Selected Procedures for Volumetric 

Calibrations

(2012 Ed)

Harris, Georgia L.

NISTIR 7383
 

 
 

 

NISTIR 7383

Selected Procedures for Volumetric 

Calibrations

(2012 Ed)

Harris, Georgia L.

Weights and Measures Division 

March 2012

U.S. Department of Commerce 

John E. Bryson, Secretary 

National Institute of Standards and Technology 

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

Foreword 

This NIST IR of Selected Publications has been updated from the 2006 version and 

includes Good Laboratory Practices, Good Measurement Practices, and Standard 

Operating Procedures for volumetric calibrations. 

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

NBS Handbook 145, Handbook for the Quality Assurance of Metrological 

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

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

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

systems. The 2012 updates include updated terminology consistent with the International 

Vocabulary of Metrology (VIM), primarily associated with metrological traceability. The 

2006 changes incorporated 1) uncertainty analyses that comply with current international 

methods in the Guide to the Expression of Uncertainty in Measurements (GUM) and 2) 

measurement assurance techniques using check standards. No substantive changes were 

made to core measurement processes or equations in the 2012 edition. 

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

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

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

any process (versus only those for volumetric calibrations as previously written.) 

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

removed in this publication: 

Standard Operating Procedures for: 

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

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

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

balances for gravimetric calibrations. 

 Small Volume Prover, Water Draw (26) and Small Volume Prover, Gravimetric 

Calibration (SVP). These two procedures are undergoing major revisions to 

consider additional technologies and will be updated at a later pending review by 

designated working groups. 

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

for the 2006 edition: 

 Kelley Larson, AZ Department of Weights and Measures (retired as of 2012) 

 Dan Newcombe, ME Department of Agriculture Metrology Laboratory 

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

Laboratory (retired as of 2012) 

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

Laboratory 

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

Laboratory 
iv

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

Laboratory (retired as of 2012) 

 Val Miller, NIST, Office of Weights and Measures 

 Carol Hockert, NIST, Office of Weights and Measures 

 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 

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 

14 Gravimetric Calibration of Volumetric Ware Using an Electronic 

Balance 

SOP 24-1 

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 
vi

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Good Laboratory Practices 

 
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May 2012 

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

Race St., Philadelphia, PA 19103. 
May 2012 

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). 
May 2012 

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

 



 







    ( )( ) ( ) ( ) 1

3 4

2

2

1

5

a t a

t a t a

a

w  t Eqn. 1 

where: 

a1 = -3.983 035 C 

a2 = 301.797 C 

a3 = 522528.9 C2

a4 = 69.348 81 C1

a5 = 999.974 950 kg m-3

tw is the temperature of the water in C. 

In Excel Format: 

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

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

. 

 

2

 M. Tanaka, G. Girard, R. Davis, A. Peuto, and N. Bignell, Recommended table for the density of water between 0 

°C and 40 °C based on recent experimental reports, Metrologia, 38, 301-309 (2001). 
May 2012 

GLP 10 Page 4 of 4 

To adjust the air-free water density in Equation 1 beween 0 °C and 25 °C to air-saturated water 

(the standard laboratory condition), use the following equation, 

kg m s s t 0 1

3  /     Eqn. 2 

where, 

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

4.612 

and 

S1/(10-3 kg m-3 °C-1)= 0.106. 

In Excel Format: 

=(-4.612+0.106*G8) 

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

water will be less dense than air free water.) 

Note: 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. When adjusting the value for air-saturated conditions, use 

Equation 2 before converting to other units. The result in Equation 2 will be in “parts per 

million,” so divide by 1 000 000 to find the change to the water density in g/cm3. 

Additional References: 

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

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

ISO 15212-1:2002, Oscillation-type density meters – Part 1: Laboratory instruments, ISO, 2002. 
March 2012 

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 to minimize contaminants from 

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

allow the flask to come to equilibrium with the environment. Obtain an initial baseline “dry 
March 2012 

GLP 13 Page 2 of 2 

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. 
Good Measurement Practices 

 
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GMP 3 Page 1 of 4

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 mercury 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 

the diameter of the tubing in which it is formed. When reading any meniscus, it is important to 
March 2012 

GMP 3 Page 2 of 4

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 – 

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

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

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

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

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

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

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

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

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

above or below the line to its proper setting. 

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.) 
March 2012 

GMP 3 Page 3 of 4

Option B 

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

around the circumference of the volumetric standard. 

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

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

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

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

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 factor 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. 

Estimate potential errors in reading the meniscus, or errors in single-mark flasks by using the 

equation for the volume of a cylinder: 

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

Graduation Line

Graduation Mid-point

Observer’s Eye Graduation Line 
March 2012 

GMP 3 Page 4 of 4

Vol r h

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

volume in question. Units will be determined based on the dimensional units that are used. For 

example radius in cm2 and height in cm, will provide results in cm3 or mL. The meniscus itself 

often has an observed “thickness” that is larger than the graduation lines so should be considered 

as well. 

Example: 

The internal diameter of a flask is 1.5 cm (15.00 mm). 

The height of the line is 0.50 mm. 

) 0.5

2

15 ( 2 Vol   = 88.36 mm3

 (0.088 mL). These values are rounded for illustrative purposes 

only; significance must be evaluated based on measuring instruments and flask resolution. 

Experimental data obtained by reading a meniscus among multiple laboratory staff members may 

also be used to incorporate an estimate of uncertainty in meniscus reading. 
March 2012 

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 
March 2012 

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. 
March 2012 

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 °C) sodium dichromate-sulfuric 

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. 
March 2012 

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. 
March 2012 

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). (See GLP 13.) 

 

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

used for drying purposes. 
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Standard Operating Procedures 

 
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March 2012 

SOP 14 Page 1 of 17 

SOP No. 14 

Recommended Standard Operating Procedure 

for 

Gravimetric Calibration of Volumetric Ware Using an Electronic Balance 

1 Introduction 

 1.1 Purpose of Test 

This procedure is a precision mass calibration converting mass values to 

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

provide calibration of either the "to deliver" or "to contain" volume of measuring 

containers that may be used as volumetric measuring standards. The procedure 

uses gravimetric calibration principles to minimize calibration uncertainties. 

Accordingly, the procedure is especially useful for high accuracy calibrations. 

The procedure references measurement control standards to ensure the validity of 

the standards and the measurement process; however, additional 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. This procedure calculates the average volume based on two runs. NOTE: 

NIST calibrations generally make use of the average of five replicates. 

1.2 Prerequisites 

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

standards used in the calibration. 

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

uncertainties for the level of calibration. Reference standards should not 

be used for gravimetric calibration. Weights of ASTM Class 2 or 3 or 

OIML Class F1 or F2 are needed for this procedure. 

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

sufficiently small resolution and 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. NOTE: standard deviations 

obtained from mass calibrations will generally not reflect the process 

repeatability of this procedure. 

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: 
March 2012 

SOP 14 Page 2 of 17 

Table 1. Laboratory environmental conditions. 

Procedure Temperature Relative Humidity

Gravimetric 20 C to 23 C, maxiumum change of 

1 C/h during the calibration.

40 % to 60 %

± 10 % stability / 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 electronic balance used. 

