMP 3 for guidance in reading a meniscus. 

2.4.3 Use water that is temperature-equilibrated with the laboratory 

environment. Equilibration can be achieved by storing the water in clean 

containers in the laboratory. 

2.4.4 All weighings ( I L, I E ) performed in this SOP should be determined with 

a mechanical balance that has verified calibration data available. A double 

substitution procedure(SOP 4) with air buoyancy correction may also be 

used. Equations must be modified if SOP 4 is used!

2.5 Calibration Procedure for Burets 

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

test tube, large enough to hold a thermometer, in the vicinity of the buret. 

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

stopcock.

2.5.3 Drain and record 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 zero mark with temperature-equilibrated 

water and also fill the test tube that holds the thermometer. Record 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 Fully open the stopcock and discharge contents of buret into a previously 

weighed flask. The tip 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.

2.5.7 Stopper and weigh the flask. 

2.5.8 Measure and record the temperature of water in the test tube. 
11/15/2006 

SOP 13 Page 4 of 7 

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

interval of test.

2.5.10 For burets with a specified waiting time, empty as in 2.5.6 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 2.5.6.

2.5.11 Make a duplicate determination.

2.5.12 Calculate the volume for each interval as described in Section 3.

2.6 Calibration Procedure for Pipets (One-Mark) 

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

in contact with the internal surface of a beaker.

2.6.2 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, using a stopcock or pinch clamp for fine control. The tip must 

be in contact with the wetted wall of a beaker while this setting is being 

made. Do not remove any water remaining on tip at this time.

2.6.3 Hold pipet in a vertical position and deliver water into a previously 

weighed weighing flask, with the tip in contact with the inside wall or 

neck.

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

contact with the flask.

2.6.5 Stopper the flask and weigh with its contained load. 

2.6.6 Make a duplicate determination. 

2.6.7 Calculate the volume as described in Section 3. 

 

2.7 Calibration of Flasks (To Contain) 

2.7.1 Clean and dry flask as described in GLP 13, then stopper and weigh the 

flask. Record the Empty Flask value. 

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

reference graduation while maneuvering the flask to wet the entire neck 

below the stopper. 

2.7.3 Let stand for two minutes then adjust the meniscus to the reference 

graduation line. 

2.7.4 Determine the temperature of the water by putting some in a beaker or test 

tube containing a thermometer. 

2.7.5 Weigh the filled flask and record the Filled Flask mass value. 

2.7.6 Make a duplicate determination. 
11/15/2006 

SOP 13 Page 5 of 7 

2.7.7 Perform volume calculations as described in Section 3. 

2.8 Calibration of Flasks (To Deliver) 

2.8.1 Clean but do not dry flask. 

2.8.2 Place an appropriately sized funnel in the neck and fill the flask to just 

below the reference graduation while maneuvering the flask to wet the 

entire neck below the stopper. 

2.8.3 Let the flask stand for two minutes, then adjust the meniscus to the 

reference graduation line, then weigh the full vessel, with cap or stopper. 

2.8.4 Empty the flask over a 30-second period by gradually inclining it so as to 

avoid splashing. When the main drainage has ceased, hold the flask in 

vertical position for 10 seconds unless another drain time is specified, then 

touch off the drop of water adhering to the top of the flask. 

2.8.5 Place a stopper or cap on the flask and reweigh. 

2.8.6 Make a duplicate determination. 

2.8.7 Calculate the volume of the flask as described in Section 3. 2.9 Calibration of Other Volumetric Glassware. 

2.9.1 Measuring Pipets - 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 

(2.7, 2.8). 

 

3 Calculations 

 

3.1 Calculate the volume at 20 °C from the weight of water, contained or delivered, 

for each run, as follows: 

[ 1 ( 20)] ( )

1

20 ( )( ) 1 t V I I Q 

B w a

a

L E ⎥ − −

⎦

⎤ ⎢

⎣

⎡

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − − α

ρ ρ ρ

ρ
11/15/2006 

SOP 13 Page 6 of 7 

Table 2. Variables for volume equation 

Variable Description 

 IL - IE the difference, in grams, obtained from the balance indications 

associated with the loaded vessel and the empty vessel. 

Q 

the apparent mass correction factor defined by the expression 

( )

( ) .0012

0.0012

20

20

−

− =

B

B

D

D Q

ρ

ρ

where ρB is the density of the balance weights in g/cm3, 0.0012 is the 

density of normal air in g/cm3 and D20 is the apparent mass to which 

the weights are adjusted. The factor has a maximum value of 

1.000013 so it may be considered as unity for most calibrations. 

ρB density of the balance weights in g/cm3

ρw density of water at the temperature of measurement in g/cm3

ρa density of air at the conditions of calibration in g/cm3

 α the thermal cubical coefficient of expansion for the vessel being 

calibrated (in per degree units that match temperature units) 

t water temperature of calibration, °C 

3.2 Air density should be calculated using formula provided in SOP 2. Water density 

should be calculated as described in GLP 10. Look up the cubical coefficient of 

expansion for the vessel material in NIST IR 6969, Table 9.10 or obtain it from 

the manufacturer. Calculations of these intermediate values are preferred. 

However, values for the density of water and air, and for the cubical coefficient of 

expansion may be found in Tables 9.8, and 9.9 in NISTIR 6969. These values are 

used in connection with equation 3.1. 

3.3 Calculate the average volume at 20 °C. If a reference temperature other than 

20 °C is needed, the equation provided in 3.1 must be appropriately modified. 

4 Measurement Assurance 

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

NISTIR 6969, Sec. 7.4) 

4.2 Plot the check standard value and verify that it is within established limits OR a ttest 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. 

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

measurement process, sp. 

5 Assignment of Uncertainty 

 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 percent 
11/15/2006 

SOP 13 Page 7 of 7 

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, for the standard 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 Standard deviation of the measurement process from control chart performance 

(See SOP 17 or 20.). 

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

estimated based on the range of duplicate measurements over time. This value 

will incorporate a repeatability factor related to the precision of the weighings and 

the setting of the meniscus, but not related to the uncertainty of internal weights 

in the balance or errors in reading the meniscus. 

5.3 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 standards used, improper observance of drainage times, viscosity or 

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

and the lack of internal cleanliness. 

Additional References: 

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, (2006). 

12/18/06 

SOP 14 Page 1 of 11 

SOP No. 14 

Recommended Standard Operations Procedure 

for 

Gravimetric Calibration of Volumetric Ware Using an Electronic Balance 

 

1 Introduction 

 1.1 Purpose of Test 

This procedure describes the 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 does not incorporate measurement control 

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

additional precautions must be taken. 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. 

1.2 Prerequisites 

1.2.1 Verify that valid calibration certificates are available for the standards 

used in the test. 

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

uncertainties for the level of calibration. Reference standards should not 

be used for gravimetric calibration. 

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

sufficiently small process standard deviation, as verified by a valid control 

chart or preliminary experiments, to ascertain its performance quality 

when a new balance is put into service. 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 supply of distilled or deionized water (see GLP 

10) is available. 

1.2.6 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 environmental conditions 

Procedure Temperature Relative Humidity

Gravimetric 20 °C to 23 °C, a set point ± 2 °C, 

maximum change 1 °C/h 

40 % to 60 % 

± 10 % max change / 4 h 
12/18/06 

SOP 14 Page 2 of 11 

2 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 SOP 15. The precision of 

calibration will depend on the care exercised in adjusting the various volumes and 

strict adherence to the various steps of the procedure. The accuracy attainable 

will depend on the uncertainties of the standard weights and the air buoyancy and 

thermal expansion corrections that are made. 

 2.2 Summary 

The electronic balance used is first calibrated by weighing a standard mass. 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 

re-weighed. The difference in mass is used to calculate the capacity of the 

container at various neck graduations. The processes of this section and section 3 

should be repeated as required to verify all neck graduations for which a 

calibrated volume is desired. 

2.3 Equipment and Standards 

2.3.1 Electronic balance having sufficient capacity to weigh the loaded vessel. 

The sensitivity of the balance will be a limiting factor in the accuracy of 

the measurement. The resolution and repeatability should be smaller than 

the accepted uncertainty of the calibration. 

2.3.2 Calibrated mass standards with adequate accuracy and traceable to NIST. 

Ordinarily, standards of ASTM Class 2 or 3 weight specifications are 

required. 

2.3.3 Calibrated thermometer accurate to ± 0.1 °C with recent calibration values 

that are traceable to NIST to determine water temperature. 

2.3.4 Calibrated thermometer accurate to ± 0.5 °C with recent calibration values 

that are traceable to NIST to determine air temperature.1

2.3.5 Calibrated barometer accurate to ±135 Pa (1 mm Hg) with recent 

calibration values that are traceable to NIST to determine the air pressure.1

2.3.6 Calibrated hygrometer accurate to ± 10 % with recent calibration values 

that are traceable to NIST to determine relative humidity.1 

 

1 Values from the thermometer, barometer and hygrometer are used to calculate the air density at the time of the 

measurement. The air density is used to make an air buoyancy correction. The accuracies specified are 

recommended for high precision calibration. Less accurate equipment can be used with only a small degradation in 

the overall accuracy of the measurement. 
12/18/06 

SOP 14 Page 3 of 11 

2.3.7 Distilled or deionized water (See GLP 10). 

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

2.4 Procedure 

2.4.1 Cleanliness check 

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. 

 2.4.2 Drying procedure 

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

contain” basis. 

2.4.3 Wet down 

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 if a transfer vessel is used to weigh a delivered volume of water. 

2.4.4 Weighings (Option A) 

2.4.4.1 Zero the balance and record reading as O1. Place a standard mass, 

MS, on the balance platform (MS should be slightly larger than the 

mass of the filled vessel.) Record reading as O2. 

2.4.4.2 Zero the balance. Place dry or “wet-down” container on balance 

platform, as appropriate, and record reading as O3.

2 Caution: all 

containers must be dry on the outside for all weighings. 

2.4.4.3 Fill container to its reference mark. Read and record the 

temperature of the water used to fill the container. Carefully 

adjusting the meniscus (if present) to minimize filling error (see 

GMP No. 3). Zero the balance. Weigh the filled vessel and record 

reading as O4. 

2.4.4.4 Immediately after weighing, check the temperature of the water in 

the filled container. If the temperature differs by more than 0.2 °C 

from that of 2.4.4.3, refill and reweigh as described in 2.4.4.3. 

 

2 When calibrating “to deliver” vessels, O4 may be measured before O3. If a transfer vessel is used, the drained 

mass or empty mass is usually measured before the filled mass. 
12/18/06 

SOP 14 Page 4 of 11 

2.4.4.5 Record air temperature, barometric pressure, and relative humidity 

at the time of the above measurements. 

2.4.4.6 Make a duplicate determination (Run 2). 

2.4.5 Weighings (Option B) 

2.4.5.1 Zero the balance and record reading as O1. Place a standard mass, 

MS1, on the balance platform (MS1 should be slightly larger than the 

mass of the drained or dry vessel.) Record reading as O2. 

2.4.5.2 Zero the balance. Place dry or “wet-down” container on balance 

platform, as appropriate, and record reading as O3. Caution: all 

containers must be dry on the outside for all weighings. 

2.4.5.3 After removing empty vessel, zero the balance and record reading 

as O4. Place a standard mass, MS2, on the balance platform (MS2

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

Record reading as O5. 

2.4.5.4 Fill container to its reference mark. Read and record the 

temperature of the water used to fill the container. Carefully 

adjusting the meniscus (if present) to minimize filling error (see 

GMP 3). Zero the balance. Weigh the filled vessel and record 

reading as O6. 

2.4.5.5 Immediately after weighing, check the temperature of the water in 

the filled container. If the temperature differs by more than 0.2 °C 

from that of 2.4.5.4, refill and reweigh as described in 2.4.5.4. 

2.4.5.6 Record air temperature, barometric pressure, and relative humidity 

at the time of the above measurements. 

2.4.5.7 Make a duplicate determination (Run 2). 

3 Calculations 

3.1 Compute the volume, Vt, for each determination using the equation: 

Option A 

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− = − 

1 1 

2 1

4 3

s w a

s a

t O O

M

V O O

ρ ρ ρ

ρ Eqn. 3.1 
12/18/06 

SOP 14 Page 5 of 11 

 Option B 

Table 2. Variables for volume equations 

Variable Description 

 Ms, Ms1, Ms2 mass of standards (i.e., true mass, vacuum mass) (g) 

ρs density of MS (g/cm3)

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

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

Vt 

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

on whether O3 or O6 represent a dry or a “wet down” container at the 

temperature of the measurement) (cm3 or mL) 

3.2 Compute V20, the volume at 20 °C, for each run, using the expression: 

where α is the cubical coefficient of expansion of the container being calibrated, 

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

3.3 Compute the mean V20 for the duplicate measurements. 

3.4 If using a different reference temperature, use the following equation and be sure 

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

V V [ 1- ( t - 20 ) ] 20 = t α

 [1 ( 20 ) ] V20 = Vt − α t −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

− −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ −

= 

1

( )

1 

 ( )

1 

 

2 1

1

3 ( )

5 4

2

6 ( )

w a

s

a

s

drained

s

a

s

t filled O O

M

O

O O

M

V O

ρ ρ

ρ

ρ

ρ

ρ

 [1 ( t ) ] ef = − − ref V V t r t α

Eqn. 3.2
12/18/06 

SOP 14 Page 6 of 11 

4 Measurement Assurance 

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

NISTIR 6969, Sec. 7.4) 

4.2 Plot the check standard value and verify it is within established limits OR 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. 

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 uncertainty of measurement, 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 

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. When multiple mass standards are 

used, see SOP 29 for treatment of dependencies. 

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 or 

estimated based on the range of duplicate measurements over time. This value 

will incorporate a repeatability factor related to the precision of the weighings and 

the setting of the meniscus, but not related to the errors in reading the meniscus. 

