CENTER NIST Measurement Services:

/ypp 1 8 1994

NIST Pressure Calibration

Service

NIST

Special

Publication

250-39

Vern E. Bean

U.S. Department of Commerce

Technology Administration

National Institute of Standards and Technology

NIST MEASUREMENT SERVICES:

NIST Pressure Calibration Service

Vern E. Bean

Chemical Science and Technology Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

February 1994

U.S. Department of Commerce

Ronald H. Brown, Secretary

Technology Administration

Mary L. Good, Under Secretary for Technology

National Institute of Standards and Technology

Arati Prabhakar, Director
National Institute of Standards and Technology Special Publication 250-39

Natl. Inst. Stand. Technol. Spec. Publ. 250-39, 98 pages (Feb. 1994)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1994

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
PREFACE

This document describes the NIST Pressure Calibration Service

so that others may benefit from the years of experience of the NIST

pressure metrologists . It is snapshot of the service on 1 October

1992. Since pressure metrology is an active area of research at

NIST, this document will become dated as methods, apparatus and

uncertainties improve.

TABLE OF CONTENTS

page

I. NIST PRESSURE CALIBRATION SERVICE. 1

II. DESIGN PHILOSOPHY AND THEORY. 1

A. Mercury Manometer. 1

B. Controlled-clearance Primary Standard Piston Gages. 4

1. Mass. 7

2. Local acceleration due to gravity. 7

3. Air buoyancy correction. 8

4. Surface tension correction. 9

5. Dimensional metrology of the piston. 11

6. Temperature correction. 13

7. Piston distortion. 14

8. Cylinder distortion. 15

9. Jacket pressure. 19

C. Total Uncertainty of the Primary Standards. 22

D. Transfer Standards and Their Uncertainty. 31

E. Calibration Quality Control. 36

III. CROSS-FLOAT CALIBRATION TECHNIQUE. 42

A. Experimental Arrangement. 43

B. Reference Levels. 47

C. Connections. 49

D. Cleaning. 50

E. Rotation. 51

F. Data Evaluation. 51

IV. INTERNATIONAL INTERCOMPARISONS . 53

A. IMGC. 53

B. BIPM. 58

V. REFERENCES. 63

VI. APPENDIX: SAMPLE CALIBRATION REPORT. 65

V

I. NIST PRESSURE CALIBRATION SERVICE

The National Institute of Standards and Technology (NIST)

provides calibration services for piston gages and pressure

transducers. For gas-operated units, the current pressure range is

7 kPa to 17 MPa (1 to 2500 psi) ; for oil, the range is 1.1 to

280 MPa (160 to 40,000 psi). Special tests for gas-operated units

may be performed as low as 1.4 kPa. Routine calibrations of piston

gages are done using the cross-floating technique with NIST

transfer standard piston gages. The uncertainties in piston gage

effective areas associated with the NIST transfer standard piston

gages are plotted in figures 1 and 2 as a function of pressure for

gas and oil respectively. Both plots represent the use of several

transfer standards. For gas, the uncertainty ranges between 2 2 to

50 parts per million (ppm) ; for oil, it ranges between 40 and 86

ppm. The uncertainties are based on tripled standard deviations

and are discussed in Sections II. C and II. D.

Shipping instructions and scheduling are available by

telephoning the Pressure Group at (301) 975-4832 for gas-operated

gages or (301) 975-4857 for oil-operated gages. The Group Secretary

can be reached at (301) 975-4840.

II. DESIGN PHILOSOPHY AND THEORY

A primary standard for pressure is an instrument that does not

require a pressure calibration in order to measure pressure; it is

characterized by measuring the fundamental units of mass, time,

length and temperature. Primary standards are used to calibrate

NIST transfer standard piston gages, which are then used to

calibrate customers' gages. The primary standards to which the

NIST transfer standards are traceable are a mercury manometer and

controlled-clearance piston gages.

In this section we consider design and operation of the

primary standards, estimated uncertainties for the NIST primary

standards, characterization of the NIST transfer gages, and the

errors due to the calibration process of the transfer gages.

A. Mercury Manometer

1
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(13

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(T3

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3
The essential feature of a manometer is a vertical column of

fluid, suitably contained and supported at the bottom by an applied

pressure. The magnitude of the pressure is the product of the

column height, the density of the fluid, and the acceleration due

to gravity plus whatever pressure is applied to the top surface of

the fluid column. Thus the manometer is a differential pressure

measurement device and is used in the absolute mode when the space

above the top surface of the fluid column is evacuated, or in the

gage mode when that space is at ambient atmospheric pressure. The

greatest limitations of accuracy are due to the uncertainties in

the density of the fluid and in the column height measurements. In

general, at atmospheric pressure, a state-of-the-art manometer will

have a lower uncertainty than a state-of-the-art primary standard

piston gage.

The piston gage has two advantages over the manometer:

portability and ease of use. These two properties and the

stability of the piston gage make it an excellent transfer

standard. In order to meet the demand for reduced uncertainties,

we have used the manometer that was developed at the National

Bureau of Standards (now NIST) for gas thermometry [1] as a primary

standard to calibrate two essentially identical piston gages,

designated as PG28 and PG29, that serve as the reference standards

for the NIST gas pressure calibration service. PG28 then was used

to calibrate several of the transfer standards used routinely in

the calibration service.

A complete description of the gas thermometer manometer and an

evaluation of its uncertainties are found in the literature [1-4].

The manometer operates at pressures up to 0.13 MPa in the absolute

mode with an uncertainty of 2 ppm based on tripled standard

deviations.

B. Controlled-Clearance Primary standard Piston Gages

The controlled-clearance piston gage has been described by

Heydemann and Welch [5] from which portions of the present

discussion have been extracted.

Essentially, a piston gage is a piston fitted into a matching

4
cylinder filled with fluid, loaded with known weights, and rotated

with respect to the cylinder to help attain concentricity of the

piston in the cylinder. The rotation both minimizes the possibility

of and aids in the detection of metal-to-metal contact, which

causes unwanted frictional forces. The upward force due to the

pressure in the system acting on the area of the piston is balanced

against the downward gravitational force due to the weights. The

pressure is defined as the ratio of the downward force to the area.

As the force can be measured with greater accuracy than the

area, the limitation of the accuracy of the gage is in the

determination of the area and how it changes with pressure due to

elastic distortion of the piston and cylinder.

One method of reducing the effect of the distortion is to

provide a means of applying an auxiliary pressure (known as the

jacket pressure) to the outer surface of the cylinder^~^tQ^ control

the width of the annulus between the piston and the cylinder, as in

the controlled-clearance piston gage shown in figure 3.