Typical containers range in capacity from 1 mL to 20 L; however, this procedure 

is also applicable for larger provers provided that facility, equipment and 

standards meet the requirements in this SOP. When larger provers (e.g., 100 gal 

or more) are tested, also see the Test Notes in the Appendix. The 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. Transfer vessels may be used for all procedures 

except for flasks and containers marked “To Contain” (TC). 

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 must be smaller than 

the accepted uncertainty of the calibration. NOTE: standard deviations 

obtained from mass calibrations will generally not reflect the process 

repeatability of this procedure, therefore repeatability must be assessed 

using this procedure. 

2.3.2 Calibrated mass standards, with recent calibration values and which have 

demonstrated metrological traceability to the international system of units 

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

as NIST.. Ordinarily, standards of ASTM Class 2 or 3 or OIML Class F1

or F2 weight specifications are required. 

2.3.3 Calibrated thermometers, accurate to ± 0.1 °C, with recent calibration 

values and which have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI through a 
March 2012 

SOP 14 Page 3 of 17 

National Metrology Institute such as NIST to determine water 

temperature. 

2.3.4 Calibrated thermometer accurate to ± 0.50 °C with recent calibration 

values which have demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST to determine air temperature. 

to determine air temperature.1

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

calibration values which have demonstrated metrological traceability to 

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

National Metrology Institute such as NIST to determine air pressure. 1

2.3.6 Calibrated hygrometer accurate to ± 10 percent with recent calibration 

values which have demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST to determine relative 

humidity.1

 

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

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

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

2.4 General Considerations 

2.4.1 Cleanliness checks 

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

uniform drainage of water. No water droplets should remain on any 

interior surface as the water drains from the container. A reproducible 

“wet-down” weight is evidence for cleanliness in cases where it is not 

possible to visually check for uniform drainage. Use GMP 6 or 7 to clean 

vessels as necessary. All glassware must be meticulously cleaned, prior to 

calibration. When clean, the walls will be uniformly wetted. Instructions 

for cleaning are given in GMP 6 or 7. An exception is plastic ware, which 

will not be wetted. Follow manufacturer's instructions for cleaning such 

vessels. Do not use cleaning agents that will attack, discolor, or swell 

plastic ware. 

2.4.2 Use water that is temperature-equilibrated with the laboratory 

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

containers in the laboratory. 

 

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. 
March 2012 

SOP 14 Page 4 of 17 

2.4.3 Volumetric calibrations to a marked interval are critically dependent on 

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

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

“To Contain” basis. 

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

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

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

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

(This is commonly called a “30 s pour, 10 s drain” emptying procedure.) 

A 30 s (± 5 s) pour followed by a 10 s drain, with the measure held 

between a 10 degree and 15 degree angle from vertical, is required during 

calibration and use for glass flasks. A wet-down is not required if a 

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

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

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

complete for 30 s and close the valve. 

2.5 Calibration Procedure for Burets 

2.5.1 Weigh an empty transfer vessel or flask. 

2.5.2 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. 

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

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

ready to test. 

2.5.4 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. 

2.5.5 Fill the buret slightly above zero mark with temperature-equilibrated 

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

temperature. 

2.5.6 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. 

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

previously weighed flask or transfer vessel. 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. 

2.5.8 Stopper (or cover) and weigh the filled transfer vessel or flask. 

2.5.9 Measure and record the temperature of water in the container. 
March 2012 

SOP 14 Page 5 of 17 

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

interval of test. 

2.5.11 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. 

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

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

2.6 Calibration Procedure for Pipets (One-Mark) 

2.6.1 Weigh an empty transfer vessel or flask. 

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

in contact with the internal surface of a beaker. 

2.6.3 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. 

2.6.4 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. 

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

contact with the flask. 

2.6.6 Stopper (or cover) and weigh the filled transfer vessel or flask. 

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

2.6.8 Calculate the volume as described in Section 3. 2.7 Calibration of Flasks (To Contain) – Transfer vessel may not be used. 

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. 
March 2012 

SOP 14 Page 6 of 17 

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

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 a transfer vessel or flask. 

2.8.2 Weigh the empty transfer vessel or flask and record the mass. 

2.8.3 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. 

2.8.4 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. 

2.8.5 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. 

2.8.6 Cover the flask or transfer vessel and reweigh. 

2.8.7 Make a duplicate determination (Run 2). 

2.8.8 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. 

2.9.2 Graduated Cylinders - Calibrate in a manner similar to that used for flasks. 

2.10 Calibration of Slicker-Plate Type Standards 

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

fully ensure wet down and smooth valve operation. 

2.10.2 Weigh an empty transfer vessel and record the mass. 

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

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

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

vessel and that no splashing occurs. 

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

and smoothly to deliver the water into the transfer vessel. Time the drain 

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

transfer vessel and move it from beneath the standard to ensure additional 

drops of water are not transferred. 
March 2012 

SOP 14 Page 7 of 17 

2.10.5 Weigh the filled transfer vessel and record the mass. 

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

2.10.7 Calculate the volume as described in Section 3. 

2.11 Calibration of Graduated Neck Type Provers 

2.11.1 Condition the graduated neck type standards with several wet-down runs 

to fully ensure wet down and smooth valve operation. 

2.11.2 Weigh an empty transfer vessel and record the mass. 

2.11.3 Fill the standard to the nominal graduation mark. Record the water 

temperature. Set the transfer vessel below the nozzle to ensure all volume 

is transferred into the vessel and that no splashing occurs. 

2.11.4 Open the standard valve smoothly to deliver the water into the transfer 

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

close the valve. Cover the transfer vessel and move it from beneath the 

standard to ensure additional drops of water are not transferred. 

2.11.5 Weigh the filled transfer vessel and record the mass. 

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

2.11.7 Calculate the volume as described in Section 3. 

2.12 Weighing Procedures 

2.12.1 Weighing (Option A – One point balance calibration) 

2.12.1.1 Zero the balance and record reading as O1. Place a standard 

mass, MS, on the balance platform (where possible, MS should 

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

reading as O2. 

2.12.1.2 Zero the balance. Place dry or “wet-down” container or empty 

transfer vessel on the balance platform, as appropriate, and 

record reading as O3.2 Caution: all containers must be dry on 

the outside for all weighing. 

2.12.1.3 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 or 

transfer vessel and record the reading as O4. 

2.12.1.4 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. 

2.12.1.5 Record air temperature, barometric pressure, and relative 

humidity at the time of the above measurements. 

2.12.1.6 Make a duplicate determination (Run 2). 

 

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. 
March 2012 

SOP 14 Page 8 of 17 

2.12.2 Weighing (Option B – Two point balance calibration.) 

2.12.2.1 Zero the balance and record reading as O1. Place a standard 

mass, MS1, on the balance platform (where possible MS1

should be slightly larger than the mass of the drained vessel, 

dry vessel, or empty transfer vessel.) Record reading as O2. 2.12.2.2 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 

weighing. 

2.12.2.3 After removing empty vessel, zero the balance and record 

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

platform (where possible MS2 should be slightly larger than 

the mass of the filled vessel.) Record reading as O5. 2.12.2.4 Fill standard 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 or transfer vessel and record reading as O6. 2.12.2.5 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. 

2.12.2.6 Record air temperature, barometric pressure, and relative 

humidity at the time of the above measurements. 