5.3 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 standards used, 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. 

Additional References: 

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, (2006) 
12/18/06 

SOP 14 Page 7 of 11 

Appendix A 

Gravimetric Calibration Data Sheet (Option A) 

Laboratory data and conditions: 

Vessel ID Operator

Date Air Temperature

Balance Pressure

Load Relative Humidity

Process standard deviation from control chart, sp

Mass standard(s) data: 

ID Nominal Mass 

Correction 

Density 

g/cm3 ID Nominal Mass 

Correction 

Density 

g/cm3

S - filled S - empty 

us, and k factor us, and k factor 

Observations: 

Run 1 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 000 

2 MS O2 

3 Empty or Drained O3 

4 Filled O4 

 tw: 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 000 

2 MS O2 

3 Empty or Drained O3 

4 Filled O4 

 tw: 

Note: dotted line represents decimal point. 
12/18/06 

SOP 14 Page 8 of 11 

Example 

Gravimetric Calibration Data Sheet (Option A) 

Laboratory data and conditions: 

Vessel ID Operator GH

Date 10/1/99 Air Temperature 22.5 °C

Balance LC 5100 Pressure 747.8 mm Hg

Load 2 L Relative Humidity 45 %

Process standard deviation from control chart, sp 0.042 mL

Mass standard(s) data: 

ID Weights Mass 

Correction 

Density 

g/cm3 ID Nominal Mass 

Correction 

Density 

g/cm3 

Ms - filled 2 kg 0.000123 g 7.95 Ms - empty not used 

us, and k factor 2 mg, k = 2 us, and k factor 

Observations: 

Run 1 Weights Balance Observations, Units___g__ 

1 Zeroed Balance O1 0000 

2 Ms O2 2000003 

3 Empty or Drained O3 654729 

4 Filled O4 2648747 

 tw: 22.8 °C 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 000 

2 Ms O2 1999998 

3 Empty or Drained O3 667351 

4 Filled O4 2661365 

 tw: 22.6 °C 

Note: dotted line represents decimal point.
12/18/06 

SOP 14 Page 9 of 11 

Calculate the air density (SOP 2) ρa: 

Look up or calculate the density of the water, ρw: 

Compute the volume, Vt, for each determination using the equation: 

Run 1: 

Compute V20 , the volume at 20 °C, for Run 1 using the expression: 

Run 2: 

Compute V20, the volume at 20 °C, for Run 2 using the expression: 

3 3 ρ a = 1.170 mg/cm = 0.001170 g/cm

3 22.8 °C = 0.997587 g/cm

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− = − O O

M

V O O

s w a

s a

t ρ ρ ρ

ρ 1 1

2 1

4 3

⎟

⎠

⎞ ⎜

⎝

⎛

− ⎟

⎠

⎞ ⎜

⎝

⎛

⎟ − ⎠

⎞ ⎜

⎝

⎛

− = − 0.997587 0.001170

1

7.95

0.001170 1 2000.003 0

2000.000123 ( 2648.747 654.729 ) Vt

 (1994.018 ) (1.003446756 ) 2000.890865 mL

 (1994.018 ) ( 0.99999856 ) ( 0.99985283 ) (1.0035959 )

= =

=

t

t

V

V

V V [ ] ( ) t 20 = t 1 − α − 20

V20 = 2000.890865 [ ] 1 − 0.000025 ( 22.8 − 20 ) = 2000.750802 mL

 (1994.014 ) (1.003400858 ) 2000.797478 mL

 (1994.014 ) (1.00000106 ) ( 0.99985283 ) (1.00354855 )

0.997634 0.001170

1

7.95

0.001170 1 1999.998 02000.000123 ( 2661.365 667.351)

= =

=

⎟

⎠

⎞ ⎜

⎝

⎛

− ⎟

⎠

⎞ ⎜

⎝

⎛

⎟ − ⎠

⎞ ⎜

⎝

⎛

− = −

t

t

t

V

V

V

V V [ ] ( ) t 20 = t 1 − α − 20

3 22.6 °C = 0.997634 g/cm
12/18/06 

SOP 14 Page 10 of 11 

Calculate the mean V20 : 

Calculate the uncertainty for the calibration: 

The uncertainty for the standard must be divided by the k factor for the standard, us. All values 

must be represented in like units. 

The volume correction and uncertainty would be reported as follows when rounded to two 

significant digits according to NISTIR 6969, GMP 9: 

V20 = 2000.797478 [ 1 − 0.000025 ( 22.6 − 20 ) ] = 2000.667426 mL

2 2 2

* 2

c s p o

c

u u s u

U u 

= + +

=

 2000.709114 mL

2

( 2000.750802 2000.667426 )

20 = + V =

 0.042012 * 2 0.084024 mL

 0.042012 mL

 ( 0.000987 ) ( 0.042 ) ( 0.00018 ) 2 2 2

= =

=

= + +

U

u

u

c

c

V20 = 2000.709 mL ± 0.084 mL

 0.00018 mL

 0.042 mL

 2 mg, 2 2 mg / 2 1mg converted to volume 0.000987 mL

=

=

= = = = =

o

p

s s

u

s

U k u
12/18/06 

SOP 14 Page 11 of 11 

Appendix B 

Gravimetric Calibration Data Sheet (Option B) 

Laboratory data and conditions: 

Vessel ID Operator

Date Air Temperature

Balance Pressure

Load Relative Humidity

Process standard deviation from control chart, sp

Mass standard(s) data: 

ID Nominal Mass 

Correction 

Density 

g/cm3 ID Nominal Mass 

Correction 

Density 

g/cm3

Ms1 - filled Ms2 - empty 

us, and k factor us, and k factor 

Observations: 

Run 1 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0000 

2 Ms1 O2 

3 Empty or Drained O3 

4 Zeroed Balance O4 0000 

5 MS2 O5 

6 Filled O6 

 tw: 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0000 

2 Zeroed Balance O2 

3 Ms1 O3 

4 Empty or Drained O4 0000 

5 Zeroed Balance O5 

6 MS2 O6 

 tw: 

Note: dotted line represents decimal point. 

11/15/2006 

SOP 15 Page 1 of 8 

SOP No. 15 

Recommended Standard Operations Procedure for 

Calibration of Intermediate and Large Volume Standards 

Gravimetric Method1 Using an Equal-Arm Balance2

1 Introduction 

 1.1 Purpose of Calibration 

 This procedure is applicable to calibrations where high accuracy is needed, or 

where the volumetric transfer method is not possible. It is especially useful for 

the capacity range of 5 gal to 100 gal (or larger) using an equal-arm balance and 

the double substitution weighing method as described in SOP 4. It may also be 

used for smaller volumes with an equal-arm balance. If an electronic balance is 

used, see SOP 14. 

1.2 Prerequisites 

1.2.1 Verify that valid calibration certificates are available for the standards 

used in the test. 

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

uncertainties for the intended level of calibration. Reference standards 

should not be used for gravimetric calibration. 

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

sufficiently small process standard deviation as verified by a valid control 

chart, or preliminary experiments to ascertain its performance quality 

when a new balance is put into service. 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, and GMP 1, GMP 

3, GMP 10, and gravimetric calibrations. 

1.2.5 Verify that the laboratory facilities meet the minimum conditions shown 

in Table 1 to meet the expected uncertainty achievable with this 

procedure. 

1.2.6 Verify that an adequate supply of distilled or deionized water (see GLP 

10) is available. 

 

1Based on the work of J. Houser "Procedure for the Calibration of Volumetric Test Measures" NISTIR 73-287. 

2 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. The reference temperature for petroleum products 

is 60 oF and volume values are typically in gallons. 
11/15/2006 

SOP 15 Page 2 of 8 

Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Gravimetric 20 °C to 23 °C, a set point ± 2 °C, 

maximum change 1 °C/h 

40 % to 60 % 

± 10 % max change / 4 h 

2 Methodology 

 2.1 Summary 

This procedure may be used to determine three calibration values: 

2.1.1 The contained volume, VC, which is the volume of water required to fill 

the vessel at a specified temperature (usually 60 °F for petroleum 

products). 

2.1.2 The delivered volume, VD, which is the volume of water that may be 

poured or drained from the vessel at a specified temperature (usually 60 °F 

for petroleum products) under specified conditions (see note 1). 

2.1.3 The neck scale calibration value, NSCV, which relates the true volume of 

the neck to the value indicated by the neck scale. 

 

 The mass of water required to fill the vessel is measured at an observed 

temperature. The known density of water and coefficient of expansion of the 

vessel are used to calculate the volume of the vessel at a reference temperature. 

 The precision attained will depend on the sensitivity of the balance and on the 

care exercised in carrying out the various operations of the procedure. 

Cleanliness of the vessel and strict adherence to the prescribed drainage 

procedure are critical for high precision. The accuracy of calibration depends on 

all of the above plus the uncertainties of the various weighings, accuracy in 

reading a meniscus (where present), the volumetric temperature equilibration and 

corrections, the proper correction for air buoyancy, and the purity of the water 

used as the standard. The metrologist must critically consider all of the above 

factors when assigning uncertainty limits to the calibrated volumes. 

 

 With careful observance of good measurement practices, an overall relative 

uncertainty of ± 0.02 % should be attainable. 

2.2 Apparatus 

2.3.1 Equal-arm balance of adequate capacity and sensitivity (standard 

deviation of 500 mg or better for 5 gal level). 

2.3.2 Weights (meeting ASTM Class 2 or 3 specifications) as appropriate for 

the accuracy requirements. 

2.3.3 Calibrated thermometer accurate to ± 0.1 °C with recent calibration values 

that are traceable to NIST to determine water temperature.3

 

3 Values from the thermometer, barometer and hygrometer are used to calculate the air density at the time of the 

measurement. The air density is used to make an air buoyancy correction. The accuracies specified are 
11/15/2006 

SOP 15 Page 3 of 8 

2.3.4 Calibrated thermometer accurate to ± 0.5 °C with recent calibration values 

that are traceable to NIST to determine air temperature. 

2.3.5 Calibrated barometer accurate to ±135 Pa (1 mm Hg) with recent 

calibration values that are traceable to NIST to determine the air pressure. 

2.3.6 Calibrated hygrometer accurate to ± 10 % with recent calibration values 

that are traceable to NIST to determine relative humidity. 

2.3.7 Distilled or deionized water (See GLP 10). 

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

2.3.9 Cap to place over neck of the vessel. 2.3 Procedure 

2.3.1 Preliminary Operations 

2.3.1.1 Clean the interior of the vessel with biodegradable low-sudsing 

detergent (see GMP 6) with gentle scrubbing as necessary. Rinse 

several times with clean water to remove all detergent, followed by 

pure water. Check for leaks and for uniform drainage. 

2.3.1.2 Clean and dry outside of container to remove any material which 

might subsequently dislodge and cause an erroneous weighing. 

2.3.1.3 Dry inside by rinsing with small amounts of alcohol or by drawing 

clean, filtered air through the vessel (several hours required). For 

large vessels the heat from a low wattage light bulb suspended 

inside the vessel overnight will aid in drying by slightly heating 

the vessel and creating convection currents through the interior. 

Allow the vessel to come to thermal equilibrium with the room 

before proceeding. 

2.3.2 Empty Weight 

2.3.2.1 Weigh the empty vessel and cap using the double substitution 

procedure (SOP 4) with air buoyancy correction. 

2.3.2.2 Record air temperature, humidity, and barometric pressure as 

needed for calculating air density (SOP 2) and performing 

buoyancy corrections. 

2.3.2.3 The empty weight is determined as shown in the calculations 

(Section 3.1, Eqn 2). 

2.3.3 Filled Weight 

 

recommended for high precision calibration. Less accurate equipment can be used with only a small degradation in 

the overall accuracy of the measurement. 
11/15/2006 

SOP 15 Page 4 of 8 

2.3.3.1 Fill the vessel with pure water to the zero point on the neck scale. 

Be sure the vessel is level. Bounce the liquid to disturb the 

meniscus to assure it has reached equilibrium level. Record the 

water temperature and readjust level if necessary. Be sure that no 

water remains on the outside of the vessel when it is weighed. 

(See note 2.) The filled weight is determined as shown in the 

calculations (Section 3.1, Eqn 2). 

2.3.3.2 Weigh filled vessel and cap as in 2.3.2. 

2.3.4 Drained Weight 

2.3.4.1 Drain vessel using appropriate discharge/pour and drain times (see 

note 1). Replace cap. The empty weight is determined as shown 

in the calculations (Section 3.1, Eqn 2). 

2.3.4.2 Weigh drained vessel and cap as in 2.3.2. 

2.3.5 Make a duplicate determination of steps 2.3.2 through 2.3.4 (Run 2). 

2.3.6 Neck scale plate verification 

2.3.6.1 Fill vessel with water to a scale division near the bottom of the 

scale range. Record reading (sr1). 

2.3.6.2 Make appropriate successive additions of water from a calibrated 

buret or other suitable volumetric measuring device. Record scale 

readings after each addition . 

2.3.6.3 A plot of scale readings with respect to volume added should be 

linear and will be a gross check of the validity of this calibration. 

2.3.6.4 Calculate the neck scale calibration value, NSCV, using the 

expression 

 Table 1. Variables for neck scale calibration value equation 

Variable Description 

NSCV Neck scale calibration value 

VW Total volume of water added to neck 

sri Scale reading, initial 

srf Scale reading, final 

 

( ) f i

W

sr sr

V NSCV − = Eqn. 1
11/15/2006 

SOP 15 Page 5 of 8 

3 Calculations 

 3.1 To calculate the filled, empty, or drained mass, use the following equation from 

SOP 4 using Option A. 