As the effect on the area due to the elastic distortion of the

cylinder is several times that due to the piston, controlling the

distortion of the cylinder can provide a significant reduction of

inaccuracy. Furthermore, the ability to control the clearance

allows one to obtain the best operating conditions for the

particular pressure transmitting fluid used.

The pressure, p, generated by a controlled-clearance piston

gage operating at its reference level is given by

Mgil - Pa/Pn,)

[1 + (a^ + ttp) (r - T^)] (1 + bp^) [1 + dip^ - pj)]

where

:

M is the mass of the piston plus the total load applied to the

piston,

g is the local acceleration due to gravity,

Pg is the density of the air,

p^ is the density of the metal from which the weights are made,

Y is the surface tension of the fluid.

5
f

p

Figure 3. Schematic representation of a controlledclearance piston gage where P is the pressure under the

piston, F is the total force applied to the piston, and

Pj is the jacket pressure.

6
C is the circumference of the piston where it emerges from the

fluid,

Aq is the area of the piston at the reference temperature and at

atmospheric pressure,

is the linear thermal expansion coefficient for the cylinder,

Op is the linear thermal expansion coefficient for the piston,

T is the temperature of the piston and cylinder at the time of the

pressure measurement,

b is the pressure coefficient of the piston,

p^ is the nominal pressure,

d is the coefficient of the change of area with jacket pressure,

p- is the jacket pressure during operation, and

is the jacket pressure for which the clearance between the

piston and cylinder is extrapolated to go to zero.

As all of the terms in eq (1) must be determined, we shall

consider each in turn.

1. Mass

The values of the masses of all the weights used in the NIST

pressure calibration service are traceable to the NIST Mass

Standards Laboratory. An identifying number stamped into each

weight is used to recall the appropriate mass value and density

from computer memory. Mass values must be known for all parts of

the piston gage supported by the pressure including the piston,

weight hanger or yoke, the weights, and may include thrust

bearings, rotation mechanisms, etc.

2. Local acceleration due to gravity.

The best value of g for a given laboratory site may be

obtained by having on-site measurements made by the Office of

National Geodetic Survey, with uncertainties on the order of 0.1

ppm or better. The next best value of g can be obtained by an

interpolation from a grid of measurements prepared by the same

organization, with typical uncertainties of a few ppm depending on

geographical location. For further information on both of these

services, contact National Oceanic and Atmospheric Administration,

7
National Ocean Survey, Office of the National Geodetic Survey,

Geodetic Information Center, Washington Science Center, Rockville,

MD 20852, [(301) 713-3242].

As a third option, the local acceleration due to gravity, g

can be computed from

9=9^- 0.000308671 + 0.0001118 (72 - h^) (2)

where g^ is the sea level acceleration due to gravity, h is the

elevation in meters of the site above sea-level, and h^ is the

elevation in meters of the general terrain for a radius of 70 km.

g^ is calculated from

= 980.6160 (1 - 0.0026373 cos 24) + 0.0000059 cos^ 2(|)) (3)

where 0 is the latitude. The value of g calculated in this manner

may have an uncertainty of between 10 and 100 ppm depending on the

locality. Without going to geographic extremes, g can vary by 0.1%

within the continental United States.

The value of g we used until recently was measured in Room 129

of the Mechanical Engineering Building, NIST, Gaithersburg , and is

9.801018 ± 0.000005 m s"^ [6]. The value of g used since 1983,

measured in Room A46 of the Metrology Building, is 9.801011 ±

0.000002 m s'^.

3. Air buoyancy correction.

The air buoyancy correction is given by l-Pg/Pm quite

large. For example, it is 147.5 ppm at 23 °C, 30 percent relative

humidity, and 100 kPa barometric pressure for a stainless steel

weight of density 8 g/cm^. The density of moist air has been

tabulated [7,8]. It can be computed from [9]

0 . 0034836 ( P - 0 . 0037960 C7e^) , ,

where P is the barometric pressure in Pa , U is the percent of

8
relative humidity, e^ is the saturation vapor pressure of water, T

is the air temperature in kelvins, Z is the compressibility factor

for moist air. is expressed in kg m^. The appropriate values

of Gg can be calculated from

-5315.56 = 1 .7526 X 10^^ e ^ (5)

where e is the base of natural logarithms. Values of Z are listed

in table 1.

A piston gage is a differential pressure measurement device

measuring the difference of the pressures applied to the top and

bottom of the piston. When the gage is used with the top of the

piston at ambient atmospheric pressure, the unit is operating in

the gage mode. When the gage is used with the top of the piston in

a vacuum, the unit is operating in the absolute mode. When the

piston gage is used in the gage mode, the values for the densities

of the metals from which the weights are made and which are used in

the calculation of the air buoyancy correction must be the

identical values used by the mass laboratory when the true mass

values are calculated. For this case, the density values can be

arbitrary in the sense that they need not be correct for the metal

in question, but they must be identical to the values used by the

mass laboratory.

The situation is different for the absolute mode. Since in

the absolute mode, the air bouyancy force is reduced to zero by

evacuating the space around the weights, an incorrect mass density

value used by the mass laboratory will result in an error in the

mass value. An error of 1 percent in the metal density yields an

error of 1.5 ppm in the pressure. In this case it may be necessary

to determine the density values of the weights by hydrostatic

weighing.

All of the NIST controlled-clearance piston gages operate only

in the gage mode.

4. Surface tension correction.

9
Table 1. Compressibility factor, Z, for COg-free air

Tctnpe r * t ur« 1 at i v« Hun Percent pasc« 1 % Hq) 0 2S 50 75 too

70OO0 C 7 cJ - - 9997 3 . 99972 . 99971 . 99968 . 99960

75000 562 99972 99970 . 99969 9996* 80000 600 0 . 999 70 - 99968 777»-» 5 8S000 637 f, 999^8 - 9996 7 ^^^^ 1 90000 675 1 - 99966 - 9996 5 9996 3 9996 1 99959

95000 712. 6 9996^ 7 7 70 7 1 99960 -99957 100000 750 1 99962 99961 .99959 99958 99956

101 }25 760 0 .99962 . 99960 . 99959 .99957 -99955 105000 787 6 99959 99958 99956 9995*

1 1 0000 825 1 999S8 7777

/

• 99956 9995* 99952

70000 525 0 999 7^ 9997 3 .99971 .99969 99966

75000 562 5 99972 9997

. 99969 99967 9996* 80000 600. 0 99970 99969 .99967 .99965 99963

85000 637. 6 99969 9996 7 99966 -9996* 99961 90000 675 1 9996 7 ^^^^^ . 9996*1 99962 99960