2.12.2.7 Make a duplicate determination (Run 2). 

3 Calculations 

3.1 Option A – One-point balance calibration. Compute the volume, Vt, for each 

determination using the equation: 

  















 













  















   

1 1 

2 1

4 3

s w a

s a

t O O

M

V O O

  



Eqn. 3.1 
March 2012 

SOP 14 Page 9 of 17 

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

determination using the equation: 

Table 2. Variables for volume equations.

 

Variable Description 

 Ms, Ms1, 

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

s density of MS (g/cm3)

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

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

Vt 

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

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

temperature of the measurement) (cm3 or mL) 

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

each run, using the expression: 

where  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. Compute the mean V20 for the 

duplicate measurements. 

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

care to match the cubical coefficient of expansion units with the units of 

temperature: 

V V  1- ( t - 20 )  20  t 

 1  20   V20  Vt   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

 









Eqn. 3.2

 1  t   ef    ref V V t r t 
March 2012 

SOP 14 Page 10 of 17 

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

liquids follow: 

Commodity Reference 

Temperature 

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

Beer 3.9 oC (39.1 oF)

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

Distilled spirits or petroleum 15.56 oC (60 oF)

Petroleum (International Reference) 15 oC (59 oF)

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)

4 Measurement Assurance 

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

and NISTIR 6969, Sec. 7.4) or conduct replicate measurements per SOP 17 

or 20. Average values of the range or standard deviation of similarly sized 

flasks or volumetric standards may be tracked on a single range chart or 

standard deviation chart according to SOP 17 or 20. A minimum of 12 

replicate measurements are required to establish initial process limits. 

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

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

value. 

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

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

changes in water quality. 

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

the measurement process, sp. 

5 Assignment of Uncertainties 

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

the mass standards used, uc, plus the 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 standards, us, is obtained from the 

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

the expanded uncertainty, U, therefore the reported uncertainty for the 

standard will usually need to be divided by the coverage factor k. Multiple 

mass standards are often used, so see SOP 29 for treatment of dependencies. 

5.2 Standard deviation of the measurement process from control chart 

performance (See SOP No. 17 or 20.) 
March 2012 

SOP 14 Page 11 of 17 

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

when a check standard is available. It may also be estimated based on 

replicate measurements over time. Replicate measurements over time may 

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

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

incorporates a repeatability factor related to the precision of the weighings 

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

uncertainties associated with errors in reading the meniscus. 

5.3 Include uncertainties associated with the reading of the meniscus when 

present. See GMP 3 for details. 

5.4 Other standard uncertainties usually included at this calibration level 

include uncertainties associated with water temperature measurements, 

thermometer accuracy, calculation of air density, standard uncertainties 

associated with the density of the 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) 
March 2012 

SOP 14 Page 12 of 17 

Appendix A 

Gravimetric Calibration Data Sheet (Option A) 

Laboratory data and conditions: 

Vessel ID Operator 

Material Date 

Cubical Coefficient of Expansion Before After 

Balance Temperature 

Load Pressure 

Standard deviation of the process, 

from control chart, sp

Relative Humidity 

Degrees of Freedom Water temperature (for 

reference)

Mass standard(s) data:

ID (Note ID and for Filled 

or Empty Load) Nominal Mass Correction* Expanded Unc: 

From cal. report 

Unc: 

k factor 

Density 

g/cm3 

S 

S 

S 

S 

S 

*Mass Correction = True Mass if using buoyancy correction. Density is required for buoyancy corrections. 

Observations: 

Run 1 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0.00 

2 MS O2 

3 Empty or Drained O3 

4 Filled O4 

 tw: 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0.00 

2 MS O2 

3 Empty or Drained O3 

4 Filled O4 

 tw: 
March 2012 

SOP 14 Page 13 of 17 

Example 

Gravimetric Calibration Data Sheet (Option A) 

Laboratory data and conditions: 

Vessel ID 321 Operator 10/1/99

Material Soda-lime glass Date GH

Cubical Coefficient of Expansion 0.000025 / °C Before After 

Balance LC 5100 Temperature 22.4 C 22.6 C

Load 2 L Pressure 747.6 mm Hg 748.0 mm Hg

Standard deviation of the process, 

from control chart, sp

0.042 mL Relative Humidity 43 % 47 %

Degrees of Freedom 216 Water temperature (for 

reference) 22.8 °C 22.6 °C

Mass standard(s) data:

ID (Note ID and for Filled 

or Empty Load) Nominal Mass Correction* Expanded Unc: 

From cal. report 

Unc: 

k factor 

Density 

g/cm3 

S 2 kg 0.000123 g 2 mg 2 7.95 

S 

S 

S 

S 

*Mass Correction = True Mass if using buoyancy correction. Density is required for buoyancy corrections. 

Observations: 

Run 1 Weights Balance Observations, Units__g____ 

1 Zeroed Balance O1 0.000 

2 MS O2 2000.003 

3 Empty or Drained O3 654.729 

4 Filled O4 2648.747 

 tw: 22.8 °C 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0.000 

2 MS O2 1999.998 

3 Empty or Drained O3 667.351 

4 Filled O4 2661.365 

 tw: 22.6 C
March 2012 

SOP 14 Page 14 of 17 





 





 



 





  

 





   0.997 586 95 0.001169 625

1

7.95

0.001169 625 1 2 000.003 0

2 000.000123 ( 2 648.747 654.729 ) Vt

Calculate the air density (SOP 2) a:

Round the results to 9 digits. 

Calculate (or look up) the density of the water, w: 

Round the results to 8 digits. 

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: 

3 3  a  1.169 625 mg/cm  0.001 169 625 g/cm

3 22.8 C  0.997 586 95 g/cm

  















 













  















   O O

M

V O O

s w a

s a

t   

 1 1

2 1

4 3

 (1994.018 ) (1.003 446 462 ) 2 000.890 307 mL

 (1994.018 ) ( 0.999 998 562 ) ( 0.999 852 877 ) (1.003 446 462 )

 



t

t

V

V

V V     t 20  t 1    20

V20  2 000.890 307   1  0.000 025  22.8  20   2 000.750 244 mL

 (1994.014 ) (1.003 401812 ) 2000.797261mL

 (1994.014 ) (1.000 001062 ) ( 0.999 852 877 ) (1.003 548 392 )

0.997 633 78 0.001169 625

1

7.95

0.001169 625 1 1999.998 0

2 000.000123 ( 2 661.365 667.351)

 







 





 



 





  

 





  

t

t

t

V

V

V

3 22.6 C  0.997 633 78 g/cm
March 2012 

SOP 14 Page 15 of 17 

 2 000.708 727 mL

2

( 2 000.750 244 2 000.667 209 )

20   V 

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

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 are reported as follows when rounded to two significant 

digits according to NISTIR 6969, GMP 9: 

V V     t 20  t 1    20

V20  2000.797 261 [ 1  0.000025 ( 22.6  20 ) ]  2000.667209 mL

2 2 2

* 2

c s p o

c

u u s u

U u 

  



 0.042 012 * 2 0.084 024 mL

 0.042 012 mL

 ( 0.001) ( 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 1 mL





    

o

p

s s

u

s

U k u
March 2012 

SOP 14 Page 16 of 17 

Appendix B 

Gravimetric Calibration Data Sheet (Option B) 

Laboratory data and conditions: 

Vessel ID Operator 

Material Date 

Cubical Coefficient of Expansion Before After 

Balance Temperature 

Load Pressure 

Standard deviation of the process, 

from control chart, sp

Relative Humidity 

Degrees of Freedom Water temperature (for 

reference)

Mass standard(s) data:

ID (Note ID and for Filled 

or Empty Load) Nominal Mass Correction* Expanded Unc: 

From cal. report 

Unc: 

k factor 

Density 

g/cm3 

S 

S 

S 

S 

S 

*Mass Correction = True Mass if using buoyancy correction. Density is required for buoyancy corrections. 