Table 2. Variables for Equation 2

Symbol Description 

S standard reference weight 

sw small calibrated weight used to evaluate the sensitivity of the 

balance 

M 

the mass (true mass) of a specific weight. Subscripts s, sw, filled, 

empty, drained are used to identify the weight (equals Nominal 

plus Correction in the case of mass standards) 

ρa density of air at time of calibration 

ρ density of masses; subscripts s, x, ts, tx, sw are used to identify the 

weight. 

O Balance observations, designated with subscripts 1, 2, 3..., for the 

observation number 

3.2 To calculate containment volume, VC, at temperature of measurement, t, 

3.3 To calculate delivered volume, VD, at temperature of measurement, t,

3.4 To correct volumes to reference temperature, tref, (be sure to match units for 

cubical coefficient of expansion, α, with temperature units (e.g., degrees C with 

°C-1). 

( )

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ − − + − + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = − ( )

1 

2

 1 

3 2

2 1 3 4

( , , ) O O

M

O O O O M M sw

a

sw

S

a

filled empty drained S

ρ

ρ

ρ

ρ

( ) ⎥

⎦

⎤ ⎢

⎣

⎡

− = − 

1 ( ) 

w a

VC t M filled Mempty ρ ρ

( ) ⎥

⎦

⎤ ⎢

⎣

⎡

− = − 

1 ( ) 

w a

VD t M filled M drained

ρ ρ

V V [1 (t t )] t ref = t − α − ref

Eqn.2

Eqn. 3

Eqn. 4

Eqn. 5
11/15/2006 

SOP 15 Page 6 of 8 

3.5 To convert the volume measured in mL (cm3) to gal: 

 Vgal = (0.000 264 172) VmL (There are 3 785.411 784 mL per gal.) 

 Table 2. Variables for volume equation 

Symbol Description 

ρw density of water at temperature of filling 

ρa density of air 

t temperature at time of test 

tref reference temperature, usually 60 °F (or 20 °C) 

α cubical coefficient of expansion of the vessel 

(must match temperature units in °C-1or °F-1) 

 

 3.6 Calculate the average volume at reference temperature (Vt ref ) 

3.7 Physical Constants 

3.7.1 Density of Air 

Value at environmental conditions at time of weighings calculated from 

the equation given in the Appendix to SOP 2. 

3.7.2 Density of Water 

Calculate the density of water using the formula given in GLP 10 or look 

up the value from appropriate tables. 

 3.7.3 Cubical Coefficient of Expansion 

Values for the cubical coefficient of expansion of various materials are 

given in NISTIR 6969, Table 9.10 and are normally printed on the vessel 

identification plate (for test measures and provers). 

4 Measurement Assurance 

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

NISTIR 6969, Sec. 7.4) 

4.2 Plot the check standard value and verify that it is within established limits OR a 

t-test may be incorporated to check the observed values against an accepted value. 

4.3 The mean of the check standard 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, sp. 
11/15/2006 

SOP 15 Page 7 of 8 

5 Assignment 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 percent 

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

calculating the uncertainty. 

5.1 The standard uncertainty for the mass 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 proper 

handling of uncertainties when multiple standards are used. 

5.2 Standard deviation of the measurement process from control chart performance 

(See SOP 17 or 20.) The value for sp is obtained from the control chart data for 

check standards or estimated based on the range of duplicate measurements over 

time. This value will incorporate a repeatability factor related to the precision of 

the weighings and the setting of the meniscus, but not related to errors in reading 

the meniscus. 

5.3 Other standard uncertainties usually included at this calibration level include 

uncertainties associated with water temperature measurements, thermometer 

accuracy, the coefficient of expansion, viscosity, reading the meniscus, 

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

standards used, improper observance of drainage times, viscosity or the surface 

effects on the volume of liquid clinging to vessel walls after draining and lack of 

internal cleanliness. 

Additional References: 

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, (2006). 
11/15/2006 

SOP 15 Page 8 of 8 

Appendix 

Test Notes 

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 conditions conventionally selected 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 85 o 

angle, so that virtually all 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 (an empty glass beaker, for example) 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. This plate must be weighed with the standard during each such operation. 
11/15/2006 

SOP 16 Page 1 of 8 

SOP 16 

Standard Operating Procedure for 

Calibration of Measuring Flasks 

Volume Transfer Method 

1 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 that, in 

turn, are 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 the standards 

used in the test. 

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). 

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. 

Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 °C to 27 °C, 

maximum change 1 °C/h 

40 % to 60 % 

± 20 % max change / 4 h 
11/15/2006 

SOP 16 Page 2 of 8 

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. 

(Calibrated pipets generally deliver slightly less than the full nominal volume.) 

Additional water is added 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 Equipment 

2.3.1 Calibrated standard pipet(s) of suitable volume with recent calibration 

certificates and values traceable to NIST. These standards are typically 

made of borosilicate glass. 

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

) capacity with 

recent calibration certificates and values traceable to NIST. These 

standards are typically made of borosilicate glass. 

2.3.3 Calibrated thermometer, accurate to 0.1 °C with recent calibration 

certificates and values traceable to NIST. 

2.3.4 Supply of pure distilled or deionized water (See GLP 10) at thermal 

equilibrium with the calibration environment. 

 

1

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

standards for use in volume transfer calibrations. These standards have higher resolution than metric standards 

provided at the same time. 
11/15/2006 

SOP 16 Page 3 of 8 

2.3.5 Meniscus reading device (See GMP 3). 

2.3.6 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 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 ° - 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. 

2.4.3 Conditioning the buret 
11/15/2006 

SOP 16 Page 4 of 8 

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. 

2.4.4 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 

"wet-down." 

2.4.4.5 Record all data using the form given in the Appendix or a similar 

format. 

2.4.5 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 when 

calibration is conducted in an unstable environment. Repeatability 

problems must be corrected before calibration can be completed. 
11/15/2006 

SOP 16 Page 5 of 8 

2.4.6 Calibration Note: If the vessel has a graduated neck (in addition to the 

nominal mark) additional graduations should be inspected for proper 

marking and calibrated as well. 

3 Computations 

3.1 Compute the individual "to deliver" volumes, VTD, for Run 1 and Run 2. 

VTD = VP +VB Eqn. 1

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 ) VTD 20 = VTD + α − β t − Eqn. 2 

 

Table 3. Variables for volume temperature correction equation 

 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 

α cubical coefficient of expansion of glass of standard (e.g., 0.000010 °C-1

for borosilicate glass) 

β cubical coefficient of expansion of glass of flask (e.g., 0.000025 °C-1 for 

soda-lime glass) 

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 
11/15/2006 

SOP 16 Page 6 of 8 

temperature remains the same in the standard as in the unknown. When standards 

and flasks are not of the same material, the water temperature 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 or have a suitable range of 

check standards for the laboratory. 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 

report. 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 is obtained from control chart 

performance (See SOP 17 or 20, and SOP 30). 

5.2.1 The value for sp is obtained from the control chart data of the check 

standard 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, the cubical coefficient of expansion for the flask 

under test, use of proper temperature corrections, the accuracy of temperature 

measurements, round robin data showing reproducibility, environmental variations 

over time, and bias or drift of the standard. 
11/15/2006 

SOP 16 Page 7 of 8 

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 Volume, uncertainty, reference temperature, 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: 

 Eqn. 3

 

Additional References: 

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, (2006). 

V V [ ( ) (t t )] TDtref = TD 1 + α − β − ref
11/15/2006 

SOP 16 Page 8 of 8 

 Appendix 

Calibration of Measuring Flask 

(Volume Transfer Method)

Laboratory data and conditions: 

Date Temperature

Operator Pressure

Test Number Relative Humidity

Vessel Calibrated Vessel ID

Process standard deviation from control chart, sp

Volume standard(s) data:

ID Nominal Calib. 

Volume 

Coeff. of 

Exp ID Nominal Volume Correction 

Coeff. of 

Exp 

Pipet Buret 

Unknown 

Flask 

 

us, and k factor 

Observations:

 TRIAL NO. 1 TRIAL NO. 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 

VTD20 = VTD [ ] 1+ ( )( ) α − β t − 20 

 Average VTD20 
11/15/2006 

SOP 17 Page 1 of 5 

 SOP 17 

 

Standard Operating Procedure for 

Control Charts of Laboratory Owned Check Standards for 

Calibration of Measuring Flasks or Small Provers using Volume Transfer Methods1

1 Introduction 

1.1 Purpose 

 This procedure may be used to develop and maintain control charts to monitor the statistical 

control of the volume transfer method for calibration of measuring flasks or 5 gallon test 

measures, especially when using the Standard Operating Procedures (SOP 16 or 18) for this 

purpose. The same principles may be applied to the development of control charts for other 

calibration procedures. 

1.2 Prerequisites 

1.2.1The procedure to be monitored must match the calibration procedure that is used. 

1.2.2 A clean quality assurance reference flask (QARF), suitable check standard (see 3.1), or 

a 5 gallon check standard must be available. Verify the cleanliness of the vessel or take 

corrective actions. 

2 Summary 

A reference volumetric flask (or a series of such) or 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 SOP 16, 18, or an equivalent procedure. Directions 

for preparing and using an x and an R control chart are given. The x control chart monitors the 

process with respect to both the standard and the variability, while the R control 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 process standard 

deviation may be used, as appropriate, to calculate the uncertainty for the calibrations using SOP 29. 

Note: If a full evaluation of the process bias is desired, it is best if the reference value of the QARF 

or check standard are provided by an independent laboratory such as NIST or a laboratory accredited 

to perform volume calibrations, preferably using gravimetric methods. 

 

1 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. 
11/15/2006 

SOP 17 Page 2 of 5 

3 Equipment 

3.1 A quality assurance reference flask(s) (QARF) or check standard is required, constructed of 

similar materials and design as the standards under calibration. A 1 pt and a 1⁄2 gal flask or 

a 2 pt and 1 qt flask are recommended for glass flasks when monitoring SOP 16 (or other 

suitable volumetric standards that match the range of items calibrated by the laboratory). A 

5 gal check standard is recommended for monitoring SOP 18. 

3.2 All equipment designated in SOP 16 or SOP 18 as appropriate. 

4 Procedure 

4.1 Initial Measurements 

4.1.1Calibrate the QARF or 5 gallon check standard a minimum of 12 times to establish the 

baseline chart. A calibration is defined as the result of duplicate measurements as 

required by the SOP (i.e., a complete test consists of two runs). 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 data may be maintained in a spreadsheet or other 

electronic program in lieu of a paper form. 

4.1.3Calculate the mean of the two trials x i and the ranges between runs. The ranges Ri, are 

the absolute differences between run 1 and run 2 for the n tests. Calculate the average 

range R of the trials, for the n tests as follows: 

 n

R

R ∑ i = Eqn. 1 

4.1.4Estimate the standard deviation of the process sp, based on the check standard 

volume on each of n occasions, as follows: 

 ( )

( ) 1

2

−

− = ∑

n

x x

s

i

p Eqn. 2 

 where: 

 

xi The mean value of each complete test. 

x The mean value of all averages made on n occasions 

4.1.5For a smaller number of measurements (less than 30) the standard deviation may be 

calculated using the average range as follows (obtain values for * d2 from NISTIR 6969 

Table 9.10 and see NISTIR 6969 Section 8.3 for additional notes): 
11/15/2006 

SOP 17 Page 3 of 5 

 * d2

R

s p = Eqn. 3 

Be sure that only absolute values are used in the determination of the range and average range! 

4.2 Construction of Control Charts 

 Construct the following control charts using the data of section 4.1. 

4.2.1Construct an x control chart for a check standard with the following control limits: 

 Reference value (if available) 

 Central Line = x (mean of the average values) 

 Lower warning limit (LWL) = p x − 2s

 Lower control limit (LCL) = p x − 3s

 Upper warning limit (UWL) = p x + 2s

 Upper control limit (UCL) = p x + 3s

4.2.2Construct an R (range chart) control chart for duplicate measurements having the 

following control (or action) limits. Note that R (the range) and |d| (absolute difference 

of duplicate measurements) are equivalent for duplicate measurements. 

 Central Line = R (average range) 

 LCL = LWL = 0 

 (There should be no negative numbers recorded when using absolute values!) 

 UWL = 2.512 R

 UCL = 3.267 R

 

 These limits are t values for 95 % and 99.7 % confidence intervals for a sample size of 

30. 

4.3 Use of Control Charts 

4.3.1An appropriate QARF or check standard is calibrated each time the laboratory performs 

calibrations using the SOP. If the calibrations extend over several days, the check 

standard is calibrated daily. The values of x and R for each calibration of the check 

standard are plotted on the respective control 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 
11/15/2006 

SOP 17 Page 4 of 5 

on the R chart is within the control limits, a source of systematic error is suspected. 

Poor drainage is a possible source of bias for low values and changes of drainage 

technique should be considered as a cause for high values. Sources of error can result 

from the use of the volumetric standards as well as of the vessels being calibrated. 

Changes in criteria for reading the meniscus are also possible sources of error or 

difference. 

4.3.3If the values for the R chart fall outside of the warning limits but inside of the control 

limits, a decrease in precision is indicated. Cleanliness and procedural 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 R 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. Corrective 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 Section 8.9, 8.10, and 8.11). 

5 Interpretation of Control Chart Data 

5.1 Demonstration 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. 

5.2 To the extent appropriate, the precision of measurement of the QARF or check standard 

may be extended to the calibration of other glassware or small volume provers calibrated 

using the same SOP. This means that the process standard deviation, p s , is transferable to 

measurements of similar nominal size made by the same measurement method. 