95000 7I2 6 9996s 9996'i .99962 99960 -99958

t 00000 750 I .99963 .99962 .99960 - 99958 -99956

101 )25 760 0 99963 99961 99960 .99958 99956

105000 787 6 9996

1

99960 .99958 .99957 9995*

I 1 0000 825 1 999S9 999S8 .99957 99955 9995)

70000 525 . 0 9997S 999 7 3 .99971 99969 99966

75000 562. 5 9997 3 999 72 .99970 -99967 -9996* 80000 600 0 9997

1

999 70 -99968 99966 99963

85000 637 6 . 9$$69 . 99966 9996* 99961 90000 675 1 99968 99966 -99965 99962 99960

95000 712 6 99966 9996s . 9996

1

99961 99958

1 00000 750 1 9996*. 9996) 99961 99959 99956

101 )25 760 0 9996*. 99962 .99961 99959 99956

105000 787 6 99962 . 9996

1

.99959 99957 99955

1 1 0000 825 1 . 99960 - 99959 .99958 99956 99953

70000 525 0 9997 7 999 99972 99969 99966

75000 562 - 999 7*« - 99972 99970 99968 80000 600 0 999 72 . 999 7

99969 99966 99963 85000 637 h . 99970 - 99969 9996* 999^ t 90000 675 1 99968 - 99967 99965 . 99963 99960

95000 7 1 2 6 99967 99965 9996 3 9996

1

99958

I 00000 750 1 99965 .9996k 99962 99960 9995 7 101 325 760 0 99965 9996 3 -99961 99959 99956

105000 787 6 . 9996 3 . 99962 99960 99958 .99955

1 1 0000 825 1 7770* 99960 . 99958 .99956 9995*

70000 525 0 - 7 7 7 /

0

QQ<1 7<; 77 7 /

7

. 99972 . 99969 . ''9966 75000 562 $ - 9997'* - 999 7

)

9997

1

99968 -9996* 80000 600 0 7 7 7 ' 5 777 /

. 99969 99966 99963 85000 637 6 9997

1

99969 99967 99965 99962 90000 675 1 99969 - 99968 99966 9996 3 99960

95000 71 2 - 99968 - 99966 9996k 99962 99959

1 00000 750 1 . 99966 9996*. . 99962 99960 .99957

101 325 760 0 99965 -9996*1 99962 99960 .99957 105000 787 6 9996^ 9996

)

99961 .99958 .99956

1 I 0000 825 1 - 99963 . 99961 99959 99957 . 9995*

70000 525 0 . 99977 . 99975 9997 3 ^^^^ 99965

75000 562 99975 . 9997) 9997

9996*

80000 600 0 99973 99972 99970 99967 .99963 85000 617 ( 99972 99970 .99962 90000 675 1 - 99970 - 99969 .99966 .9996* -99960 95000 71 ? - 99968 . 99967 99965 99962 999^9

1 00000 ^50 1 99967 99965 .99963 .99961 .99957

101 325 760 0 .99966 99965 -999*3 99960 -99957

105000 787 6 . 99965 99964 99962 . 99959 99956

1 1 0000 825 I - 9996^ . 99962 99960 - 9995 7 . 9995*

70000 J'

J

Q 99977 . 99976 9997 3 99970 99965

75000 562 - 99976 - 999 7*» 99971 9996*

Rnono 600 0 9997^ . 99972 99970 9996 3 85000 6X7 0 ) / 9997) . 99971 99968 99965 . 99962 90000 67^ . 99971 99969 .9996* 99960

.99969 . V9968 99965 . 99962 99959

7CA - 99968 - 7 7 7OO 9996* _ I 99958

101 325 760 0 99967 99966 9996) 99961 .99957 105000 787 6 99966 .9996<i .99962 .94960 .99956

1 10000 825 . 1 99965 99963 99961 .99958 .99955

70000 525 .0 99978 -99976 9997) .99970 99965

75000 562 .5 99976 .99975 .99972 .99968 9996*

80000 600 .0 .99975 .9997) .99970 .99967 -9996) 85000 637 .6 .99973 .99971 -99969 99966 99961 90000 675 . 1 .99972 .99970 .99967 .9996* 99960

95000 712 .6 .99970 99968 99966 .99963 .99959

100000 750 . I .99969 99967 .9996* -99961 .99958

101 J25 760 .0 .99968 99966 .9996* -99961 .99957

1 05000 787 .6 99967 99965 .9996) 99960 99956

1 10000 825 . 1 .99966 9996* .99961 .99959 99955

2J.0

2*.0

25.0

Z6.0

10
yC is the force generated by the surface tension of the fluid

acting on the piston where it emerges from the fluid. y is the

surface tension of the fluid and C is the circumference of the

piston where it emerges from the fluid. The value of the surface

tension for the oil commonly used in NIST piston gages is 3.05 x

-2 10 N/m and is assumed to be accurate within 10 percent. This is

a small and perhaps negligible correction for high pressure gages

but it may have to be taken into account for oil-operated gages at

low pressures . For example, at 1 . 1 MPa, the correction for a gage

with a piston diameter of 0.010 m is 11 ppm. This correction does

not apply to gas-operated gages.

5. Dimensional metrology of the piston.

Aq is the average cross-sectional area of the piston at

atmospheric pressure as determined from numerous measurements of

the diameter along the length of the piston. For a primary

standard every effort is made to obtain a straight and round

piston. Polar plots of the deviation of actual piston diameter

from a nominal diameter are a useful way to check the roundness o

the piston. Figure 4 is such a plot for the piston in the NIST

controlled-clearance gage known as PG27 with a nominal diameter of

8 mm. In this case, the deviations from being perfectly round do

not exceed 7.5 nm.

The Dimensional Metrology Group of NIST presently claims an

"8 uncertainty (one standard deviation) o^ 3.3 x 10 m in the

determination of the diameter of pistoi\s for primary gages

irrespective of their diameter. Thus, on a part-per-million basis,

a perfectly round and straight piston of large diameter will have

a smaller uncertainty in area then a small diameter piston of equal

quality.

The value of used in eq (1) is calculated using the

expression

= ^M^) [1 + 2ap(23 - TJ] (6)

where D is the average piston diameter determined from the

dimensional measurements and T is the temperature in °C at which

11
Figure 4. Talyrond of the piston for PG27.

12
these measurements were made. This expression now defines T^ of eq

(1) to be 23 °C. The NIST dimensional laboratory is maintained at

20 °C to match the dimensional laboratory temperatures of the

European national standards laboratories while the NIST pressure

laboratory is maintained at 2 3 "C to match the normal temperature

of the pressure laboratories in American industry; hence, the

temperature correction.