Observations: 

Run 1 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0.000 

2 Ms1 O2 

3 Empty or Drained O3 

4 Zeroed Balance O4 0.000 

5 MS2 O5 

6 Filled O6 

 tw: 

Run 2 Weights Balance Observations, Units______ 

1 Zeroed Balance O1 0.000 

2 Zeroed Balance O2 

3 Ms1 O3 

4 Empty or Drained O4 0.000 

5 Zeroed Balance O5 

6 MS2 O6 

 tw: 
March 2012 

SOP 14 Page 17 of 17 

Appendix 

Test Notes for Large Provers 

1 Pour and drain times. 

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

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

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

The 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 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 (unless a 

transfer vessel is used). 
This page intentionally made blank. 
March 2012 

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. The 

test itesm are then used as volumetric measurement standards, often for packaged 

commodity verification. If “to contain” calibrations are to be performed, 

appropriate modifications are needed in the procedure to ensure complete drying 

of the flask between calibration runs. 

1.2 Prerequisites 

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

standards used in the calibration. 

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 during the calibration

40 % to 60 %

± 20 % max change / 4 h
March 2012 

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. (This 

procedure relies on calibrated pipets that deliver slightly less than the full nominal 

volume.) Additional water is added to the test flask from a calibrated buret until 

the meniscus in the test item coincides with the calibration graduation mark. The 

sum of the volumes delivered into the wetted flask is equivalent to its "to deliver" 

volume. The process described assumes that the flask is marked with a 10-second 

drain time. If the flask is marked with a drain time other than 10 s, the specified 

drain time should be used rather than the 10 s drain time described. A 30-second 

drain time should be used when a flask has no drain time specified. 

2.3 Equipment 

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

values and which have demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST. 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 values and which have demonstrated metrological 

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

SI through a National Metrology Institute such as NIST. These standards 

are typically made of borosilicate glass. 

2.3.3 Calibrated thermometers, accurate to ± 0.1 °C, with recent calibration values and 

which have demonstrated metrological traceability to the international system of 

 

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. 
March 2012 

SOP 16 Page 3 of 8 

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

NIST to determine water temperature. 

2.3.4 Distilled or deionized water (See GLP 10) of sufficient quality and 

quantity for the calibration. Do not use tap water for this procedure to 

ensure the reference standards are maintained with valid reference values! 

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

inclining the flask so as to avoid splashing of the walls as much as 

possible. When the main drainage stream has ceased, the flask will 

be nearly vertical. Allow an additional 10 second drainage after 

discharge of the flask contents while holding the flask at a 10  to 

15  angle from vertical, then touch off the rim of the flask to 

remove any drops adhering to it. At the same time, check that 

uniform drainage has been achieved. This establishes the "to 

deliver" condition of the flask. Note that some small amount of 

water will remain in the flask. Each flask to be calibrated must be 
March 2012 

SOP 16 Page 4 of 8 

given this "wet-down" treatment immediately before the start of 

the test. 

2.4.3 Conditioning the buret 

2.4.3.1 Fill the standard buret to overflow and drain several times to verify 

uniform drainage. Refill with water. Note that the stopcock bore 

and delivery tip should be filled with water at all times, in contrast 

to the condition for the pipet. 

2.4.3.2 Touch off the delivery tip against the wall of the receiving vessel, 

to remove any droplet adhering to the external surface of the tip. 

This is an operation that must be done every time a measured 

volume of water is delivered from the buret to ensure consistent 

volume delivery. 

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. 
March 2012 

SOP 16 Page 5 of 8 

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 conduct of 

the calibration in an unstable environment. Repeatability problems must 

be corrected before calibration can be completed. 

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

nominal mark) additional graduations should be inspected for proper 

marking and calibrated as well. 

3 Calculations 

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     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 

 Cubical coefficient of expansion of glass of standard (e.g., 0.000010 °C-
March 2012 

SOP 16 Page 6 of 8 

1

 for borosilicate glass) 

 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 

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 (Quality Assurance 

Reference Flask, QARF) or have a suitable range of check standards for the 

laboratory with similar size graduations and neck diameters. See SOP 17 and SOP 

30. 

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

Alternatively a t-test may be incorporated into the process to check the observed 

value against an accepted reference value. (See NISTIR 6969, Section 8). 

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

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

measurement process. 

5 Assignment of Uncertainties 

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

laboratory volumetric standards used, us, plus the standard deviation of the process, sp, at the 95 

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

calculating the uncertainty. 

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

reports for the pipet and buret used for the calibration. The combined standard 

uncertainty, uc, from the calibration report must be used and not the expanded 

uncertainty, U. Therefore, the reported uncertainty for the standard will usually 

need to be divided by a coverage factor, k. Multiple standards are used in this 

procedure; however, they are typically calibrated independently. Multiple 

standard uncertainties are handled according to SOP 29. 

5.2 The standard deviation of the measurement process is obtained from control chart 

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

5.3 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. 
March 2012 

SOP 16 Page 7 of 8 

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 (See GMP 3), the cubical coefficient of 

expansion for the flask under test, use of proper temperature corrections, the 

accuracy of temperature measurements taking into consideration potential 

gradients in the glassware during calibration, round robin data showing 

reproducibility, environmental variations over time, and bias or drift of the 

standard. 

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, applicable reference temperature, 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      ref
March 2012 

SOP 16 Page 8 of 8 

 Appendix 

Calibration of Measuring Flask 

(Volume Transfer Method)

Laboratory data and conditions: 

Test Number Date

Vessel ID Operator

Nominal Volume Before After

Coefficient of Expansion Temperature 

Process standard deviation 

from control chart, sp 

Pressure 

Degrees of Freedom Relative Humidity 

Volume standard(s) data:

ID 

(enter interval if 

needed) 

Nominal Calibrated 

Volume 

Volume 

Correction 

Coefficient of 

Expansion Uncertainty k factor 

Pipet 

Buret 

Buret 

Buret 

Observations:

 Run 1 Run 2 

Calibrated Pipet Volume: Vp 

Buret Volume: 

Final Reading 

Initial Reading 

Difference 

Calibration Correction (if required) 

Corrected Buret Volume, VB 

VTD = VP + VB 

Water temperature at time of test (t) 

  1    20 VTD20  VTD     t  

 Average VTD20 
March 2012 

SOP 17 Page 1 of 5 

 SOP 17 

 

Standard Operating Procedure for 

Control Charts of Laboratory Owned Check Standards 

1 Introduction 

1.1 Purpose 

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

control laboratory owned check standards. 

1.2 Prerequisites 

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

1.2.2 Either a check standard at each nominal value is used or a set of check standards are 

selected to monitor the range of items that are calibrated by the laboratory. 

2 Summary 

A check standard is obtained and calibrated several times initially to establish a reliable mean value 

and to estimate the standard deviation of calibration. All such calibrations are made using the 

applicable procedure that is used for calibration. A reference value may be obtained using a better 

calibration than the one that will be monitored. Directions for preparing and using a control chart for 

monitoring the mean ( x ) and the standard deviation and range chart are given. The x control chart 

monitors the process with respect to both the standard and the variability, while the standard 

deviation or range 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 check 

standard are provided by an outside laboratory accredited to perform the applicable calibrations. 