5.3 Extension of the p s for the QARF to other calibrations assumes that all aspects of its 

calibration correspond to those for the other calibration. If the volumes of the respective 

glassware are comparable as well as the sizes of necks and graduation lines, this may be 

justified. It may be necessary to have a series of QARF's or check standards with 

corresponding control charts to monitor the calibration process for a range of volumetric 

calibrations. 
11/15/2006 

SOP 17 Page 5 of 5 

 Appendix 

 Control Chart Data 

 QARF/Check Std ID Nominal Capacity _____________ 

Test 

Number 

Date 

Trial No. 1 

VTD

X1

Trial No. 2 

VTD

X2

VTDM

(x) |d| = 

|X1 - X2|

*

standard 

deviation*** 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

 SUM 

∑x ∑ d pooled std 

dev: 

n** = = n

x

x ∑= 

= = ∑

n

R

R UWL = 2.512 R = 

( )

( ) 1

2

−

− = ∑

n

x x

s UCL = 3.267 R = 

* This is the range, R, of the two trials and is actually the larger value minus the smaller value. 

**n is the number of tests used to calculate the control limits. 

***Use of the standard deviation and pooled standard deviations are preferred when a standard artifact is maintained in 

the laboratory as a check standard. 

11/15/2006 

SOP 18 Page 1 of 6 

SOP 18 

Standard Operating Procedure for 

Calibration of Graduated Neck-Type Metal Volumetric Field Standards 

Volumetric Transfer Method1

 

1 Introduction 

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 procedure assumes that the water temperature is stable during the 

transfer from the standard to the unknown test measure. 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. 

Limiting factors: For a 5 gal test with a stainless steel standard and stainless steel 

unknown test measure, the temperature change between the standard and 

unknown must be less than 0.5 oC during the calibration. If the unknown test 

measure is mild steel, the change in temperature between standard and unknown 

must be less than 0.2 oC during the calibration. If these limits are exceeded, use 

SOP 19. This is to ensure that the impact on measured values is less than the 

resolution and repeatability on a 5 gal test measure with 1 in3 graduations. If 

smaller graduations are present, error due to temperature variations must be 

evaluated further. 

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 valid calibration certificates are available for the standards 

used in the test. 

1.2.3 Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of calibration 

 

1

 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. Most laboratory standards for this calibration procedure 

are 5 gal “slicker-plate” type standards. Very few laboratories have 20 L “slicker-plate” type standards. 
11/15/2006 

SOP 18 Page 2 of 6 

1.2.4 Verify the availability of an adequate supply of clean water (GLP 10). 

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 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Volume transfer 18 °C to 27 °C, maximum 

change 2.0 °C/h 

40 % to 60 % 

± 20 % maximum change / 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 and uncertainties must reflect the conditions of the calibration. 

1.3.2 The care required for field calibrations includes proper safety, a clean and 

air-free water supply, measurement control programs, and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and test liquid (water) to reach an equilibrium temperature 

with minimal evaporation. Environmental conditions should be selected to 

be as close to laboratory conditions as possible. All data and appropriate 

environmental conditions must be documented regardless of test location. 

SOP 19 is a more suitable procedure when poor conditions are noted. 

1.3.3 An increased number of check standard verifications are required to 

ensure continued suitability of calibration values generated in field 

conditions. 

2 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 will depend 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 volu-
11/15/2006 

SOP 18 Page 3 of 6 

metric vessels which can influence their drainage characteristics. The accuracy 

will depend on the uncertainties of the calibrations 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 "wetdown" vessel. The gauge scale is adjusted to a correct reading, as necessary, and 

then sealed. 

2.3 Equipment 

2.3.1 Calibrated slicker-plate standard made of stainless steel, with recent 

calibration certificate traceable to NIST, and whose volume equals that of 

the vessel to be calibrated. 

2.3.2 Calibrated thermometer, accurate to ± 0.1 °C, with recent calibration 

certificate traceable to NIST. 

2.3.3 Meniscus reading device. (See GMP 3). 

2.3.4 Timing device (Calibration is not required.) 

2.3.5 Supply of clean water, preferably soft water (filtered if necessary). 

 

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 detergent and water, as necessary, and rinse thoroughly. (See 

GMP 6). 

2.4.2 Fill vessel with water to its nominal level and pour contents during a 30 ± 

5 s period then drain for a 10 s period after cessation of flow. Touch off 

any adhering drop from the neck. This constitutes the "wet-down" 

condition. Filling the vessel from the standard following the instructions 

in steps 2.4.3 and 2.4.4 will ensure that both the standard and vessel are 

properly “wet-down”. 

2.4.3 Run 1 - Fill slicker-plate standard with water, raised by surface tension, 

slightly higher than the rim. Use slicker-plate to strike off excess water, 

checking to see that no air bubbles are entrained in the water during the 

leveling process. 
11/15/2006 

SOP 18 Page 4 of 6 

2.4.4 Open valve at base and transfer water from the standard to the wet-down 

vessel. Allow a 30 s drain period after cessation of flow. 

2.4.5 Level vessel (or suspend it by its handle, if appropriate) and read scale on 

its neck. Record reading. 

2.4.6 Adjust the scale of the vessel as described in 3.3. Seal the scale adjustment 

device. 

2.4.7 Run 2 - Make a duplicate determination, which should agree with the 

former within ± 0.02 % of the volume (± 0.2 in3

 for 5 gal test measure). If 

excess disagreement, check all vessels for cleanliness and repeat duplicate 

determinations until satisfactory agreement between consecutive runs is 

obtained. 

2.4.8 The test measure or prover must be capable of repeating within 0.02 % of 

the test volume during calibration. Repeatability problems may be due to 

contamination or lack of cleanliness, or poor field conditions, such as 

when calibration is conducted in an unstable environment. Repeatability 

problems must be corrected before calibration can be completed. 

3 Calculations 

3.1 Because the water temperature is usually 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, no 

temperature corrections are made. When conditions are not reasonably close to 

60 oF and temperature corrections are needed, use SOP 19. If prover volumes, 

errors and/or corrections are reported, use calculations provided in SOP 19. 

3.2 Within the accuracy requirements, no corrections arising from dissimilarities of 

the standard and vessel are necessary. If differences are suspected, 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. 

Note: If the accuracy requirements necessitate a temperature correction, the 

temperature of the water must be measured in both the standard and the unknown 

and the calibration is made according to the procedure given in SOP 19. 

3.4 Determination of the test vessel volume: 

Prover volume =VNom + Cs - gauge reading Eqn. 1 

where: 
11/15/2006 

SOP 18 Page 5 of 6 

VNom = Nominal Volume (taking care to match units) 

Cs = Correction on standard 

4 Measurement Assurance 

4.2 Duplicate the process with a suitable check standard or have a suitable range of check 

standards for the laboratory. See SOP 17 and SOP 30. 

4.3 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. 

4.4 The mean of the check standard observations is used to evaluate bias and drift over 

time. 

4.5 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 % level of confidence. See SOP 29 for the complete standard operating 

procedure for calculating the uncertainty. 

5.2 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. 

5.3 Standard deviation of the measurement process, sp, is obtained from control chart 

performance (See SOP 17 or 20, and SOP 30). 

5.4 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, the cubical coefficient of expansion for the prover 

under test, use of proper temperature corrections, the accuracy of temperature 

measurements, round robin data showing reproducibility, environmental variations 

over time, and bias or drift of the standard. 

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 
11/15/2006 

SOP 18 Page 6 of 6 

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. 

6 Report 

6.2 Report results as described in SOP 1, Preparation of Calibration/Test Results, with the 

addition of the following: 

6.2.1 Volume, uncertainty, reference temperature, material, thermal coefficient 

of expansion (assumed or measured), construction, any identifying 

markings, tolerances (if appropriate), laboratory temperature, water 

temperature(s), barometric pressure, relative humidity, and out–oftolerance conditions. 
11/15/2006 

SOP 19 Page 1 of 11 

SOP 19 

Standard Operating Procedure for 

Calibration of Large Neck-Type Metal Provers 

(Volume Transfer Method)1

1 Introduction 

1.1 Purpose of Test 

This procedure is used to calibrate large graduated neck type metal provers (40 L 

(10 gal) and larger) that are used in verification of petroleum, biodiesel, ethanol, 

milk, and/or water meters. It may also be used for the calibration of test measures 

(20 L (5 gal)) when temperature corrections are needed. 

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. 

1.2.2 Verify that valid calibration certificates are available for the standards 

used in the test. 

1.2.3 Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of calibration. 

1.2.4 Verify the availability of an adequate supply of clean water (GLP 10) 

(Note: this is critical when calibrating food-grade provers.) 

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

19, SOP 17, GMP 3, 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 make possible the expected uncertainty achievable with this 

procedure: 

 

1

 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. 
11/15/2006 

SOP 19 Page 2 of 11 

Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 °C to 27 °C, maximum 

change 2.0 °C/h 

40 % to 60 % 

± 20 %, maximum change / 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, clean and 

air-free water supply, measurement control programs, and a stable 

temperature environment shaded from direct sunshine to allow the prover, 

field standard, and test liquid (water) to reach an equilibrium temperature, 

with minimal evaporation. Environmental conditions should be selected to 

be as close to laboratory conditions as possible. All data and appropriate 

environmental conditions must be documented regardless of test location. 

2 Methodology 

2.1 Scope, Precision, Accuracy 

This procedure is applicable for the calibration of any size metal prover within the 

limitations of the standards available. The precision attainable will depend on 

strict adherence to the procedure, the care in volumetric adjustments, and the 

number of transfers, in the case of multiple transfers. The accuracy will depend 

on the standards used. 

2.2 Summary 

Water is delivered from a volumetric standard to the 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 cannot be considered to be constant 

during multiple 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. 
11/15/2006 

SOP 19 Page 3 of 11 

2.3 Equipment 

2.3.1 Calibrated volumetric standard with recent calibration certificate traceable 

to NIST. 

2.3.2 Calibrated 1 gal flask (or other suitable size) to calibrate neck of prover 

and a funnel. 

2.3.3 Meniscus reading device (See GMP 3). 

2.3.4 Calibrated thermometer, accurate to ±0.1 °C, with recent calibration 

certificate traceable to NIST. 

2.3.5 Timing device (calibration is not required.) 

2.3.6 Supply of clean water, preferably soft water (filtered if necessary). 

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 should 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. 

2.4 Procedure 

2.4.1 Cleanliness verification 

Fill and drain both standard and prover to be calibrated and check for 

visual evidence of soiling and of improper drainage. If necessary, clean 

with detergent and water (see GMP 6). 

2.4.2 Neck scale plate verification 

2.4.2.1 Fill the 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. Check the prover system for leaks. This is a 

wet-down 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. 
11/15/2006 

SOP 19 Page 4 of 11 

Read and record this setting. This is in preparation for verification 

of the neck scale plate. 

2.4.2.3 Recheck the scale reading, then add water from calibrated 

standards equal to 1

/4 or 

1

/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 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 volume added should be 

linear and will be a gross check of the validity of this calibration. 

2.4.2.6 Calculate and check accuracy of the neck scale for each interval. 

The error should be less than 0.5 % of the graduated neck volume 

or 1

/4 of a graduation (whichever is smaller). If more than this, the 

scale should be replaced. Otherwise issue the NSCV and 

instructions to user. 

2.4.2.7 The neck scale calibration value is calculated as follows: 

( ) f i

w

sr sr

V NSCV − =

Table 2. Variables for neck scale verification value equation 

NSCV Neck scale calibration value 

Vw Total volume of water added to neck 

f sr Scale reading, final 

i sr Scale reading, initial 

2.4.3 Body Calibration 

2.4.3.1 Fill prover with water and level it. Drain water, then wait 30 s 

after cessation of full flow, before closing drain valve. This 

establishes a "wet-down" condition for provers with no bottom 

zero. 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 gage glass, close the valve and allow the water to 

drain 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 
11/15/2006 

SOP 19 Page 5 of 11 

before the end of the drain period.) Alternatively, the prover may 

be completely drained with a 30 s drain time 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, ti, 

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 full flow 

to attain specified drainage, then close the delivery 

valve. 

 

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 level. Level the prover if necessary and record 

the neck reading. Measure the temperature of the water 

in the prover, tw, and record. 

2.4.3.2.3 Perform the calculations described in section 3 to find 

the prover volume. 

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. 

2.4.3.5 Run 2 - Repeat the process described in 2.4.3.2. 

2.4.3.6 The test measure or prover must be capable of repeating to 0.02 % 

of the test volume during calibration. Repeatability problems may 

be due to a leak in the valves or seals of the prover, contamination 

or lack of cleanliness, air bubbles, inconsistent retention in 

delivery hoses, or poor field conditions such as when a calibration 

is conducted in an unstable environment. If excessive 

disagreement is found, clean the prover and take other corrective 

actions as necessary, then recalibrate until consecutive duplicate 

determinations agree within 0.02 % of the nominal volume. 

Repeatability problems must be corrected before the calibration 

can be completed. 

2.4.3.7 Seal equipment as specified in laboratory policy. 

3 Calculations 

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 
11/15/2006 

SOP 19 Page 6 of 11 

reference temperature of 60 °F (15.56 °C). Equations for situations where different 

reference temperatures are involved will follow. 

3.1 Single Delivery 

3.1.1 Calculate VX60, the volume of the unknown prover at 60 °F, using the 

following equation: 

{( )[ ( )]} [ ] 1 ( ) 60 F

1 60 1 1 1 60 F

60 o

o

+ −

+ ∆ + − =

x x

S

X t

V t V

ρ β

ρ α

 Eqn. 1 

3.2 Multiple 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 1 1 60 F 2 60 2 1 2 60 F ... 60 1 60 F

60 o

o o o

+ −

+∆ + − + +∆ + − + + +∆ + − =

x x

S S N S N N

X t

V t V t V t V

ρ β

ρ α ρ α ρ α Eqn. 2 

Table 3. Variables for VX60 equations 

Symbols Used in Equations 

VX60 volume of the unknown vessel at 60 °F 

VS60 volume of the standard vessel at 60 °F 

ρ ρ ρ N , ,..., 1 2

density of the water in the standard prover where ρ1 is the density of the water 

for the first delivery, ρ2 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 

t1, t2, ..., tN temperature of water for each delivery with the subscripts as above 

α coefficient of cubical expansion for the standard in units / oF 

ß coefficient of cubical expansion for the prover in units / oF 

tx temperature of the water in the filled unknown vessel in units oF 

ρx density of the water in the unknown vessel in g/cm3

Note: Values for the density of water at the respective temperatures may be found in Table 

9.8 (in NISTIR 6969) or it may be calculated from the equation given in GLP 10. 
11/15/2006 

SOP 19 Page 7 of 11 

3.3 Prover Error/Correction or Deviation From Nominal 

The total calculated volume of the prover at its reference temperature should be reported 

on the calibration report. 