The appropriate value of D to use in eq (6) is a matter of

judgment where one must consider the piston roundness,

straightness , and the most probable location along its length where

controlling the clearance between the piston and cylinder will

define the gage's working area to be. The uncertainty assigned to

the value of D must take into account all of these considerations

as well as the uncertainties of the dimensional measurement

process

.

6. Temperature correction.

The temperature correction for the area is given by

Cj. = 1 + (a^ + ttp) (r - r^) (7)

The reference temperature T^ is the temperature at which the piston

area assumes the value A^. For a tungsten carbide piston inside a

steel cylinder the correction is on the order of 17 ppm per °C.

An operating piston gage generates heat in three ways:

(a) adiabatic heating in the fluid due to a rapid pressure change;

(b) heat generated by friction in the fluid as it flows up the

annulus; and (c) heat generated by the rotation of the piston.

The temperature gradient along the cylinder length of a

hydraulic piston gage is due only to the heat generated by the flow

of the fluid up through the annulus and is a function of pressure,

viscosity and location along the engagement length. The only

reported measurements of the temperature gradient are for a simple

gage operating at 2 0 MPa. The maximum temperature difference

between the fluid under the piston and the fluid at any location

along the piston engagement length was of the order of 60 mK [10].

Heat generated by piston rotation and that due to adiabatic effects

13
serve only to increase the overall temperature of the system but do

not contribute to the temperature gradient.

Temperature measurements of the cylinder of an operating gage

as a function of jacket pressure indicate the temperature increases

by several hundredths of a degree when a jacket pressure close to

the upper end of the operating range is chosen. This rise has been

used as an indication for the upper limit of the jacket pressure

range

.

Platinum resistance thermometers, thermocouples, and

thermistors have been used to detect the small changes in

temperature in piston gages.

The temperature sensing elements, leads, and read-out should

be calibrated as a unit. The optimum location for the sensor would

be at the working area of the piston and cylinder but this is

seldom possible. Normally, the operating temperature of piston

gages is determined either on the base supporting the cylinder or

on the lower end of the cylinder, which is a compromise of the

measurement. The effect of this compromise must be considered on

a case-by-case basis because of the wide variety in gage design and

in materials of construction.

Thermal expansivity data for many gage materials are listed in

table 2.

7. Piston distortion.

The piston pressure coefficient, b, is computed from elastic

theory using the expression [11]

2) = -ilH-l-ii (8) E

where ju is Poisson's ratio and E is the modulus of elasticity for

the material from which the piston is made. Both values can be

obtained from ultrasonic measurements on the piston material with

an uncertainty of less than 1 percent.

14
Pistons are frequently made from cemented tungsten carbide.

Data for the elastic constants of this and other materials are

listed in table 2. With the data for tungsten carbide C93, the

piston distortion, bp^^, amounts to 2.3 ppm at 4 MPa and to 117 ppm

at 200 MPa.

The calculation of the uncertainty for each parameter in eq

(1) is discussed in Section C. The value of b is the only

parameter of eq (1) that is determined from theory. Since no

satisfactory way of determining the contribution to the uncertainty

due to the inadequacy of the theory for calculating b is available,

Heydemann and Welch [5] suggested that one might multiply the

uncertainty for this term as determined in Section C by a factor of

three as a conservative measure.

8. Cylinder distortion.

The cylinder distortion correction term is

= 1 + G?(p, - Pj)

The value of d can be measured either of two ways:

1. Vary Pj and make corresponding changes in the load on the

piston such that the generated pressure remains constant.

2 . Measure the changes in the generated pressure corresponding to

the changes in Pj

.

Either method requires monitoring the generated pressure which

can be done with any transducer of sufficient sensitivity and short

term stability. In particular, it can be done with a second piston

gage cross-floated against the controlled-clearance piston gage.

In order to develop an expression to determine d from the first

method, we rearrange eq (1) obtaining

W = pAo [1 + (ap + a^) (T - T^) ] (1 + b^) [1 + dip^ - Pj) ] (10)

where W is the numerator of the right hand side of eq (1)

.

Let us designate the controlled-clearance gage as the standard

15
m rt~i oo rf^ C

3 " ° ^ 5

" >^ CO <^J ^ 4_ t

(_ 0) o.

a. Oo

o o o o

o ^ •— ^ oD CO cr.

EE

CD Q. O

c

0) M

>.

r-t > E

t- c

nj (S a.

(U

enc

o

<nm

o

an m

3

c 3 3 o

CO

It) ^

3 ^ 00 O

e

c^ CO ^

t— 3- in -3- ^

^ ^ ^ ^

I I I I I

I o o o o o o

X X X X X

CO m Ln lh in J J J

in ro vD en o o

a\ ro CO o o

(\j m (\j c\j f\j oj m

o o o o o o o

o o o o o o o

in ro ^ •- <NJ ro

(\J CO fM

oo ro

0^ O

e TO •-' -1 <u L

3 j_> X) r) X3 0) <D --<<!) 5_ s_ t. u i:

(0 E (D n) to <o o o o ^ X > c

oj (d (tj <u

0)

c c

0) <D

(n to to 00 00

E- t- f16
and the other gage as the reference. The two piston gages are

brought into balance with some given load on the reference gage.

Then a series of small changes in Pj are made with corresponding

changes in W on the standard such as to keep the two gages in

balance. Experience has shown that during the time required for

these measurements, the temperature change in both gages is of no

consequence. Hence, as we apply eq (10) to the standard, the

variables for the cross-float measurements are W, and Pj . In the

term 1+bp^, bp^ is negligible compared to 1 for the present purpose

and we will regard the entire term as invariant. Since d already

has been used in eq (10) , we use A to denote the total

differential. The relative change in W for the standard gage

becomes

Aw

W

dAp.

(11)

For the purpose of determining d, we now assume d(p2-Pj) is

negligible compared to 1. Solving for d, we obtain

d = AW

WApj

For the second method where the change of the generated

pressure is measured as a function of Pj, an analogous analysis

yields

d = - Ap 13)

The value of d must be determined for a series of pressures

over the operating range of the gage. The value of d is a function

of the pressurizing fluid used in the gage and must be measured for

each fluid.

Figure 5 is a plot of d as a function of load for PG27 which

was determined by the cross-floating technique.