3 Equipment 

3.1 A check standard is required, and should be constructed of similar materials and design as 

the standards under calibration. 

3.2 All equipment designated in the applicable SOP. 

4 Procedure 

4.1 Initial Measurements 
March 2012 

SOP 17 Page 2 of 5 

4.1.1Calibrate the 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. 

4.1.3A standard deviation may be calculated for each set of runs according to the 

appropriate SOP with a pooled standard deviation determined for the measurement 

process. This is preferred. 

4.1.4Calculate 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. Be sure that only 

absolute values are used in the determination of the range and average range! 

4.1.5Calculate the average range R of the trials, for the n tests as follows: 

 n

R

R  i  Eqn. 1 

Estimate the standard deviation of the process sp, for each set of made runs 

according to the SOP. 

4.1.6 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): 

 * d2

R

s p  Eqn. 2 

4.2 Construction of Control Charts (See also SOP 9) 

4.2.1Construct the following control charts using the data of section 4.1. 

4.2.2Construct an x control chart for a check standard with the following control limits: 

 Reference value (when available) 

 Central Line = x (mean of the average values) 

 Lower warning limit (LWL) = p x  2s

 Lower control (or action) limit (LCL) = p x  3s
March 2012 

SOP 17 Page 3 of 5 

 Upper warning limit (UWL) = p x  2s

 Upper control (or action) limit (UCL) = p x  3s

4.2.3 Construct a Standard Deviation or Range chart using the same approach. However, 

you may use 2 and 3 as the respective multipliers for the Upper Warning Limit and 

Upper Control Limits. Note that there will be no negative numbers when calculating 

standard deviations. 

4.2.4Construct 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

 

4.2.5These limits are t values for 95 % and 99.7 % confidence intervals for a sample size 

of 30. 

4.2.6The recommended format for construction of R control charts is given in NISTIR 

6969, Section 7.4. 

4.3 Use of Control Charts 

4.3.1An appropriate 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 sp or 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 on the standard deviation or range chart is within the control limits, a source 

of systematic error is suspected. 

4.3.3If the values for the standard deviation or range chart fall outside of the warning 

limits but inside of the control limits, a decrease in precision is indicated. Other 

problems should be investigated. 

4.3.4No calibration data should be accepted when the system is out of control. 
March 2012 

SOP 17 Page 4 of 5 

4.3.5If the plotted values for either x , sp 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). 

4.4 Interpretation of Control Chart Data 

4.4.1Demonstration of "in control" status indicates that the calibration process is 

consistent with the past experience of the laboratory. That is to say, there is no 

reason to believe that excessive systematic error or changes in precision have 

occurred. 

4.4.2To the extent appropriate, the precision of measurement of the check standard may 

be extended to the calibration of other standards of similar nominal size made by the 

same measurement method. 

4.4.3Extension of the sp for the check standard to other calibrations assumes that all 

aspects of its calibration correspond to those for the other calibration. 
March 2012 

SOP 17 Page 5 of 5 

 Appendix 

 Control Chart Check Standard Data 

 Check Std ID Nominal Value _____________ 

Test 

Number 

Date Run 1 Run 2 Average of 

Runs

Range* 

|d| = |Run 1 - 

Run 2|

(Max – Min)

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

R

R 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. 

** Use of the standard deviation and pooled standard deviations are preferred to the use of range as an 

estimate of the standard deviation. 

***n is the number of tests used to calculate the control limits.
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March 2012 

SOP 18 Page 1 of 7 

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 test measure prover should be evaluated for conformance to 

appropriate specifications if being used for legal weights and measures 

applications. 

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 of the water between the standard and 

unknown must not change more than 0.5 oC during the calibration. If the unknown 

test measure is mild steel, the change in water 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 or SOP 19 is recommended. 

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 all of the 

standards used in the test. 

 

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. 
March 2012 

SOP 18 Page 2 of 7 

1.2.3 Verify that the slicker-plate type standard to be used has sufficiently small 

standard uncertainties for the intended level of calibration (i.e., less than 

0.2 in3

 with a 95 % confidence interval). 

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, stable to ± 2.0 

C/h 

35 % to 65 % 

± 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 must be selected to 

be within stated laboratory conditions during the measurements. All data 

and appropriate environmental conditions must be documented regardless 

of test location. SOP 19 is a more suitable procedure for non-laboratory 

conditions. 

1.3.3 An increased number of check standard verifications are required to 

ensure continued suitability of calibration values generated in field 

conditions as well as to verify the validity of any standards taken out of a 

secure laboratory environment 

2 Methodology 
March 2012 

SOP 18 Page 3 of 7 

2.1 Scope, Precision, Accuracy 

This procedure is applicable for the calibration of a small test measure within the 

limitations of the standards available. The precision attainable depends on the care 

used in the various volumetric adjustments and readings, in the strict observance 

of drainage times, and the internal cleanliness of the various volumetric vessels 

which can influence their drainage characteristics. The accuracy depends 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 wet-down also ensures consistent retention in the slicker-plate 

type standard. The gauge scale of the test vessel is adjusted to a correct reading, 

as necessary, and then sealed. 

2.3 Equipment 

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

calibration certificate and demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST, and whose volume is 

equivalent to that of the vessel to be calibrated. 

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

certificate and demonstrated metrological traceability to the international 

system of units (SI), which may be to the SI through a National Metrology 

Institute such as NIST. 

2.3.3 Meniscus reading device. (See GMP 3). 

2.3.4 Timing device (Calibration is not required; uncertainty of the 

measurement only needs to be less than 5 s for a 30 s pour time.) 

2.3.5 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 non-foaming detergent and water, as necessary, and rinse 

thoroughly. (See GMP 6). 
March 2012 

SOP 18 Page 4 of 7 

2.4.2 Fill a hand-held 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. If a stationary test 

measure is being calibrated, the valve is opened, the measure is emptied, 

followed by a 30 s drain time after the cessation of flow. This constitutes 

the "wet-down" condition. Filling the vessel from the slicker-plate type 

standard following the instructions in steps 2.4.3 and 2.4.4 will ensure that 

both the standard and vessel are properly “wet-down”. 

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

tension, slightly higher than the rim. Use the slicker plate to strike off 

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

during the leveling process. 

2.4.4 Open the valve at the base at the same time as removing the slicker plate 

from the top of the standar to transfer water from the standard to the 

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

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

neck scale. Record the reading. 

2.4.6 Adjust the graduated 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). 

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

the test volume during calibration. 

NOTE: If excess disagreement, check all vessels for cleanliness, leaks, or other 

damage, identifying and correcting any problems. 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, 

temperature corrections are not made in this procedure. When conditions are not 

reasonably close to 60 oF and temperature corrections are needed, use SOP 19. If 

prover volumes, errors and/or corrections are reported, use calculations provided 

in SOP 19. 
March 2012 

SOP 18 Page 5 of 7 

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. Run 2 will validate the 

setting. Alternatively, the average of Run 1 and Run 2 may be used with the 

adjustment made after Run 2. In that case, a validation run should be conducted to 

ensure correct setting of the gage plate. 