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). 

Prover volume =VX 60 - gauge reading Eqn. 3

VNom Prover error = Prover volume - Eqn. 4 

X VNom Prover error V - gauge reading - = 60 Eqn. 5 

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 nominal. 

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 nomival); 

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 

nominal.) 
11/15/2006 

SOP 19 Page 8 of 11 

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: 

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)

Equations for calculations when using alternative reference temperatures follow: 

3.5 Single Delivery 

3.5.1 Calculate VXtref, the volume of the unknown prover at its designated 

reference temperature (°F), using the following equation: 

{( )[ ( ) ]}

[ ] 1 ( ) t

 1 t 

ref X

1 1 1 ref S

+ −

+ ∆ + − =

x x

S tref

Xtref t

V t

V

ρ β

ρ α

 Eqn. 6

3.6 Multiple Deliveries 

3.5.1 Calculate VXtref, the volume of the unknown prover at its designated 

reference temperature, using the following equation: 

{( )[ ] ( ) } {( )[ ( )]} {( )[ ( )]}

[ ] 1 ( )

1 1 ... 1

r X

1 S 1 1 1 refS 2 2 2 2 S

X x x ef

N N N ref S S ref S N tref S trefS Stref

Xtref t t

V t t V t t V t t

V

+ −

+∆ + − + +∆ + − + + +∆ + − = ρ βρ α ρ α ρ α

 Eqn. 7 
11/15/2006 

SOP 19 Page 9 of 11 

Table 3A. Variables 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

ρ ρ ρ N , ,..., 1 2

density of the water in the standard where ρ1 is the density of the water 

for the first delivery, ρ2 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 

t1, t2, ..., tN temperature of water for each delivery with the subscripts as above 

α coefficient of cubical expansion for the standard in its designated units 

ß coefficient of cubical expansion for the prover in its designated units 

tx

temperature of the water in the filled unknown vessel in designated 

units 

ρx density of the water in the prover in g/cm3

Note: Values for the density of water at the respective temperatures may be found in 

Table 9.8 (in NISTIR 6969) or it may be calculated from the equation given in GLP 10. 

Note: The cubical coefficient of the material used must match the unit assigned to the 

temperature measurement. 

4 Measurement Assurance 

4.1. If a check standard is used (See SOP 20, SOP 30), repeat the process for the 

unknown artifact on the check standard, without adjustments. 

4.2 Plot the check standard volume and verify it is within established limits. 

Alternatively a t-test may be incorporated to check the observed value against an 

accepted value. 

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

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

measurement process. 
11/15/2006 

SOP 19 Page 10 of 11 

4.5 When a check standard is not used, a range chart may be used to monitor 

repeatability and estimate the standard deviation of the measurement process using 

the equation (see SOP 20 for details): 

* d2

R

s p = Eqn. 11

5 Assignment 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. 

5.2 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. 

5.3 Neck calibration uncertainty should be estimated based on the uncertainty of 

standards used, errors observed during calibration and the repeatability of the neck 

calibration. 

5.4 The standard deviation of the measurement process from control chart performance 

(See SOP 20 and SOP 30). 

5.4.1 The value for sp is obtained from the control chart data of the check 

standard, or may be estimated using the range from the control chart, using 

large volume transfer procedures. 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. 

5.5 Other standard uncertainties usually included at this calibration level may include 

uncertainties associated with the ability to read the meniscus, only part of which is 

included in the process variability, the cubical coefficient of expansion for the 

prover under test, use of proper temperature corrections, the accuracy of 

temperature measurements, water density equation, uncertainties due to water 

viscosity, round robin data showing reproducibility, environmental variations over 

time, and bias or drift of the standard. 

 5.5.1 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 
11/15/2006 

SOP 19 Page 11 of 11 

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, 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. 

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 Total prover volume, uncertainty, reference temperature, material, thermal 

coefficient of expansion (assumed or measured), construction, any 

identifying markings, tolerances (if appropriate), laboratory temperature, 

water temperature, barometric pressure, relative humidity, out-of-tolerance 

conditions, and the total drain time from opening of the valve, including 

the 30 s drain after cessation of flow. 

Additional References: 

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, (2006). 

11/15/2006 

SOP 20 Page 1 of 4 

 SOP 20 

 

Standard Operating Procedure 

for 

Control Charts for Calibration of Neck-Type Provers 

(Volume Transfer Method) 

 

1 Introduction 

 

 1.1 Purpose 

 This procedure describes a process to be followed to monitor the statistical control of 

the volume transfer method for the calibration of neck-type provers, especially when 

using the Standard Operating Procedure (SOP) 19 for this purpose. The same principles 

may be adapted to the development of control charts for other calibration procedures. 

 

 1.2 Prerequisites 

 The verification procedure is the same as that required by SOP 19. 

 

2 Summary 

 

 Because of the size and cost of neck-type provers, 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 a range (R) chart for each size prover to establish the standard deviation 

of the measurement process. Directions for preparing and using an R control chart that 

monitors the precision of the test procedure are given. It is assumed that provers 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 prover 

to determine the repeatability, the absolute difference between two test results on individual 

provers of the same nominal size are graphed on the same R chart to reflect the repeatability 

of measurement of the provers tested in the laboratory. Provers of similar readability may be 

grouped together on the same chart (e.g., provers greater than and equal to 500 gal generally 

have 20 in3

 graduations and similar repeatability.) 

 

3 Equipment 

 

 All equipment is designated in SOP 19. 

 
11/15/2006 

SOP 20 Page 2 of 4 

4 Procedure 

4.1 Data Collection 

 4.1.1 Conduct a minimum of two runs on each prover. A minimum of 12 provers must 

be tested before a reasonably adequate data base is established. Note: 25 to 30 

points are recommended to determine 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 prover is 

adjusted after the first trial to indicate zero error at a reference temperature, the 

first trial reading is evaluated after the adjustment.) 

4.1.3 Calculate the absolute difference |d| of the two trials and the summation Σ|d|. 

Note that |d| = R, the range of the two trials. 

 4.1.4 Calculate the average range of the trials, R , for the n tests as follows: 

n

d

R ∑= Eqn. 1 

 4.2 Construct a Range Control Chart 

 

 4.2.1 Construct an R control chart having the following limits: 

 Central Line = R

 Lower control and warning limits LCL = LWL = 0 

 (There should be no negative numbers recorded when using absolute values!) 

 Upper warning limit UWL = 2.512 R

 Upper Control limit UCL = 3.267 R

 

 4.2.2 The recommended format for construction of R control charts is given in NISTIR 

6969, Section 7.4. 

 

 4.3 Use of Control Charts 

 4.3.1 Two trials are run on each prover submitted to the laboratory for calibration. The 

values for R 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 R chart fall outside of the control limit, a decrease in 

precision is indicated. Cleanliness, valve leaks, or procedural problems (e.g., 
11/15/2006 

SOP 20 Page 3 of 4 

meniscus reading, drain times) should 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 R is outside of the warning limit but inside the control limit, 

a second set of duplicate calibrations should be made. If the new value for R 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. Corrective action should 

be taken and attainment of control demonstrated 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. 

5 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. 

 

 5.2 The accuracy is inferred from a consideration of control of the sources of bias. These 

include drain characteristics of the prover, time required to drain the prover, and prover 

design (geometry and piping). 

 

 5.3 To the extent appropriate, the precision of measurement of provers may be extended to 

the calibration of other provers of the same capacity and design. Care must be 

exercised in this approach because each prover is custom made and has unique 

metrological characteristics. The lack of precision in the test of a prover may indicate a 

defect in that particular standard and may not reflect inconsistency in the measurement 

process. Uncertainty values may need to be adjusted when prover design problems are 

indicated. 

 5.4 It is expected that the maximum imprecision (the upper control limit) of the volumetric 

method of prover calibration will be less than one-third of the applicable prover 

tolerance in field applications. If this is not the case, contact the NIST Weights and 

Measures Division to discuss the problem. 
11/15/2006 

SOP 20 Page 4 of 4 

Appendix 

 Control Chart Data 

 Prover Capacity & Graduation Size: 

 Laboratory: 

Test 

Number 

 Date VTD, X1

 Trial No. 1 

 VTD, X2

 Trial No. 2 

 VTDM

 x

 |d| = |Trial 1 - 

 Trial 2|*

 1 

 2 

 3 

 4 

 5 

 6 

 7 

 8 

 9 

 10 

 11 

 12 

 13 

 14 

 15 

 SUM 

∑x ∑ d

n** = = n

d

R= Σ 

UWL = 2.512 R = UCL = 3.267 R = 

* This is the range, R, of the two trials and is actually the larger value minus the smaller value. 

**n is the number of tests used to calculate the control limits. 
11/15/2006 

SOP 21 Page 1 of 17 

SOP 21 

Standard Operating Procedure for 

Calibration of LPG Provers1

 

1

 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. The majority of LPG provers in use are 20 gal, 25 gal, 

and 100 gal nominal sizes. The volume of LPG provers is established at 60 oF and 100 psig. 

1 Introduction 

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). 

 

1.2 Prerequisites 

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. 

1.2.2 Verify that valid calibration certificates are available for the standard used 

in the test. 

1.2.3 Verify that the standards to be used have sufficiently small standard 

uncertainties for the intended level of the calibration. 

1.2.4 Verify the availability of an adequate supply of clean water (GLP 10). 

1.2.5 Verify that the operator has had specific training in SOP 18, SOP 19, SOP 

21, GMP 3, and SOP 20. 

1.2.6 Cylinder of nitrogen or compressed air 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: 
11/15/2006 

SOP 21 Page 2 of 17 

Table 1. Laboratory environmental conditions 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 °C to 27 °C, maximum 

change 2.0 °C/h 

40 % to 60 % 

± 20 %, maximum change / 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 

air-free water supply, measurement control programs, and a stable 

temperature-controlled environment shaded from direct sunshine to allow 

the prover, field standard, and test liquid (water) to reach an equilibrium 

temperature, with minimal evaporation. Environmental conditions should 

be controlled (or selected) to be as close to laboratory conditions as 

possible. All data and appropriate environmental conditions must be 

documented regardless of test location. 

2 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 the 

latter capacity (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 prover should be within 5 in3

 (0.02 gal). 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 application 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 these should be minimized, a 
11/15/2006 

SOP 21 Page 3 of 17 

maximum number of 15 transfers are permitted to ensure that final calibration 

uncertainties are sufficiently small to meet user applications. 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 pressure. 

2.3 Equipment 

2.3.1 Calibrated standard prover of minimum volume of 10 gal but preferably of 

the same volume as the LPG prover, with recent calibration certificate 

traceable to NIST. 

2.3.2 A funnel and a calibrated 1 gal flask (or other suitable size) with recent 

calibration certificate traceable to NIST, to calibrate the neck of prover. 

2.3.3 Calibrated thermometers (2) accurately calibrated to 0.1 °C, with recent 

calibration certificate traceable to NIST. 

2.3.4 Meniscus reading device (See GMP 3). 

2.3.5 Timing device (calibration is not required.) 

2.3.6 Supply of clean water, preferably soft water (filtered if necessary) (GLP 

10). 

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 should 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. 

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. 

2.4 Procedure 

 

2.4.1 Preliminary Operations 
11/15/2006 

SOP 21 Page 4 of 17 

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 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. 

2.4.2 Cleanliness Check 

Both the standard and the 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 detergent (see GMP No. 

6) to attain good drainage characteristics. 

2.4.3 Neck scale plate verification 

2.4.3.1 Fill the prover with water from the standard. Check the 

prover levels and adjust if necessary. 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. Read and record this setting. This is in 

preparation for calibration of the neck scale. 

2.4.3.3 Remove the fill hose or pipe from the top and insert a 

funnel. 
11/15/2006 

SOP 21 Page 5 of 17 

2.4.3.4 Recheck the scale reading, then add 1 gal of water (or a 

volume equal to approximately 1⁄4 or 1/5 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). Record scale readings after each addition. 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 volume added 

should be linear and will be a gross check of the validity of 

this calibration. 

2.4.3.6 Calculate and check 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 

be replaced or issue the NSCV and instructions to user. 

2.4.3.7 The neck scale calibration value is calculated as follows: 

( ) f i

w

sr sr

V NSCV − = Eqn. 1 

where: 

NSCV Neck scale calibration value 

Vw Total volume of water added to 

neck 

f sr Scale reading, final 

i sr Scale reading, initial 

2.4.4 Body Calibration 

2.4.4.1 Drain the 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.) 
11/15/2006 

SOP 21 Page 6 of 17 

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 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. 

2.4.4.2 Transfer 100 gal (or other suitable 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. "Rock" the prover to 

"bounce" the liquid in the upper gauge glass before reading. 

Record the scale reading after the nominal volume has been 

transferred into the unknown LPG prover. 

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 measurements at the bottom, middle, and top of the 

provers. If the prover thermometer wells are used, ensure that 

the prover has equalized with the temperature of the water. 

2.4.4.3 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 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 should 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 

repeatability is larger than 0.02 % of the prover volume, 

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. 

Repeatability problems may also be due to poor field 

conditions, such as when calibration is conducted in unstable 

environments. Repeatability problems must be corrected before 

calibration can be completed. 