Experimental values of d are generally dependent upon the

applied load. In order to have an expression for interpolation, we

17
200 250 300 350 400 450 500 550 Force jnewtonsj

Figure 5. Experimental values of d plotted as a function of load.

18
find it convenient to use an empirical equation of the form

d = D + EW + FW^ (14)

which is fitted to the experimental values of d and W.

9. Jacket pressure.

To determine the jacket pressure for which the clearance c is

reduced to zero we make the assumption that the leak rate past the

piston is proportional to the third power of the clearance or that

(dV/dt)^^^ = const ' c (15)

where V is the volume of oil bypassing the pa^ton in time t.

Equation (15) is the basic law for laminar flow betweeh lnf initely

extended plane and parallel plates. Instead of observing the leak

rate, dV/dt, it is equivalent and more convenient to measure the

fall rate of the piston, ds/dt, where s is the vertical position of

the piston. Now we rewrite eq (15) as

(ds/dt) = const • c = const ip^ ~ Pj^ ^1^)

where we have assumed c is directly proportional to the difference

between p^, and pj . We can now determine p^ from a measurement of

ds/dt. as a function of Pj.

The piston position of an operating piston gage can be

conveniently measured with a non-contact capacitance proximity

sensor. One method is to mount an aluminum disk on the top of the

weight hanger directly over the piston and then position the sensor

over the center of the disk. The output of the sensor is displayed

on a 250 mm wide strip chart recorder. While the weight stack is

resting on the bottom stops, we raise the disk with shims of known

thickness and thereby calibrate the sensor-recorder combination.

The sensor-recorder combination is adjusted such that the pen

travels about 80 percent of its full range as the piston falls from

0.5 mm above its reference level to 0.5 mm below its reference

level and the pen is at the center of the chart when the piston is

19
at its reference level. A stop watch is used to time the piston's

fall through this central 1 mm. Abnormalities in the recorded

trace are helpful in trouble-shooting.

Linear voltage displacement transducers, laser

interferometers, and dial gages have also been used to make fall

rate measurements.

The gage is valved off from the rest of the pressure system so

as to be leak-tight with the exception of the leakage past the

piston through the clearance. Fall rate measurements are then made

as a function of jacket pressure for each of several different

loads over the operating pressure range. During these

measurements, the clearance must be large enough to maintain a

fluid film between piston and cylinder at all times. The cube root

of the fall rate is a linear function of the jacket pressure over

part of the range. The data may deviate from this linear

relationship at very high and very low jacket pressures. When

either very high or very low jacket pressures are used the

temperature of the piston and cylinder increases by several

hundredths of a degree. At high values of pj this is due to

friction between piston and cylinder. At low jacket pressures it

is due to viscosity in the oil passing through the clearance at

high speed. Either region should be avoided. Friction between

piston and cylinder may cause rapid deterioration of both.

In figure 6, the jacket pressure is plotted as a function of

the cube root of the fall rate for several loads on PG27. The

individual fall rate lines are extrapolated to zero fall rate where

they intersect the vertical axis at corresponding values of p^.

The right hand side of figure 6 shows a plot of the p^ as a

function of load. The extrapolation of this curve to zero load

intersects the vertical axis at p^^. A dashed line in the graph

indicates the operating jacket pressures, which are chosen from the

linear portions of the fall rate curves near the upper ends.

An equation of the form

= - Kids/dt)^/^ (17)

is fitted to data from within the linear portions of the curves of

20
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21
Pj as a function of (ds/dt) for each load W yielding a value of

for each W. Then to obtain an expression for interpolation, an

expression of the form

Pz = Pzo + S^W + q^W^ (18)

is fitted to the p^CW) data.

Pj and p^ are dependent upon the pressurizing fluid and must

be measured for each fluid used.

C. Total Uncertainty of the Primary Standards.

As of 1 October 1992, the primary standard supporting the gas

pressure calibration service is the NIST gas thermometer manometer

(GTM) . The primary standards for the oil pressure calibration

service are three controlled-clearance piston gages.

Identification numbers and pressure ranges are listed in table 3.

The uncertainty for the GTM over its pressure range is 2 ppm

based on tripled standard deviations [1-4]. For the controlledclearance piston gages, each of the parameters of eq (1)

contributes to the overall uncertainty of the pressure calculation

for these piston gages. The fractional uncertainty in p can be

calculated from

^ = P

where the Xj are the parameters of eq (1).

As the estimated uncertainties for some of the parameters

increase as the pressure increases, it is customary to state the

most pessimistic case, that is, the uncertainty at maximum

pressure. Tables 4-6 list the values of the parameters of eq (1)

required to specify the maximum pressure, the expressions and

values for each of the normalized partial derivatives, the

uncertainties in the measurement of the parameters, and the

resulting relative pressure uncertainties for each of these

controlled-clearance gages.

^[p dx^ \

22
Table 3. NIST Primary Pressure Standards

NIST designation Pressure ranges Media

(MPa)

GTM

PG27

PG20

PG67

0.01 to 0.13

2 to 28

30 to 140

37 to 280

gas

oil

oil

oil

23
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26
The temperature of the NIST Dimensional Metrology Laboratory

is maintained at 20 "C to match the temperature of the dimensional

laboratories in European national standards laboratories. The NIST

Pressure Measurement Laboratories are maintained at 2 3 °C to match

the temperature most commonly found in U.S. industrial metrology

laboratories. The last two entries in tables 4-6 marked (*) are

the uncertainties due to changing the reference temperature from

2 0 °C to 2 3 °C.

The estimates for the uncertainties of each parameter (dx,)

are given as one standard deviation (1 a). These estimates come

from a number of sources. In the case of M, g, a^, and a., the

estimates are provided by the laboratories that made the

corresponding measurements. The uncertainty in is estimated on

the basis of the comparison in other laboratories of measurements

with the calculations we have used. Since the controlled-clearance

gages operate only in the gage mode and the identical values of

used by the mass laboratory in determining the true mass values

were used for the air buoyancy correction, the uncertainty in p^^ is

zero. The measurements of y are assumed to be accurate to within

10 percent. As previously mentioned, the uncertainty in is

based on judgment of the departure of the piston from a perfectly

round and straight cylinder and on the quality of the dimensional

measurement process. The uncertainty in the value of b is assumed

to be within three percent. The uncertainty in T-T^ is based on

the calibration and location of the temperature probes. For p^, and

d, the uncertainties are the standard deviations of the residuals

from fitting empirical equations to the pertaining data. The

calibration of the gage on the jacket pressure system gives rise to

the uncertainty in Pj

.