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 Determine and report the volume of the test vessel as follows: 

Prover volume V C - gauge reading  Nom  s Eqn. 1 

where: 

VNom = Nominal Volume (taking care to match units) 

Cs = Correction from the calibration report for the slicker-plate standard 

4 Measurement Assurance 

4.1 Duplicate the process with a suitable check standard. See SOP 17, SOP 20 and 

SOP 30. Plot the check standard volume and verify it is within established limits 

OR a 

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

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

over time. Check standard observations are used to calculate the standard 

deviation of the measurement process which contributes to the Type A 

uncertainty components. 

4.2 If a standard deviation chart is also used for measurement assurance, the standard 

deviation of each combination of Run 1 and Run 2 is calculated and the pooled 

(or average) standard deviation and may be used to estimate the short-term 

variability in the measurement process. The short-term standard deviation may be 

used to incorporate an F-test (Observed vs. Accepted) into the measurement 

process and represents the variability in condition of test measures submitted for 

calibration. 
March 2012 

SOP 18 Page 6 of 7 

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. 

5.1 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 The standard deviation of the measurement process, sp, is obtained from control 

chart for the check standard to reflect performance over time (See SOP 17 or 20, 

and SOP 30). The larger of the value from the standard deviation over time for a 

check standard from Section 4.1 or from the standard deviation chart taken from 

Section 4.2 should be used in the uncertainty calculations. 

5.3 Other standard uncertainties usually included at this calibration level primarily 

include 1) uncertainties associated with the ability to read the meniscus, only part 

of which is included in the process variability due to parallax and visual 

capabilities, and 2) uncorrected temperature corrections related to the cubical 

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

corrections, and the accuracy of temperature measurements. Additional factors 

that might be included are: round robin data showing reproducibility, 

environmental variations over time, and bias or drift of the standard as noted in 

control charts. 

5.4 To properly evaluate uncertainties and user requirements (tolerances), assessment 

of additional user uncertainties may be required by laboratory staff. Through 

proper use of documented laboratory and field procedures, additional uncertainty 

factors may be minimized to a level that does not contribute significantly to the 

previously described factors. Additional standard uncertainties in the calibration 

of field standards and their use in meter verification may include: how the prover 

level is established, how delivery and drain times are determined, the use of a 

proper “wet-down” prior to calibration or use, the cleanliness of the prover and 

calibration medium, prover retention characteristics related to inside surface, 

contamination or corrosion, total drain times, and possible air entrapment in the 

water. 
March 2012 

SOP 18 Page 7 of 7 

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 Volume, reference temperature, uncertainty, material, thermal coefficient 

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

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

temperature(s) at time of test, barometric pressure, relative humidity, and 

any out–of-tolerance conditions. 
This page intentionally made blank. 
March 2012 

SOP 19 Page 1 of 11 

SOP 19 

Standard Operating Procedure for 

Calibration of Graduated Neck-Type Metal Provers 

(Volume Transfer Method)1

1 Introduction 

1.1 Purpose of Test 

This procedure is used to calibrate graduated neck type metal test measures and 

provers (20 L (5 gal) and larger) that are used in verification of petroleum, 

biodiesel, ethanol, milk, and/or water meters. The test measure prover should be 

evaluated for conformance to appropriate specifications if being used for legal 

weights and measures applications. 

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 all of 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 

18, SOP 19, SOP 17, SOP 20, 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. . 
March 2012 

SOP 19 Page 2 of 11 

Table 1. Laboratory environmental conditions. 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 C to 27 C, stable to 

± 2.0 C/h 

35 % to 65 % 

± 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, 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 must be selected to 

be within stated laboratory conditions during the measurements. . All data 

and appropriate environmental conditions must be documented regardless 

of test location. 

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. 

2.3 Equipment 
March 2012 

SOP 19 Page 3 of 11 

2.3.1 Calibrated volumetric standard with recent calibration certificate and 

demonstrated metrological traceability to the international system of units 

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

as NIST. 

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

and a funnel with demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST. 

2.3.3 Meniscus reading device (See GMP 3). 

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

certificate and demonstrated metrological traceability to the international 

system of units (SI), which may be to the SI through a National Metrology 

Institute such as NIST. 

2.3.5 Timing device (calibration is not required; uncertainty of the measurement 

only needs to be less than 5 s for a 30 s pour time.) 

2.3.6 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 must be minimized to 

reduce water retention errors. Care must be taken during wet-downs and 

runs to ensure complete drainage and consistent retention in all hoses or 

pipes. 

2.4 Procedure 

2.4.1 Cleanliness verification 

Fill and drain both the standard and unknown test measure or prover to be 

calibrated and check for visual evidence of soiling and of improper drainage. If necessary, clean with non-foaming detergent and water (see GMP 

6). 

2.4.2 Neck scale plate verification 

2.4.2.1 Fill the unknown prover with water from the standard. Check the 

prover level condition in the same way in which it will be used and 

adjust if necessary. Check the prover system for leaks. This is a 

wet-down run. 
March 2012 

SOP 19 Page 4 of 11 

2.4.2.2 Bleed the liquid level down to a graduation near the bottom of the 

upper neck. "Rock" the prover to "bounce" the liquid level, 

momentarily, to ensure that it has reached an equilibrium level. . 

Read and record this setting to be used as the initial scale reading 

sri for 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 last 

reading will be the final scale reading, srf. The closer the water is 

to the top of the neck, the harder it may be to "bounce" the liquid 

in the gauge. 

2.4.2.5 A plot of scale readings with respect to the total volume of water 

that is added Vw should be linear and will be a gross check of the 

validity of this calibration. 

2.4.2.6 Calculate and assess the accuracy of the neck scale for each 

interval. . The error should be less than 0.5 % of the graduated 

neck volume or 1/4 of a graduation (whichever is smaller). . If more 

than this, the scale should ideally be replaced. Alternatively, a 

Neck Scale Correction Value (NSCV) may be issued with 

instructions to the user if it is anticipated that this correction value 

will be used. 

2.4.2.7 The neck scale correction value is calculated as follows: 

  f i

w

sr sr

V NSCV  

Table 2. Variables for neck scale correction value equation. 

NSCV Neck scale correction 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 
March 2012 

SOP 19 Page 5 of 11 

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 

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 in the 

standard, t1, then adjust the standard prover to its 

reference mark or record the neck reading, and then 

discharge into the unknown prover. Wait 30 s after 

cessation of 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. Record the temperature of water in the 

standard for each drop, t1 to tN. Level the unknown 

prover as necessary and record the neck reading. 

Measure the temperature of the water in the unknown 

prover, tx, and record. An average temperature, 

calculated from temperatures taken at multiple locations 

from within the unknown prover may be appropriate. 

2.4.3.2.3 Perform the calculations described in section 3 to 

determine the prover volume at the appropriate 

reference temperature. 

2.4.3.4 Adjust the scale as needed. If adjusted, record the adjusted prover 

gauge reading for determining the “as left” value for Run 1. Run 2 

will validate the setting. Alternatively, the average of Run 1 and 

Run 2 may be used with the adjustment made after Run 2. In that 

case, a validation run should be conducted to ensure correct setting 

of the gage plate. 
March 2012 

SOP 19 Page 6 of 11 

2.4.3.5 Run 2 - Repeat the process described in 2.4.3.2. The duplicate 

determination should agree with the former within ± 0.02 % of the 

volume. The test measure or prover must be capable of repeating 

within 0.02 % of the test volume during calibration. 