2.4.4.4 Replace the relief valve and plug in the top of the prover using 

suitable pipe joint compound or tape. Allow water from 2.4.4.3 

(the second run) to remain in prover. 

2.4.5 Prover Adjustments 
11/15/2006 

SOP 21 Page 7 of 17 

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 3.4) 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 3.4. 

2.4.5.2 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. 

2.4.5.3 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: 
11/15/2006 

SOP 21 Page 8 of 17 

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. 

Note: The correction factor 1.00032 corrects for the compressibility of the water at 100 psig. If the upper scale is not 

adjustable, see 2.4.5.4. 

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: 

( ) C X NOM u L V V *1.00032 s r = 60 − − Eqn. 3 

where: 

LC Prover correction at 100 psig 

VX60 Volume of unknown prover at 60° F 

VNOM Nominal volume of prover 

u sr 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 calculation. 

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

π = Eqn. 4 

where: 

h Distance in inches the bottom scale is to be 

moved, up or down 

LC Prover correction at 100 psig in cubic inches

d Inside diameter of the lower neck of the 

prover in inches (as noted on identification 

plate) 

2.4.6 Pressure Correction 
11/15/2006 

SOP 21 Page 9 of 17 

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 

increase in pressure, 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 should 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 repeatability errors must be 

identified and corrected before continuing the calibration. 

 

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 
11/15/2006 

SOP 21 Page 10 of 17 

through the system to remove the water to prevent it from 

freezing in the pump when LP gas is used. 

3 Calculations 

3.1 Single Delivery 

3.1.1 Calculate VX60, the volume of the unknown prover at 60 °F, using the 

following equation: 

{( )[ ( )]} [ ] 1 ( ) 60 F

1 60 1 1 1 60 F

60 o

o

+ −

+ ∆ + − =

x x

S

X t

V t V

ρ β

ρ α Eqn. 5

3.2 Multiple 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 1 1 60 F 2 60 2 1 2 60 F ... 60 1 60 F

60 o

o o o

+ −

+∆ + − + +∆ + − + + +∆ + − =

x x

S S N S N N

X t

V t V t V t V

ρ β

ρ α ρ α ρ α Eqn. 6

Table 2. Variables for VX60 equations

Symbols Used in Equations 

VX60 volume of the unknown vessel at 60 °F 

VS60 volume of the standard vessel at 60 °F 

ρ ρ ρ N , ,..., 1 2

density of the water in the standard prover where ρ1 is the density of the water for 

the first delivery, ρ2 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 

t1, t2, ..., tN temperature of water for each delivery with the subscripts as above 

α coefficient of cubical expansion for the standard in units / oF 

ß coefficient of cubical expansion for the prover in units / oF 

tx temperature of the water in the filled unknown vessel in units oF 

ρx density of the water in the unknown vessel in g/cm3

Note: Values for the density of water at the respective temperatures may be found in Table 9.8 

(in NISTIR 6969). It may also be calculated using the formula given in GLP 10. 
11/15/2006 

SOP 21 Page 11 of 17 

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: 

( ) ⎟

⎠

⎞ ⎜

⎝

⎛ − +

= −

100

100

@100 @

psig X psig water compressiblity factor

P Scale reading psig scale reading X psig corr

 Eqn. 7 

 where the water compressibility factor is 7.4 in3 or 0.032 gal for a 100 gallon 

prover and 1.8 in3

 or 0.008 gal for a 25 gallon prover. The compressibility 

value is 0.00032 gal per gallon for 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. At 100 psig, the prover reading will be lower by at least 0.032 

gal/gal than it was at 0 psig due to the compressibility of water under pressure. 

Therefore, a prover of 100 gal should be set to read the VX60 value at 0 psig minus 

7.4 in3. (The water level on the prover’s upper scale will be below the calculated 

VX60 reading when pressurized to 100 psig). The prover must not be set to read 

the VX60 value plus the compressibility factor at 0 psig because, in addition to 

compressibility of water, the prover expands as pressure is applied. 

4 Measurement Assurance 

4.1 If a check standard is used (See SOP 20, SOP 30), repeat the process for the 

unknown prover on the check standard without adjustments. 

4.2 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. 
11/15/2006 

SOP 21 Page 12 of 17 

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

4.4 Check standard values may be used to calculate the standard deviation of the 

measurement process. 

4.5 If a check standard is not used, the laboratory will need to maintain a Range chart 

according to SOP 20 to determine the repeatability for this procedure. 

 

5 Assignment 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. 

5.2 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. 

5.3 Neck calibration uncertainty should be estimated based on the uncertainty of 

standards used, errors observed during calibration, and the repeatability of the 

neck calibration. 

5.4 Standard deviation of the measurement process from control chart performance 

(See SOP No. 20 and SOP 30) 

5.4.1 The value for sp is obtained by estimation using the range from the control 

chart data for large volume transfer procedures. 

Note: 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. 

5.5 Other standard uncertainties usually included at for this type of calibration level 

include uncertainties associated with the ability to read the meniscus, only part of 

which is included in the process variability, viscosity effects, the cubical 

coefficient of expansion for the prover under test, use of proper temperature 

corrections, the accuracy of temperature measurements, water density equation, 

the compressibility of water, round robin data showing reproducibility, 

environmental variations over time, and bias or drift of the standard. 

5.5.1 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 
11/15/2006 

SOP 21 Page 13 of 17 

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. 

6 Report 

6.1 Report results as described in SOP No. 1, Preparation of Calibration/Test Results, 

with the addition of the following: 

6.1.1 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 humidity, 

out-of-tolerance conditions, and the total drain time from opening of the 

valve, including the 30 s drain after cessation of flow. 

The report should also include a pressure correction table or chart, along 

with a note regarding possible differences in retention characteristics 

between water, the calibration medium, and LPG products. 
11/15/2006 

SOP 21 Page 14 of 17 

Figure 1. LPG Prover Schematic
11/15/2006 

SOP 21 Page 15 of 17 

Appendix A 

SOP No. 21 

Recommended Standard Operations Procedure for 

Calibration of LPG Provers 

1 Compressibility of Water 

The water compressibility factor is calculated based on an equation given in a paper by Frank E. 

Jones and Georgia L. Harris, "ITS-90 Density of Water Formulation for Volumetric Standards 

Calibration", as published in the Journal of Research of the National Institute of Standards and 

Technology, Vol. 97, No. 3, 1992. 

Compressibility factor (V )( ) 231 ( kT )( P ) = NOM

where 

VNOM Nominal volume of Prover in gal 

kT Thermal compressibility of water in (atm)-1 

P Pressure in atm 

And 

8 9 11 2 13 3 15 4 kT 50.83101x10 3.68293x10 t 7.263725x10 t 6.597702x10 t 2.87767x10 t − − − − − = − + − + 

where kT is in (kPa)-1 and 1 atm = 101 325 Pa (exactly). 

The thermal compressibility of water for the reference temperature 60 °F (15.56 °C) is 

4.66264002 x 10-9/kPa. LPG provers are calibrated at a nominal reference point at a specified 

temperature and pressure, typically 60 °F and 100 psig. A pressure of 100 psig correlates to 

6.8 atmospheres. The following equation was used to calculate the compressibility factor: 

Compressibility factor = (VNom)(231)(kT)(P) 

Compressibility factor = 100 gal (231 in3

/gal)(4.72442x10-5/atm)(6.8 atm) = 7.4 in3 or 0.032 gal 

1 Example of Pressure Corrections 

The following example is printed from a Lotus 1, 2, 3 program written by L. F. Eason, 

Metrologist (NC) to perform calculation for volume transfer. The program was modified by 

Georgia Harris (NIST) to provide calculations and corrections for LPG prover testing. 
11/15/2006 

SOP 21 Page 16 of 17 

VOLUME TRANSFER CALIBRATION - METAL LPG PROVER

DATE: 04/09/91

 COMPANY NAME: 

 ADDRESS: 

 CITY, STATE:

Handbook 145 Example 

12321 Some Street 

Anywhere, USA

NOMINAL VOLUME OF PROVER: 

PROVER SERIAL NO: 

MANUFACTURER: 

NUMBER OF DELIVERIES REQUIRED:

100 GALLONS 

100-234LP 

Provers Unlimited 

1 (0-15)

DATA FOR INDIVIDUAL STANDARD DELIVERIES

DROP 

NO

VOL 

(GAL)

METAL 

(MS/SS)

EXP 

COEF

TEMP 

DEG C

TEMP 

DEG F

WATER 

DENSITY

DELTA 

(CU IN)

1 100 stainless 0.00003 15.55 59.99 0.999013 0

 TYPE OF METAL FOR THE UNKNOWN: 

 COEFFICIENT OF EXPANSION: 

 WATER TEMPERATURE: 

 WATER DENSITY: 

 GAUGE AT 0 PSIG: 

 GAUGE AT 50 PSIG: 

 GAUGE AT 100 PSIG: 

 GAUGE AT 150 PSIG: 

 GAUGE AT 200 PSIG: 

 DELIVERY VOLUME AT 60 °F: 

 UNKNOWN PROVER'S ERROR AT 100 PSIG:

mild steel 

0.0000186 /°F 

15.55 C 

59.99 F 

0.999013 g/cm3

0.09 gal 

0.02 gal 

-0.05 gal 

-0.10 gal 

-0.16 gal 

100.0000 VX60, gallons 

4.2 in3

ADJUSTMENT INSTRUCTIONS 

To adjust prover to deliver exactly 100 gallons at 60 F, adjust scale to read -0.032 gallons or -7.4 in3, at 100 psig. Move to 

-0.032 gals, -7.4 in3

, by 0.34 inches if 4" lower scale. 

PROVER PRESSURE CORRECTIONS 

psig Pcorr Prover 

Error

Prover Error Volume of the Adjusted Prover (gal)

0 

50 

100 

150 

200 

-0.108 

-0.054 

0.000 

0.034 

0.078

-0.108 

-0.054 

0.000 

0.034 

0.078 

 Adj.

-0.090 

-0.036 

0.018 

0.052 

0.096 

Not Adj.

99.829 

99.946 

100.000 

100.034 

100.078
11/15/2006 

SOP 21 Page 17 of 17 

LPG Pressure Correction Chart

Adjusted Prover Data

 Adjusted

-0.150

-0.100

-0.050

0.000

0.050

0.100

0 50 100 150 200 250

Pressure (psig)

Pressure Corr's (gal)

11/15/2006 

SOP 26 Page 1 of 10 

SOP 261

Standard Operating Procedure for 

Calibration of Dynamic Small Volume Provers by the Water Draw Method2

1.0 Introduction 

1.1 Purpose of Test 

This procedure may be used to calibrate dynamic small volume prover systems 

such as those used to conduct liquid metering device (e.g., Positive Displacement, 

Turbine) provings at wholesale marketing terminals. A volumetric water draw 

process is used. 

1.2 Prerequisites 

1.2.1 Verify that the standards used have been calibrated and that a valid 

certificate is available. The standard calibration should include a neck scale 

calibration as recommended in SOP 18 or SOP 19. 

1.2.2 Verify the cleanliness of the water to be used. 

1.2.3 Verify that the person performing the calibrations is trained and proficient 

in carrying out this test procedure and related liquid calibration procedures. 

1.2.4 The water draw location should provide for a stable ambient temperature. 

Direct sunlight must be avoided. An enclosed shelter is preferred. 

2.0 Methodology 

2.1 Scope, Precision, Accuracy 

This procedure is applicable for the calibration of a dynamic small volume prover 

(SVP) system within the limitations of the standards available. The precision 

attainable will depend directly on the care used in the various procedures required 

for this test. Strict observance of drainage times, internal cleanliness of vessels 

used, careful volumetric readings (menisci) and the adherence to the sequence of 

events outlined in this procedure are essential. 

 

1

 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. 2

 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. 
11/15/2006 

SOP 26 Page 2 of 10 

2.2 Summary 

The small volume prover system (SVP) must be filled with clean water and 

purged of all entrapped air. Using an external pressure source (pump, head tank), 

the calibrated volume section of the SVP is discharged into a calibrated 

"wet-down" vessel while the SVP system remains packed with clean water. This 

"water-draw" process is repeated three times for each calibrated volume section 

within the SVP system. The calibrated vessel volume and SVP volume are 

corrected for the effects of temperature and pressure to establish a volume at 

standard reference conditions. The established SVP calibrated volume is 

programmed and sealed into the SVP control electronics console to establish the 

reference for dynamic liquid measurement device proving. 

2.3 Equipment 

2.3.1 A graduated neck stainless steel calibrated vessel (including neck scale 

calibration) whose volume is equivalent to the SVP calibrated section. The water 

draw procedure may also be implemented using multiple smaller calibrated vessel 

readings (e.g., 15 gal SVP water drawn using three readings of a 5 gal calibrated 

vessel also having had a neck scale calibration). 

2.3.2 Supply of clean pressurized water (minimum 15 psi). If a pump system is 

used, care should be taken to provide a bypass loop to prevent excessive liquid 

heating during dead-ended conditions. 

2.3.3 Auxiliary piping and valves required to direct the water from the SVP to 

the calibrated vessel to perform the water draw. This is a vendor supplied kit or 

accessory option and is necessary to perform the water draw test. 

2.3.4 Three temperature sensing devices with a resolution of 0.1 oF or better are 

required to measure inlet water, outlet water and position sensor mounting 

temperature. In order to properly measure inlet and outlet temperatures, an 

adequate thermometer well must be available in the plumbing and filled with a 

suitable liquid medium. 

2.4 Procedure 

2.4.1 Cleanliness Verification 

Fill and drain the calibrated standard vessel and check for any soiling that 

would affect drainage, as evidenced by clinging droplets or greasy films. 

Fill and circulate clean water through the SVP. Check for any foreign 

material in the discharge stream. Circulate until discharge is clean. 