Each of these controlled-clearance standard piston gages has

its own peculiarities that require some comment in addition to the

data given in tables 4-6.

PG27

This gage represents a departure from the earlier design

philosophy in that formerly the pistons and cylinders were usually

custom made by outside contractors to NIST specifications. PG27

27
was designed around a commercially available piston and cylinder.

Because of the required roundness and straightness of the piston

and the cylinder bore and because of the small clearance between

them, the manufacture of these parts demands great skill developed

by long experience. Typically, a firm that produces excellent

pistons and cylinders in a given material, geometry, and size

cannot maintain that quality for a custom job wherein any of these

three factors are changed until they have again developed the skill

required by the new circumstances through long experience. Thus,

custom designs of the highest quality are now far more expensive

than commercially available designs of equal quality.

The piston and cylinder of PG27 were made of tungsten carbide.

The mounting as a controlled-clearance piston gage is an NIST

design employing as many commercially available parts as possible.

Figure 7 is a diagram of PG27.

The values of d and p^ given in table 4 are appropriate for

28 MPa. For any pressure, d can be expressed by the empirical

relation

diPa"^) = 3.425 X 10"^2 - 2.974 x 10"^^ Pv^

where W is in newtons. p^ is given by

p^(Pa) = 4.013 X 10'' + 1.498 X 10^ W

PG2 0

PG20 is an NIST design and is shown in figure 8. In this case

the piston and cylinder are made of tool steel. The unusual

feature of this gage is the nonuniform wall thickness of the

cylinder, the outer diameter of which was tailored in an attempt to

obtain smoother and more uniform operation. As a result, d is an

exponential function of W,

28
n-r-1 nrj ^

thrust bearing

housing

pressure port jacket pressure port

Figure 7. PG27 controlled-clearance piston gage.

29
upper stop bearing

Figure 8. PG20 controlled-clearance piston gage.

30
d(Pa-i) = 8.662 X 10-^2 ^^"•'1''

and

p^(Pa) = 9.3 09 X 10^ + 2.620 x 10"^ W - 0.84 01Pv^2

PG67

Like PG27, PG67 has a commercially available tungsten carbide

piston and cylinder mounted as a controlled-clearance piston gage

of NIST design. The mounting design incorporates as many

commercially available parts as possible. It is shown in figure 9.

For this gage,

diPa'^) = 3.691 X 10'^2 _ 2.470 x 10""^"

and

p^iPa) = 3. 9 52 xlO^ + 2. 965 x 10^ W

D. Transfer Standards and Their Uncertainty.

NIST controlled-clearance primary standard piston gages are

used to calibrate NIST transfer standard piston gages which are

then used to calibrate customers' gages. The NIST transfer

standards are all unmodified, commercially available piston gages.

Use of the transfer standards saves wear on the primary standards

and saves time. The primary standards are generally used only for

international intercomparisons , to calibrate the master gages for

piston gage manufacturers, and to calibrate NIST transfer gages.

As of 1 October 1992, there are four transfer standards used

in the gas calibration program and four for oil. Their NIST

designations, pressure ranges and pressure media are listed in

table 7.

31
CPc c c •H •Hu c m o C m nH -H

to M-t J-i ^ Q)

4-> 0

inw

(d

(dCnco

-p

yj •H

0)oc

(0

<uuI T3

Q) rHo

4->CooO

04

0)

•H

PL4

32
Table 7. NIST Transfer Standard Piston Gages

NIST designation Pressure ranges Mediu

PG22 7 to 105 kPa gas

PG34 69 to 1370 kPa gas

PG13 0.41 to 4T MPa gas

PG23 0.7 to 17.3 MPa gas

PG42 1.1 to 29 MPa oil

PG6 7.2 to 104 MPa oil

PG41 14 to 139 MPa oil

PG21 13.8 to 276 MPa oil
A transfer standard is calibrated against a primary standard

using the cross-floating technique. To calibrate a piston gage is

to determine its area as a function of pressure, known as the

effective area, through pressure measurements. This is done by

connecting both gages to a common pressure line, floating both

pistons at their respective reference levels, and assuring both are

in equilibrium. The process is repeated for several pressures.

The effective area of the transfer standard is calculated from

the known weights on both gages and the known effective area of the

standard. The details of this procedure are considered in the next

section.

In general the effective area of a transfer standard can be

expressed as

A, = A,{1 ^ b^p^ + b,p^') (20)

where A^ is the area at atmospheric pressure, b^ and bj are the

first and second order pressure coefficients, respectively, and p^

is the nominal pressure. The values of these coefficients and the

total estimated uncertainties for the eight transfer standard gages

are listed in table 8.

The basis for the total estimated uncertainty for the oil

transfer standards is the sum of the estimated uncertainty (3 o)

for the primary standard and the tripled standard deviation of the

predicted values resulting from the least squares fit to the

calibration data for the transfer standard.

The situation is somewhat more complicated for the gas

transfer standards. The calibrations of the gas transfer standards

are traceable to the GTM. The GTM was designed to operate only in

the absolute mode. While the gas transfer standards can operate

either in the gage or the absolute mode, the gas calibration

service is operated in the gage mode. There is evidence to suggest

that the effective area for a gas piston gage may not be identical

in the two modes [12]. There is also a body of data that suggests

the effective area of a gas piston gage also depends upon the gas

used [12]. Both of these effects are under investigation. To

establish the total estimated uncertainty for the gas transfer

standards, we again sum the estimated uncertainty (3 o) for the

34
Table 8. Areas, pressure coefficients, and total estimated uncertainties

of NIST pressure transfer standards

Gage Aq, by b. Uncertainty, ppm

PG22 3.357243x10" 0 0 Note 1 PG34 8.397343x10' 0 0 27

PG13 8.389264x10' 0 0 50

PG23 8.390322x10' -1.48x10-'- 0 50

PG42 8.402138x10-' -2.4xl0-'' 0 Note 2

PG6 1.679672x10' -2.8x10-'' 0 77

PG41 1.680278x10' -2.64x10-'' 0 79

PG21 8.402922x10' -2.81x10-'' 0 85

Note 1. From 7 kPa to 34 kPa, 35 ppm.

From 35 kPa to 105 kPa, 22 ppm.

Note 2. From 1.1 MPa to 2 MPa, 86 ppm.

From 2 MPa to 2.3 MPa, 66 ppm.

From 2.3 MPa to 29 MPa, 60 ppm.