NOTE: If excess disagreement, check all vessels for cleanliness, leaks, or 

other damage, identifying and correcting any problems. 

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. 

2.4.3.7 Seal the equipment as specified in the 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 

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 



 

    

x x

S

X t

V t V

 

 

 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 

  

 

            

x x

S S N S N N

X t

V t V t V t V

 

      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 

   N , ,..., 1 2

density of the water in the standard prover where 1 is the density of the water 

for the first delivery, 2 is the density of the water for the second delivery, and 

so on until all N deliveries are completed 
March 2012 

SOP 19 Page 7 of 11 

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 

 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 

x 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. 

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 
March 2012 

SOP 19 Page 8 of 11 

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.) 

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

 

 

 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

 

                   

 Eqn. 7 

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 
March 2012 

SOP 19 Page 9 of 11 

temperature, tref S

   N , ,..., 1 2

density of the water in the standard where 1 is the density of the water 

for the first delivery, 2 is the density of the water for the second 

delivery, and so on until all N deliveries are completed 

1, 2,..., N

volume difference between water level and the reference mark on the 

standard where the subscripts 1, 2,..., N, represent each delivery as 

above. If the water level is below the reference line,  is negative. If the 

water level is above the reference line,  is positive. If the water level is 

at the reference line,  is zero. NOTE: units must match volume units 

for the standard. 

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

 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 

x 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 materials must match the unit assigned to the 

temperature measurement. 

4 Measurement Assurance 

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

standards for the laboratory. .See SOP 17, SOP 20 and SOP 30. .Plot the check 

standard volume and verify it is within established limits OR a 

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

mean of the check standard observations is used to evaluate bias and drift over time. 

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

measurement process which contributes to the Type A uncertainty components. 

4.2. If a standard deviation chart is used for measurement assurance, the standard deviation 

of each combination of Run 1 and Run 2 is calculated and the pooled (or average) 

standard deviation is used as the estimate of variability in the measurement process. 

Note: the pooled or average standard deviation over time will reflect varying 

conditions of test items that are submitted to the laboratory. 

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, 
March 2012 

SOP 19 Page 10 of 11 

sp, at the 95 % level of confidence. See SOP 29 for the complete standard operating 

procedure for calculating the uncertainty. 

5.1.1 The standard uncertainty for the standard, us, is obtained from the calibration 

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

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

need to be divided by the coverage factor k. See SOP 29 for the complete 

standard operating procedure for calculating the uncertainty when multiple 

deliveries or multiple standards are used. Fifteen is the maximum 

recommended number of deliveries from a laboratory standard to a prover 

under test to minimize calibration uncertainties to the levels identified 

previously. 

5.2 Neck calibration uncertainty should be estimated based on the uncertainty of standards 

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

5.3 The standard deviation of the measurement process sp, is taken from control chart for a 

check standard or from standard deviation charts from provers of similar size (See 

SOP 17, SOP 20 and SOP 30). 

5.4 Other standard uncertainties usually included at this calibration level primarily 

include 1) uncertainties associated with the ability to read the meniscus, only part of 

which is included in the process variability due to parallax and visual capabilities, and 

2) uncertainties associated with temperature corrections that include values for the 

cubical coefficient of expansion for the prover under test, the accuracy of temperature 

measurements, and factors associated with potential gradients in measuring the 

temperature in test measures or provers. Additional factors that might be included are: 

round robin data showing reproducibility, environmental variations over time, and bias 

or drift of the standard as noted in control charts. 

5.4.1 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 

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. 
March 2012 

SOP 19 Page 11 of 11 

6 Report 

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

addition of the following: 

Prover volume, reference temperature, uncertainty, material, thermal coefficient of 

expansion (assumed or measured), construction, any identifying markings, tolerances 

(if appropriate), laboratory temperature, water temperature(s) at time of test, 

barometric pressure, relative humidity, and any out–of-tolerance conditions. 

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). 
This page intentionally made blank. 
March 2012 

SOP 20 Page 1 of 4 

 SOP 20 

 

Standard Operating Procedure 

for 

Standard Deviation and Range Charts 

 

1 Introduction 

 

 1.1 Purpose 

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

measurement process using standard deviation charts or range charts for any calibration 

method where it is not practical or feasible to maintain laboratory check standards. 

 

 1.2 Prerequisites 

 The procedure must match the calibration procedure that is being monitored. 

 

2 Summary 

 

 Because of the size and cost of some laboratory standards, it is not always practical to have 

check standards remain in the laboratory for the purposes of measurement control. However, 

it is practical to maintain standard deviation (sp) charts or range (R) charts for each nominal 

size standard to evaluate the standard deviation of replicate runs. Directions for preparing and 

using an R control chart that monitors the precision of the test procedure are given. It is 

assumed that standards of the same nominal capacity and design will have similar 

characteristics with respect to the repeatability of tests. Since it is not practical to run a 

sufficient number of tests on each unknown standard to determine the repeatability, the 

absolute difference between replicate test results on are graphed on the same sp or R chart to 

reflect the repeatability of measurement of the unknown standards tested in the laboratory. 

Note: Provers of similar readability may be grouped together on the same chart (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 the respective calibration SOP. 

 
March 2012 

SOP 20 Page 2 of 4 

4 Procedure 

4.1 Data Collection 

4.1.1 Conduct a minimum of two runs on the unknown test item per the designated 

SOP. A minimum of 12 sets of data must be available before a reasonably 

adequate data base is established. Note: 25 to 30 replicate sets of data are 

recommended to determine valid uncertainties. 

 

4.1.2 Tabulate the measured errors as determined by each of the two trials using a 

form such as the one contained in the Appendix. The data may be maintained in 

a spreadsheet or other electronic program in lieu of a paper form. (If the 

unknown item is adjusted after the first trial to indicate zero error the first trial 

reading is evaluated after the adjustment.) 

4.1.3 A standard deviation may be calculated for each set of runs according to the 

appropriate SOP with a pooled standard deviation determined for the 

measurement process. This is preferred. 

4.1.4 Calculate the absolute difference |d| of the two trials and the summation |d|. 

Note that |d| = R, the range of the two trials. Be sure that only absolute values 

are used in the determination of the range and average range! 

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

n

d

R  Eqn. 1 

4.1.6 The estimated 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): 

 * d2

R

s p  Eqn. 2 

4.2 Construct Appropriate Charts 

4.2.1. Construct Standard Deviation Charts and Range Charts using the same 

approach. However, you may use 2 and 3 as the respective multipliers for the 

Upper Warning Limit and Upper Control Limits. Note that there will be no 

negative numbers when calculating standard deviations. 

4.2.2. Construct an R control chart having the following limits: 

 Central Line = R
March 2012 

SOP 20 Page 3 of 4 

 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

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

size of 30. 

 

 4.2.3 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 standard deviation or range are plotted on the appropriate control chart, 

preferably in sequential order. The limits of the charts are such that 95 % of the 

values should fall within the warning limits and rarely should a value fall outside 

the control limits, provided that the system is in a state of statistical control. 

 

 4.3.2 If the values plotted on the standard deviation or range chart fall outside of the 

control limit, a decrease in precision is indicated. Problems with the standards or 

process will need to be investigated. 

 

 4.3.3 No calibration data should be accepted when the system is out of control. 

 

 4.3.4 If a plotted value for standard deviation or range is outside of the warning limit 

but inside the control limit, a second set of 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. 