Discharge water should be handled in an environmentally safe manner 

since the SVP system may have previously filled with petroleum products. 
11/15/2006 

SOP 26 Page 3 of 10 

A thorough cleaning of the internals of the SVP system is required prior to 

the set-up for the water draw process. 

2.4.2 Air Purge and Temperature Stabilization 

All air must be purged from the SVP system to implement a successful 

water draw. Vent the SVP system from the highest possible point with the 

pressurized water source attached. Cycle the SVP Displacer several times 

in both directions to help release any trapped air pockets. Continue to 

circulate clean water through the system until the SVP system temperature 

is stabilized. This will help minimize variability and uncertainty in the 

procedure. 

2.4.3 Leak Detection 

SVP systems have some form of elastomeric or fluoropolymer seals 

between the displacer and the wall of the calibrated pipe section. A leak 

past one of these seals will cause an inaccurate water draw. It is prudent to 

conduct a leak detection test as defined by the SVP vendor prior to the 

water draw process. A typical leak check procedure is illustrated in 

Appendix A. 

2.4.4 Downstream Volume Calibration 

2.4.4.1 Return the SVP displacer to the upstream park position. Adjust 

water inlet/outlet valves to permit displacer travel downstream. 

Move the displacer downstream to the first sensor position and 

with the calibrated standard vessel filled. 

2.4.4.2 With the SVP displacer automatically stopped at the first sensor 

position, empty the contents of the standard vessel. Use a 30 s 

drain after cessation of flow on bottom drain type standards or a 

30 s pour/10 s drain on neck drain type standards, touching off 

any adhering drops from the neck to complete the drain. This 

constitutes the "wet-down" condition. 

2.4.4.3 Start the movement of the SVP displacer downstream discharging 

the water into the standard vessel. While the standard vessel is 

filling the following data should be recorded on Form-A 

(downstream section): 

 

 Inlet Water Temperature - T1 (± 0.1 oF) 

 Outlet Water Temperature - T2 (± 0.1 oF) 

 Position Sensor Mounting Temperature (Ambient) - Td (± 0.5 oF) 

 Outlet Water Pressure - P (± 1.0 psi) 
11/15/2006 

SOP 26 Page 4 of 10 

The displacer movement should stop automatically at the final 

sensor position using the vendor supplied water draw apparatus. 

The easiest method is to use a standard vessel that is the same 

nominal volume of the SVP system. This permits direct 

comparison of the standard vessel volume to the SVP volume with 

a single scale reading. Multiple readings of a smaller standard 

vessel can be used (i.e., a 5 gal standard vessel can be filled three 

times to calibrate a 15 gal SVP) but will increase uncertainty of 

measurement. The process is more complicated since only the last 

fill of the standard vessel can be stopped automatically. The 

previous fillings must be stopped manually by the operator and 

does not duplicate SVP use in field. 

2.4.4.4 Read and record the standard vessel scale reading on Form-A. 

Measure and record the average temperature of the standard vessel 

water (Tm) by submersion of the thermometer into the fluid. 

Average these temperature readings if using multiple readings 

from standard vessels smaller than the nominal value of the SVP. 

After the final standard vessel water temperature reading is taken, 

move the SVP displacer downstream past the final sensor position. 

2.4.5 Upstream Volume Calibration 

2.4.5.1 Adjust the water inlet/outlet valves to permit displacer travel 

upstream. Move the SVP displacer to the final sensor position 

filling the standard vessel. 

2.4.5.2 With the SVP displacer stopped at the first sensor position, dump 

the contents of the standard vessel. Use a 30 s drain after cessation 

of flow on bottom drain type standards or a 30 s pour/10 s drain on 

neck drain type standards, touching off any adhering drops from 

the neck to complete the drain. This constitutes the "wet-down" 

condition. 

2.4.5.3 Start the movement of the SVP displacer upstream discharging the 

water into the standard vessel. While the standard vessel is filling 

the following data should be recorded on Form A (upstream 

section): 

 

 Inlet Water Temperature - T1 (± 0.1 o F) 

 Outlet Water Temperature - T2 (± 0.1 o F) 

 Sensor Mounting Temperature (Ambient) - Td (± 0.5 o F) 

 Outlet Water Pressure - P (± 1.0 psi) 

The displacer movement should stop automatically at the final 

sensor position using the vendor supplied water draw apparatus. 
11/15/2006 

SOP 26 Page 5 of 10 

The easiest method is to use a standard vessel that is the same 

nominal volume of the SVP system. This permits direct 

comparison of the standard vessel volume to the SVP volume with 

a single scale reading. Multiple readings of a smaller standard 

vessel can be used (i.e., a 5 gal standard vessel can be filled three 

times to calibrate a 15 gal SVP). The process is more complicated 

since only the last fill of the standard vessel can be stopped 

automatically. The previous fillings must be stopped manually by 

the operator. 

2.4.5.4 Read and record the standard vessel scale reading on Form A. 

Measure and record the average temperature of the standard vessel 

water (Tm) by submersion of the thermometer into the fluid. 

Average these temperature readings if using multiple readings 

from standard vessels smaller than the nominal value of the SVP. 

After the final standard vessel water temperature reading is taken, 

move the SVP displacer upstream past the first sensor position. 

2.4.6 Repeated Runs 

Sections 2.4.4 and 2.4.5 should be completed at least two more times each. 

A minimum of three runs should be completed for each calibrated volume 

section of the SVP system. In some SVP systems the downstream and 

upstream volumes are not equal due to internal displacer geometry. It 

should be noted that some SVP systems have more than one calibrated 

volume section. Each volume section must be water drawn independently. 

3.0 Calculations 

A summary of the water draw calculations is provided in Form B (Small Volume 

Prover - Water Draw Calculations.) Form B provides the necessary calculations 

for each calibrated section of the SVP in one direction. The result obtained from 

Form B will be the net SVP volume corrected for 60 oF and 0 psig. The new net 

volume value, Vtp, must be entered into the SVP control electronics for use during 

dynamic operation of the SVP system. 

The net SVP volume corrected to 60 oF & 0 psig is determined using the equation: 

Vtp = Vm *Tmp*Cts *Cpl*Cps Eqn. 1 

where: 

Vtp Volume, corrected for temperature and pressure 

Vm Volume in the measure (uncorrected) 

Tmp Correction for the difference in the temperature between 

test measure and the small volume prover, SVP 
11/15/2006 

SOP 26 Page 6 of 10 

Cts Correction for the effect of temperature on the prover 

Cpl Correction for compressibility of the prover liquid 

Cps Correction for the pressure on the standard prover 

During the water draw process the SVP system is pressurized, therefore a 

pressure correction must be applied. The Cplfactor corrects for the compressibility 

of the water in the SVP and the Cps factor corrects for the effects of pressure on 

the SVP tube. 

The temperature effects on both the test measure and the SVP materials are 

corrected for with the Cts factor. The calibrated section of the SVP is a tube, thus 

the temperature compensation is applied only in two dimensions. A twodimension thermal coefficient of expansion is used for the SVP tube material (i.e., 

two times the linear coefficient of thermal expansion). The temperature effects in 

the third dimension are corrected using a linear thermal coefficient of expansion 

for the position sensor mounting material. 

The final factor, Tmp, corrects for the difference in water temperature between the 

test measure and the SVP system. This correction factor can be obtained from the 

table available in API Chapter 11.2.3 - "Water Calibration of Volumetric 

Provers". This table of correction factors is derived using the Wagenbreth 

equation for density of water at a given temperature (ρw). The correction factor, 

Ctdw, is determined by solving the equation: 

m

p

tp

tm

tdw V

V

C = = ρ

ρ Eqn. 2 

where 

 

Ctdw Correction for the liquid thermal expansion of water 

ρtm Density of the water in the test measure 

ρtp Density of the water in the prover 

VP Volume in the prover 

Vm Volume in the test measure 

4.0 Measurement Assurance 

4.1 If a check standard is used (See SOP 20, SOP 30), repeat the process for the 

unknown artifact on the check standard, without adjustments. 

4.2 Plot the check standard volume and verify it is within established limits. 

Alternatively a t-test may be incorporated to check the observed value against 

thean accepted value. 

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

time. 
11/15/2006 

SOP 26 Page 7 of 10 

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

measurement process. 

4.5 When a check standard is not used, a range chart may be used to monitor 

repeatability and estimate the standard deviation of the measurement process using 

the equation: 

* d2

R

s p = Eqn. 3 

5.0 5 Assignment of Uncertainty 

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. 

5.2 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. For multiple use of the same standard, 

uncertainty is additive. 

5.3 The standard deviation of the measurement process from control chart 

performance (See SOP No. 20 and SOP 30). 

5.4.1. The value for the standard deviation of the process, sp, is obtained from 

the control chart data of the check standard, or may be estimated using the range 

from the control chart, using large volume transfer procedures. 

5.5 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, the thermal coefficients of expansion for 

both the standard and the prover under test, use of proper temperature corrections, 

the accuracy of temperature measurements, water density equation, round robin 

data showing reproducibility, environmental variations over time, positioning of 

the prover sensor at the start and stop swiches, or alternatively the diverter errors 

of flow direction valves, the modulus of elasticity for pressure corrections to 

volume, and bias or drift of the standard. 

6.0 References 

6.1 Manual of Petroleum Measurement Standards; Chapter 11.2.3 - Water Calibration 

 of Volumetric Provers; First Edition, August 1984. 
11/15/2006 

SOP 26 Page 8 of 10 

Appendix A - Typical Leak Detection Procedure 

All Small Volume Prover systems have some form of displacer that travels with the 

liquid through the calibrated tube section. In addition there is some type of valve that is 

used to control the direction of the displacer to make a calibration run. The displacer and 

direction valve contain dynamic elastomeric seals. A leak past these seals will cause 

inaccurate dynamic performance and cause a false water draw measurement. The 

integrity of these seals must be verified before a water draw test can be considered valid. 

Typically a SVP leak check is similar to that described below. Specific instructions and 

measurement equipment to be followed for each SVP model must be supplied by the 

vendor. 

a) Block the SVP inlet and outlet using a blind flange or double/block and bleed 

valve (bubble tight shut off). 

b) Fill the SVP with water and bleed all air from the system. 

c) Launch the displacer down the flow tube. 

d) Attach a dial indicator as illustrated below to measure the movement of optical 

switch shaft. A downstream movement of 0.004 in or less in 5 min indicates the 

system is leak free. An indicator movement of greater then 0.004 in indicates that 

a system leak is present and displacer/valve seals should be inspected or replaced. 
11/15/2006 

SOP 26 Page 9 of 10 

Small Volume Prover 

Water Draw Data Summary 

Form A

Customer: _____________________________ 

Address: _______________________________ 

 _______________________________ 

Serial No.: _____________________________ 

Model No.: _____________________________ 

Date: __________________________________ 

Time: _________________________________ 

Calibrator: _____________________________ 

Standard I.D.: __________________________ 

 __________________________

Draw 

No. 

Inlet 

Water 

Temp(T1) 

Outlet 

Water 

Temp(T2) 

Prover 

Temp 

(Tp) 

Test 

Measure 

Temp(Tm) 

Sensor 

Mounting 

Temp(Td) 

Water 

Press. 

(P) 

Test 

Measure 

Scale (in3)

Downstream Volume 

1 

3 

5 

7 

9 

11 

Upstream Volume 

2 

4 

6 

8 

10 

12

Tp = SVP water temperature, Average of T1 and T2 

Tm = Temperature of water in Test Measure 

P = Water pressure during test draw 

Td = Temperature of displacer position sensors 
10/18/2006 

SOP 26 page 10 of 10 

Small Volume Prover - Water Draw Calculations 

Form B 

Customer: _____________________________ 

Serial No.: _____________________________ 

Model No.: _____________________________ 

Volume: Downstream _____ Upstream _____ 

SVP Tube Inside Diameter (D): __________ inches 

SVP Tube Wall Thickness (t): ___________inches

Vtp = Net Volume Corrected for 60 oF & 0 psig 

 = Vm * Tmp * Cts * Cpl * Cps

Tp = SVP Temperature 

Td = SVP Sensor Temperature 

Tm = Test Measure Temperature 

Tmp = Temperature differential factor for water 

 from API Chapter 11.2.3 

P = Water pressure during test draw 

Emod = Modulus of elasticity of the SVP tube 

 material 

Cts = Correction factor for temperature of the 

 test measure, SVP tube and sensor 

 mounting material 

 = 1 + (Tm - 60) * ALPHAtm . 

 [1 + (Tp - 60) * ALPHAsvp] [1+ (Td - 60) * ALPHAsens] 

 = [_________________] 

Cpl = Correction for the compressibility of 

 water 

 = 1 - (0.0000032 * P)

ALPHAtm = Cubical Thermal Coefficient for test measure material 

 = [_________________] 

ALPHAsvp = Square Thermal Coefficient for SVP tube material 

 = [_________________] 

ALPHAsens = Linear Thermal Coefficient for the SVP sensor 

 mounting material 

 = [________________] 

Cps = Correction for pressure on the SVP 

 tube 

 = 1 .

 1 + P * D . 

 (Emod) * t

Test 

Measure 

Volume 

( in3) 

Scale 

Vol + 

(in3) 

Reading 

Vol - 

(in3) 

Actual 

Volume 

Vm

(in3) 

SVP 

Temp 

Tp

Test 

Measure

Temp 

Tm

Temp

Diff. 

Diff. 

Temp. 

Factor

Tmp

SVP 

Sensor

Temp 

Td

Material 

Correct. 

Factor 

Cts

Volume 

Adjusted to 

60 oF 

Vm * Tmp * Cts

 

 

 Repeatibiliy Verification: Max. Adjusted Volume - Min. Adjusted Volume

 Min. Adjusted Volume * 100

% 

 A) Average of Consecutive runs Repeating within 0.02% in3

 B) Cpl = 1 - (0.0000032 * P) = 1 - (0.0000032 * ________ ) = 

 C) Cps = 1 .