Note 3. All uncertainties are based on tripled standard

deviations.

i 35
primary standard and the tripled standard deviation of the

predicted values for the calibration of the transfer standards and

then increased the sums enough to cover the upper limits of the

mode and species-of-gas effects. We expect these uncertainties to

be reduced as research progresses and we learn how to calculate and

predict these two effects.

The calibration traceability of the transfer standards and

various intercomparisons are shown by the diagram in figure 10.

PG23 is a gas-operated gage. Both PG27 and PG6 operate with oil.

Intercomparisons between PG23 and PG6 or PG27 were done using a

gas/oil interface device.

E. Calibration Quality Control.

Primary pressure standards are characterized in terms of

fundamental units, namely: mass, length, time, and temperature.

Transfer standards are calibrated through pressure measurements

against primary standards.

Confidence in the characterization of a primary standard can

be derived through careful error analysis and by intercomparison

with other primary standards characterized in other laboratories by

other people. Such intercomparisons have been done with other

national standards laboratories and are described in Section IV.

International Intercomparisons.

Confidence in the stability over time of a primary standard

can be achieved through periodic recharacterization or by periodic

calibration of transfer standards and tracking the areas of the

transfer standards as a function of time on control charts. If the

areas of the transfer standards remain within acceptable limits

over time, we can then assume both the primary and the transfer

gages are stable. If the areas do not remain within acceptable

limits, then we may need to recharacterize the primary standard in

terms of fundamental units in an effort to identify the problem.

Figures 11-14 are control charts wherein the relative change

of area with respect to the average has been plotted as a function

of the calendar year in which the NIST pressure transfer standards

were calibrated. There are no control charts for PG2 3, PG3 4, PG41,

36
GAS OIL

PRIMARY

STANDARDS

GTM

REFERENCE

STANDARDS

PG28 (0 . 5)

TRANSFER

STANDARDS

PG22 (0.1)

PG34 (1.4)

PG13 (4

)

PG23 (17

PRIMARY

STANDARDS

TRANSFER

STANDARDS

PG2 7 (28)

PG2 0 ( 14 0)^^— .PG21 (276)

PG67 (290)

Figure 10. Intercomparisons involving NIST primary and transfer

standard piston gages. The numbers in parenthesis are the maximum

pressures of the gages expressed in MPa.

37
a

a,

c

-rH

(UCPc

u

>

•H

4-)

(T3 rH

QJ

20 —

-20

1970 1980 1990

Year

Figure 11. The relative change in the area with respect to the

average (3.357205 E-4) for PG22 as a function of calendar year.

The current total uncertainty at the maximum pressure is

represented by the error bar at the right.

38
30 —

a;

c

•H

0)CPc

u

a)>

•H

-P

n3 iH

Q)

-30

1970 1980 1990

Year

Figure 12. The relative change in the area with respect to the

average (8.389305 E-6) for PG13 as a function of calendar year.

The current total uncertainty is represented by the error bar at

the right.

39
m

Q4

to

0)u

«ac

-H

0)CPc

(0o

a)>

-H

+J

rO rH

40

-40

1970 1980 1990

Year

Figure 13. The relative change in the area at the maximum pressure

with respect to the average (1.679203 E-5) for PG6 as a function of

calendar year. The current total uncertainty is represented by the

error bar at the right.

40
to

0)u

«jc

•H

<utpc

o

>

-H

+J

<0

r-i<D

50

0

-50

1970 1980 1990

Year

Figure 14. The relative change in the area at the maximum pressure

with respect to the average (8.396495 E-5) for PG21 as a function

of calendar year. The current total uncertainty is represented by

the error bar at the right.

41
and PG42 as they are too new to have a recalibration history.

The recalibration schedule for a transfer standard is an open

question which depends upon use, abuse, age of the gage, and the

materials from which the piston and cylinder are made. It is

generally accepted by the pressure metrology community that pistons

and cylinders made of tungsten carbide are stable and a

recalibration cycle of a few years is appropriate. However, such

is not the case for steel. There is a report of a new steel piston

in a tungsten carbide cylinder that increased in area by 24.6 ppm

over a period of 15 months and by an additional 9.6 ppm during the

next 21 months suggesting the area was becoming asymptotically

stable with time [13]. The suggested cause was the relieving over

time of strains induced by the manufacturing process. Clearly,

such a unit would warrant frequent recalibration until one became

confident of the stability.

III. CROSS-FLOAT CALIBRATION TECHNIQUE

In principle, we can determine the area and the pressure

coefficient of a piston gage from measurements of the internal

diameter of the cylinder, the diameter of the piston and a

computation of the pressure coefficient using elastic distortion

theory. However, the resulting uncertainties are so large that in

practice piston gage calibrations are done by cross-floating

against a standard.

For this technique, both piston gages are connected to a

common pressure line along with an appropriate pressure generator.

The effective area, A^, of the test gage is

= F/p (21)

where p is the pressure generated at the reference level of the

test instrument by the standard gage and F is the force exerted on

the piston of the test gage which is

42
1 + (ttp + a^) (r - (22)

For simplicity, the temperature correction of the area has been

included with the force. The two gages are brought into pressure

equilibrium by adjusting F and then is calculated by eq (21) . Values of Ag are thus determined over the entire operating pressure

range of the test gage. The effective area at atmospheric

pressure, A^, and the coefficients b, and can be obtained by

fitting

= Aq{1 + b^p + b^p^) - t/p (23)

to the Ag(p) data obtained from the cross-float measurements, t is

a tare that may indicate an error in the data or may be a property

of the gage.

A. Experimental Arrangement.

It is essential that the pistons be vertical so that the force

due to the weights is totally supported by the fluid under the

piston and no component of the force is supported by the cylinder

wall. Manufacturers usually mount levels on the piston gage base,

provide leveling screws, and assure that the piston is normal to

the base. With many designs a level can be temporarily placed

directly on the top of the cylinder.