 

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

to the calibration of other standards of similar type, capacity and design. 
March 2012 

SOP 20 Page 4 of 4 

Appendix 

 Standard Deviation and Range Data 

Standard Capacity: : Laboratory: 

Test 

Number Date Run 1 Run 2 Average of 

Runs

Range* 

|d| = |Run 1 - 

Run 2|

(Max – Min)

Standard 

deviation** 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

SUM 

x  d

n*** = = n

d

R=  

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. 

** Use of the standard deviation and pooled standard deviations are preferred to the use of Range 

as an estimate of the standard deviation. 

***n is the number of tests used to calculate the control limits. 
March 2012 

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 17, SOP 18, SOP 

19, SOP 20, SOP 21, and GMP 3. 

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: 
March 2012 

SOP 21 Page 2 of 17 

Table 1. Laboratory environmental conditions. 

Procedure Temperature Relative Humidity 

Volume 

Transfer 

18 C to 27 C, stable to ± 

2.0 C/h 

35 % to 65 % 

± 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 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 must be selected to 

be within stated laboratory conditions during the measurements. All data 

and appropriate environmental conditions must be documented regardless 

of test location. 

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 
March 2012 

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 and 

demonstrated metrological traceability to the international system of units 

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

as NIST. 

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

calibration certificate and demonstrated metrological traceability to the 

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

National Metrology Institute such as NIST, to calibrate the neck of prover. 

2.3.3 Thermometers (2) accurately calibrated to 0.1 C, with recent calibration 

certificate and demonstrated metrological traceability to the international 

system of units (SI), which may be to the SI through a National Metrology 

Institute such as NIST. 

2.3.4 Meniscus reading device (See GMP 3). 

2.3.5 Timing device (calibration is not required; uncertainty of the measurement 

only needs to be less than 5 s for a 30 s pour time.) 

2.3.6 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 must be minimized to reduce water retention errors. 

Care must be taken during wet-downs and runs to ensure complete 

drainage and consistent retention in all hoses or pipes. 

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 
March 2012 

SOP 21 Page 4 of 17 

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 

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 unknown prover must be internally clean. This 

should be verified by checking that water drains properly from them. If 

necessary, either or both should be cleaned with water and non-foaming 

detergent (see GMP No. 6) to attain good drainage characteristics. 

Additional effort may be required to eliminate scaling from the inside of 

LPG provers. 

2.4.3 Neck scale plate verification 

2.4.3.1 Fill the unknown 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. 
March 2012 

SOP 21 Page 5 of 17 

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 to be used as 

the initial scale reading sri. 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. 

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 last 

reading will be the final scale reading, srf. The closer the 

water is to the top of the neck, the harder it may be to 

"bounce" the liquid in the gauge. 

A plot of scale readings with respect to the total volume of 

water that is added Vw should be linear and will be a gross 

check of the validity of this calibration. 

2.4.3.6 Calculate and assess the accuracy of the neck scale for each 

interval. The error should be less than 0.5 % of the 

graduated neck volume. If more than this, the scale should 

ideally be replaced. Alternatively, a Neck Scale Correction 

Value (NSCV) may be issued with instructions to the user 

if it is anticipated that this correction value will be used. 

2.4.3.7 The neck scale correction value is calculated as follows: 

  f i

w

sr sr

V NSCV   Eqn. 1 

Table 2. Variables for neck scale correction value equation.

NSCV Neck scale correction value 

Vw Total volume of water added to 

neck 

f sr Scale reading, final 

i sr Scale reading, initial 
March 2012 

SOP 21 Page 6 of 17 

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.) 

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 the volume from the standard in the usual manner, and 

record the standard and prover temperature readings. If multiple 

transfers are required, record temperature of the standard at the 

time of each transfer, but that of the prover only after the final 

transfer. "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 
March 2012 

SOP 21 Page 7 of 17 

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 

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 
March 2012 

SOP 21 Page 8 of 17 

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: 

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 60 °F and 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: 
March 2012 

SOP 21 Page 9 of 17 

2

4

d

L

h C

  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 

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. 
March 2012 

SOP 21 Page 10 of 17 

2.4.7.2 Drain prover, then remove plug (5) at the lower neck to 

facilitate drainage below the lower gauge. If time permits, 

let the prover drain overnight. 

2.4.7.3 With the nitrogen cylinder or compressed air connected, 

blow nitrogen or air through the prover to remove 

remaining moisture. Be sure to blow out the drain line and 

any other portions of the system that may have become 

contaminated with water. 

2.4.7.4 If water has entered the pump-off system, pour several 

gallons of alcohol into the prover and pump the alcohol 

through the system to remove the water to prevent it from 

freezing in the pump when LP gas is used. 

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 



 

    

x x

S

X t

V t V

 

  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 

  

 

            

x x

S S N S N N

X t

V t V t V t V

 

      Eqn. 6

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 

   N , ,..., 1 2

density of the water in the standard prover where 1 is the density of the water for 

the first delivery, 2 is the density of the water for the second delivery, and so on 

until all N deliveries are completed 
March 2012 

SOP 21 Page 11 of 17 

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 

 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 

x 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. 

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 
March 2012 

SOP 21 Page 12 of 17 

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

check standards for the laboratory. See SOP 17, SOP 20 and SOP 30. Plot the 

check standard volume and verify it is within established limits OR a 

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

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

over time. Check standard observations are used to calculate the standard 

deviation of the measurement process which contributes to the Type A 

uncertainty components. 

4.2 If a standard deviation chart is used for measurement assurance, the standard 

deviation of each combination of Run 1 and Run 2 is calculated and the pooled 

(or average) standard deviation is used as the estimate of variability in the 

measurement process. Note: the pooled or average standard deviation over time 

will reflect varying conditions of test items that are submitted to the laboratory. 

. 

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. 

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. 

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

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

neck calibration. 
March 2012 

SOP 21 Page 13 of 17 

5.4 The standard deviation of the measurement process sp, is taken from a control 

chart for an LPG check standard (not from charts for a refined fuel check 

standard) or standard deviation charts for LPG calibrations (See SOP 17, SOP 20 

and SOP 30). 

Other standard uncertainties usually included at this calibration level primarily 

include 1) uncertainties associated with the ability to read the meniscus, only part 

of which is included in the process variability due to parallax and visual 

capabilities, and 2) uncertainties associated with temperature corrections that 

include values for the cubical coefficient of expansion for the prover under test, 

the accuracy of temperature measurements, and factors associated with potential 

gradients in measuring the temperature in test measures or provers. Additional 

factors that might be included are: round robin data showing reproducibility, 

environmental variations over time, and bias or drift of the standard as noted in 

control charts. 

5.5 To properly evaluate uncertainties and user requirements (tolerances), assessment 

of additional user uncertainties may be required by laboratory staff. Through 

proper use of documented laboratory and field procedures, additional uncertainty 

factors may be minimized to a level that does not contribute significantly to the 

previously described factors. Additional standard uncertainties in the calibration 

of field standards and their use in meter verification may include: how the prover 

level is established, how delivery and drain times are determined, the use of a 

proper “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: 

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. 
March 2012 

SOP 21 Page 14 of 17 

Figure 1. LPG Prover Schematic
March 2012 

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 spreadsheet 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. 
March 2012 

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
March 2012 

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)
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