 1 + ( ) * ( ) 

 ( ) * ( )

 Vtp = Lines A * B * C = in3

 Convert to Gallons (divide by 231) gal
11/15/2006 

SOP SVP page 1 of 10 

SOP SVP1

Standard Operating Procedure 

For 

Gravimetric Calibration of Dynamic Small Volume Provers2

 

1 Introduction 

 1.1 Purpose of Test 

This procedure describes the calibration of the "to deliver" volume of dynamic 

small volume provers (SVP) 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 does not incorporate measurement control steps to 

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

precautions must be taken. 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. The procedure can be used for both upstream and 

downstream calibrations. Each direction will be treated as a separate calibration. 

1.2 Prerequisites 

1.2.1 Verify that valid calibration certificates are available for the standards 

used in the test. 

1.2.2 Verify that the standards and instruments (e.g., thermometer, barometer, 

and hygrometer) to be used have sufficiently small standard uncertainties 

for the level of calibration. Reference standards should not be used for 

gravimetric calibration. 

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

sufficiently small process standard deviation as verified by a valid control 

chart or preliminary experiments to ascertain its performance quality when 

a new balance is put into service. 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 10, and 

gravimetric calibrations such as those used in SOP 14. 

1.2.5 Verify that an adequate supply of distilled or de-ionized water (see GLP 

10) is available. 

 

1

 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. 2

 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. 
11/15/2006 

SOP SVP page 2 of 10 

1.2.6 Verify that the laboratory facility is free of air currents and/or temperature 

fluctuations where the SVP will be set up for testing. 

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 environmental conditions 

Procedure Temperature Relative 

Humidity 

SVP/ Large Volume 

Gravimetric 

20 °C to 23 °C, a set point ± 2 °C, 

maximum change 1.0 °C/h 

40 % to 60 % 

± 10 % maximum change / 4 h 

1.2.8 All necessary maintenance to the test artifact 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. Replace the seals 

on the prover if there is any doubt as to their integrity. If “as found” data 

is required, that data should be obtained before any seal replacements. 

1.2.9 The prover inlet and outlet must be blocked by the device owner before 

calibration by using a blind flange or double-block and bleed valve. 

1.2.10 The device owner must provide all necessary manufacturers’ manuals as 

well as trained personnel to operate the device. 

2 Methodology 

 

 2.1 Scope, Precision, Accuracy 

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

SVP that, when filled with water, will not overload the electronic balance used. 

Typical containers SVPs range in capacity from 15 gal to 120 gal. The precision 

of calibration will depend on strict adherence to the various steps of the 

procedure. The accuracy attainable will depend on the uncertainties of the 

standard weights, the air buoyancy, density of water, thermal expansion 

corrections that are made, and the repeatability of the SVP. 

 2.2 Summary 

The mass of the water delivered by the SVP is determined by weighing the water 

on an electronic balance and comparing it to mass standards. Volume is derived 

from mass using the equations provided. 

2.3 Equipment and Standards 

2.3.1 Electronic balance having sufficient capacity to weigh the loaded vessel. 

The sensitivity of the balance will be a limiting factor in the accuracy of 

the measurement. The resolution and repeatability should be smaller than 

the accepted uncertainty of the calibration. 

2.3.2 Calibrated mass standards with adequate accuracy and NIST traceable 

mass values. Ordinarily, weights of ASTM Class 2 or 3 specifications, or 

equivalents are required. 
11/15/2006 

SOP SVP page 3 of 10 

2.3.3 Thermometer, calibrated to ± 0.1 °C for measuring the temperature of the 

water, prover, and detector bar; ± 0.5 °C for measuring the temperature of 

the air and calculating the air density, traceable to NIST. 

2.3.4 Barometer, calibrated to ± 1 mm Hg and a hygrometer, calibrated to ± 5 % 

for calculating the air density, traceable to NIST. 

2.3.5 Pressure gauge for determining the prover pressure, with calibration 

traceable to NIST. (Include the uncertainty of the pressure gauge in the 

uncertainty calculations.) 

2.3.6 Distilled or de-ionized water and methods to verify its purity (See GLP 

No. 10). 

2.4 Procedure 

2.4.1 Install SVP volumetric test kit per manufacturer’s instructions. (Provided 

by device owner.) 

2.4.2 Connect water supply to prover. 

2.4.2.1 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. Set device valves as 

appropriate for the test to be conducted. 

2.4.2.2 For Calibron (brand) SVPs, turn water supply on, and open 

appropriate valves to eliminate entrapped air according to 

manufacturer’s instructions. After all air is bled off, close 

associated valves. Then open the appropriate valves and allow 

water to circulate until the temperature has stabilized. 

2.4.2.3 For Daniels (brand) SVPs, establish valve position for control of 

upstream or downstream flow. 

2.4.3 Install certified thermometers to record air temperature, water temperature, 

detector bar temperature (Td), and prover temperature (Tp). 

2.4.4 Install calibrated pressure gauge to record prover pressure (Pp). 

2.4.5 Connect prover control cable to controller (from the volumetric test kit.) 

2.4.6 Apply power to the prover and the water draw circuit. One of the valves 

will switch on immediately. Note which valve switches on, and mark it as 

the overboard or bypass valve. The other valve is the draw valve and will 

only be on while the flag is between the two volume switches. 

2.4.7 Record all of the prover-specific variables on the data entry form. 

Note: All references in the following weighing options to the empty 

receiving vessel assume that the empty receiving vessel has been placed in 

a “wet-down” condition. This wet down condition is achieved when the 
11/15/2006 

SOP SVP page 4 of 10 

vessel has been filled with water and then drained using the same process 

that will be used throughout this calibration. 

2.4.8 Weighings (Option A) 

2.4.8.1 Zero the balance and record the balance indication as O1. Place a 

standard mass, Ms1, on the balance platform (Ms1 should be slightly 

larger than the mass of the empty receiving vessel.) Record the 

balance indication as O2. 

2.4.8.2 Place the empty receiving vessel on balance platform and record 

the balance indication as O3. Caution: the receiving vessel must 

be dry on the outside for all weighings. 

2.4.8.3 Record air temperature, barometric pressure and humidity at the 

time of these measurements. 

2.4.8.4 Zero the balance and record the balance indication as O4. 

2.4.8.5 Manipulate the system to cause the prover piston to move to the 

starting position and begin the water draw sequence. Record all 

pertinent test artifact temperatures and pressures during the water 

draw sequence. Immediately upon completion of the water draw 

sequence, place the filled receiving vessel on the balance and 

record the balance indication as O6. Read and record the 

temperature of the water in the container immediately after 

weighing. 

2.4.8.6 Remove the filled receiving vessel and 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 O5. 

2.4.8.7 Record the air temperature, barometric pressure and humidity at 

the time of these measurements. 

2.4.8.8 Make five duplicate runs with two runs at a flow rate differing 

from the others by at least 25 %. The measured result (V60) of each 

of these calibration runs must repeat within 0.02 %. 

2.4.9 Weighings (Option B) 

2.4.9.1 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. 

2.4.9.2 Place additional mass standards approximating the nominal 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 indication as O1. 
11/15/2006 

SOP SVP page 5 of 10 

2.4.9.3 Remove all mass standards. Record the air temperature, 

barometric pressure, and relative humidity readings. 

2.4.9.4 Place the empty receiving vessel on the balance, with the padding 

material and zero the balance indication. Remove the transfer 

vessel, lid, and padding material and record the base empty vessel 

reading (B). 

2.4.9.5 Manipulate the system to cause the prover piston to move to the 

starting position and begin the water draw sequence filling the 

receiving vessel. Read and record all pertinent test artifact 

temperatures and pressures during the water draw sequence. Place 

the lid on the receiving vessel to limit evaporation. 

2.4.9.6 Immediately prior to weighing full vessel record balance reading 

as (d1). This reading will be used to calculate drift while filling the 

vessel. 

2.4.9.7 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. 

2.4.9.8 Remove the filled receiving vessel and record the balance 

indication as (d2). This reading will be used to calculate drift over 

the entire process. 

2.4.9.9 Immediately after removing the filled receiving vessel from the 

balance, record the temperature of water in the vessel. 

2.4.9.10Make five duplicate runs with two runs at a flow rate differing 

from the others by at least 25 %. The measured result (V60) of each 

of these calibration runs must repeat within 0.02 %. 

3 Calculations 

3.1 Compute the volume at the temperature of the measurement, Vt, for each 

determination using the equation: 

(Option A) 

( ) ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

−

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

− −

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

ρ ρ

ρ

ρ

ρ

ρ

w a

s

a s

( drained )

s

a

s

T ( filled )

-

1

O O

M 1-

O

O O

M 1-

V = O

2 1

1

1

3

5 4

2

2

6 Eqn. 1
11/15/2006 

SOP SVP page 6 of 10 

Table 2. Variables for volume equation 

Variable Description 

 Ms, Ms1, Ms2 mass of standards 

ρs density of MS 

ρw density of water at the temperature of measurement 

ρa density of air at the conditions of calibration 

Vt Volume at the temperature of the test 

(Option B) 

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞ ⎜

⎜

⎝

⎛

ρ ρ ρ

ρ

ρ

ρ

t w a

a

t

s

s a

T 2c

-

1 1- - M 1- O

M V = O

1

 Eqn. 1

( )

⎭

⎬

⎫

⎩

⎨

⎧ −⎥

⎦

⎤ ⎢

⎣

⎡ + = + B d d O c O

2

1 2

2 2 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 

ρa Air density 

ρs Density of MS 

ρt Density of Mt

ρw Water density 
11/15/2006 

SOP SVP page 7 of 10 

3.2 Compute V60, the volume at 60 °F, for each run, using the equation: 

Table 4. Additional Variables for Volume Equations 

Variable Description 

Tb Reference (Base) temperature 

Td Detector bar temperature (Temperature, detector) 

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 expansion (switchbar)

Ga Coefficient of flow tube area thermal expansion

CPL Correction for the pressure on the liquid 

CTS Correction for the temperature on the standard prover 

CPS Correction for the pressure on the standard prover 

CCF Combined correction factor 

3.3 Calculate water density using the equation provided in GLP 10. 

3.4 Calculate the air density per SOP 2. 

3.5 Calculate the uncertainty for the calibration using Appendix B: 

[ ] ( )

{ } ( ) [ ] ( ) ( ) [ ] ( )

( )

p p p

p

p

p p b a d b l

p

p

CCF CPL CTS CPS

E WT

P ID

CPS

CTS T T G T T G

P

CPL

CCF

Vw V

* *

*

*

1

1 * * 1 *

1 (0.0000032 *

1

where

60

=

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = +

= + − + −

− =

= Eqn. 2
11/15/2006 

SOP SVP page 8 of 10 

4 Measurement Assurance 

4.1 Record and plot standard deviations of each five run calibration to determine shortterm variations of the measurement process. 

5 Assignment 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 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. 

5.2 Standard deviation of the measurement process from control chart performance 

(See SOP 17 or 20.) 

The value for sp is obtained from the control chart data or estimated based on the 

range of duplicate measurements over time. This value will incorporate a 

repeatability factor related to the precision of the weighings. 

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. 

6 References 

6.1 Manual of Petroleum Measurement Standards; Chapter 11.2.3 - Water Calibration 

 of Volumetric Provers; First Edition, August 1984. 
Appendix B 11/15/2006

SOP SVP page 9 of 10 

Gravimetric Calibration Data Sheet 

Company Name: ________________________________________ Test No: __________________ 

Address: ________________________________________ Purchase Order No: __________________ 

City, State, Zip: ________________________________________ Date Scheduled: __________________ 

Representative: ________________________________________ Date Received: __________________ 

Phone: __________________ Fax: ________________ Date Tested: __________________ 

Email: ________________________________________ Date Returned: __________________ 

Company URL: ________________________________________ Next Appointment: __________________ 

General Description ________________________________________ 

Manufacturer: ________________________________________ 

Model Number: _______________ Serial Number: ___________ 

Condition: ________________________________________ 

Compressibility factor for water 3.2000E-06 Area Thermal Expansion Coefficient (Ga) 

Reference Temperature(Tb) (oF) 60 Detector Thermal Expansion Coefficient (GI) 

Reference Temperature (oC) 15.55555556 Modulus of Elasticity (flow tube) (E) 

Reference Pressure (psig) 0 Flow Tube Inside Diameter (inches) (ID) 

 Flow Tube Wall Thickness (inches) (WT) 

Standards Used 

Full Vessel Empty Vessel 

 

Observations 

Fill Number Fill # 1 Fill # 2 Fill # 3 Fill # 4 Fill # 5 

Flow Rate Fast Fast Fast Slow Slow 

Run Time (sec) 

Zero Balance, O1 

Balance Reading O2 (Standards Empty) 

Balance Reading O3 (Empty Vessel) 

Zero Balance, O4 

Balance Reading O5 (Standards Full) 

Balance Reading O6 (Full Vessel) 

Air Temperature (oC) 

Barometric Pressure (mmHg) 

Relative Humidity (% RH) 

Water Temperature (oC) 

Detector Bar Temperature (Td) (oC) 

Prover Temperature (Tp) (oC) 

Prover pressure (Pp) (psig) 

Total True Mass 
Appendix B 11/15/2006

SOP SVP page 10 of 10 

Example uncertainty components listed in order of effect on total uncertainty: • Standard deviation of the measurement process, sp

• Water temperature 

• Reproducibility 

• Mass calibration uncertainty 

• Water density 

• Prover temperature 

• Water compressibility 

• Detector temperature 

• Prover pressure 

• Area thermal expansion (Ga) 

• Air temperature 

• Detector thermal expansion (Gl) 

• Barometric pressure 

• Relative humidity 

• Modulus of elasticity 

• Flow tube diameter (ID) 

• Tube wall thickness (WT)