The pressure connections for a cross-float are shown

schematically in figure 15. The test instrument (A) is connected

to the standard (B) through a short length of tubing. A valve (C)

can interrupt this connection. The differential pressure indicator

(D) can be by-passed by valve (E) . Valve (G) connects to the fluid

supply consisting of a screw pump (H) , gage (K) and reservoir (P) . If a controlled-clearance piston gage serves as the standard, a

separate supply of jacket pressure is required. Valves (C) and (E)

must be constant-volume valves. Markus [14] has developed a pneumatically operated constant-volume valve that has been used at

pressures up to 420 MPa and gives very satisfactory service. The

differential pressure indicator should have a sensitivity of at

least one part in one million and should be rugged enough to

withstand the full line pressure applied differentially without

43
o

4-) oIy)

(/] ouu

V-i owco

+Jo

CDCCOo

x:

-poE

(13 -H

73O

-H

4-1

(T3 £

s:uw . w

-p • c

IT) 0)

<u

Q)

M

^1

p

t7> (d -H 0)

CO

UJ

44
damage

Generally, to calibrate a piston gage using cross-float

techniques, the NIST practice is to make ten measurements at seven

pressures ranging from about ten percent of the full range to the

full range, alternating the direction of rotation of the two

instruments as shown in table 9. A list of weights to be used on

both gages is prepared in advance and if a controlled-clearance

gage is used, the appropriate operating jacket pressures are chosen

from the plot of jacket pressure as a function of the cube root of

fall rate with load as parameter, such as figure 6.

With valves (C) and (E) open and the weight hangers down on

the stops, both gages are loaded and spun. We prefer to spin gages

by hand and allow them to coast to avoid possible vertical force

components resulting from continuous motor drives. Both pistons

are then raised above their operating level by means of the screw

pump (H) and left coasting with valve (G) closed until both gages

have reached temperature equilibrium. With valve (C) closed the

differential pressure indicator is zeroed by opening valve (E) and

making the necessary electrical/mechanical adjustments to the

indicator. Valve (E) is closed and (C) opened, and the weights on

the test gage are adjusted to zero differential pressure. When

balance is attained, the applied loads, the jacket pressure, and

the gage temperatures are recorded. Finally valves (E) and (G) are

opened and the pressure is lowered to bring the weight hangers down

to the bottom stop before loading up for the next point.

The function of the differential pressure indicator is to

detect when the two gages are in pressure equilibrium. While the

indicator is convenient, it is not essential. Equilibrium can be

determined by making fall rate measurements. For this technique

the plumbing system is modified by replacing the differential

pressure indicator with a pressure line and removing the bypass

line and valve. The connection between the two gages now is simply

a pressure line with a constant-volume valve so each gage can be

isolated such that the only fluid loss for each gage is that

bypassing its own piston. With this valve open, the gages are

loaded with appropriate weights to bring the gages near to

equilibrium. Then with the valve closed the fall rate of one of

the gages is measured as the piston is falling through the

45
Table 9. Schedule of points taken during a cross-float

calibration of a piston gage.

Point Pressure Direction of rotation

% of full range standard test

1

2

3

4

5

6

7

8

9

10

10

10

40

70

100

100

85

55

55

25

CW

cw

CW

cw

cw

ccw

ccw

ccw

ccw

ccw

cw

ccw

cw

ccw

cw

ccw

cw

ccw

cw

ccw

46
reference level. The weights on the test gage are then adjusted

until the fall rate is unchanged whether the valve is open or

closed. This is the equilibrium condition.

There are a variety of ways of making the fall rate

measurements. A convenient method is to use commercially available

proximity indicators specifically designed for the purpose.

Another way is to use the capacitance proximity sensor-strip chart

recorder system described above and observe the slope of the

recorded trace as the valve is opened when the falling piston

reaches the reference level. If the slope does not change, the two

gages are in equilibrium. A more cumbersome method is to use a cathetometer and a stop watch. Whatever the choice of fall rate

measurement apparatus, it must not add any unknown vertical forces

to the pistons.

B. Reference Levels.

For piston gages with straight pistons, the reference level is

normally defined as the lower end of the piston. For pistons with

an irregular shape of the submerged part, an adjustment of the

reference level is made as illustrated in figure 16. In this

example the piston has a flange at the lower end serving as a stop.

The volume of the shaded part of the flange is

V = ihTz/4) {D^ - c?2) (24)

If the piston were lengthened such that the volume produced by the

additional length was equal to the volume given by eq (24) , the

length of the piston would increase by

L = SDl^d^ iil.) (25)

where P^/Pj^ ratio of the density of the metal in the shaded

area of figure 16 to the density of the metal in the nonshaded

area. The reference level for a piston of this shape would be

defined as being L below the bottom of the piston.

In a piston gage cross-float, or whenever a piston gage is

47
^

D

REFERENCE LEVEL

Figure 6. Adjustment of reference level for irregularly shaped

pistons.

48
used to generate a known pressure at the reference level of another

instrument, a correction has to be made for the fluid head in the

connecting line. This correction can be expressed as

P

= gHiPfj^ (1 + pK) - p^^J (26)

where g is the acceleration due to gravity, H is the vertical

separation between the reference levels, p^^ is the density of the

pressurizing fluid, p is the pressure, k is the compressibility of

the fluid, and pg-^ is the density of the air. /? is subtracted from

the pressure generated by the standard instrument at its reference

level. The level difference, H, is counted positive upwards from

the reference level of the standard instrument. The term 1 + pK

corrects for the change of density of the fluid with pressure. The

term -pg,,,gH is the head correction due to atmospheric air density

and is used only when the piston gage is operated in the gage mode.

C. Connections.

When connections are made in a pressure system, care should be

taken to install the properly rated tubing, fittings, valves, etc.

Plumbing material should be chosen to be fully compatible with the

pressure fluid. Stainless steels are widely used in liquid

systems, whereas copper, plastics, rubber, etc., are commonly found

in low pressure gas systems. When threading and coning high

pressure tubing, it is essential that the threads be carefully made

and that cones have the correct angle and proper finish.

All plumbing should be carefully cleaned. If filters are used

in a system, it is necessary to choose a type that will not break

up or expel particles into the pressure fluid.

To obtain the optimum in response time, lines are usually kept

short and internal diameters should be as large as is practicable.

Damping of a system, if necessary, may be achieved through the use

of needle valves, filters or other types of line restrictions.

Proper valve arrangement can make a system highly efficient

and more 1;han one type of valve may be useful. A constant volume

valve, which operates without disturbing the internal pressure of

the system, is a great advantage when used as the isolation valve

49
between two piston gages in a cross-float situation. Damping

valves may be employed in a piston gage intercomparison set-up

where short or long-term oscillations have been detected. Response

time may suffer as a result of using damping valves, but this

situation may be acceptable if the system is made more stable by

using the valves. Nonrotating stem valves offer the advantage of

long valve seat life.

D. Cleaning.

As in most high precision set-ups containing mechanical

components with moving parts, a clean system is necessary. The oil

piston gage will function properly over a longer period of time if

the instrument, lines, and fittings are carefully cleaned. Damage

can result if particles of dirt become lodged between the piston

and cylinder. Oil piston gages should be cleaned with appropriate

solvents whenever a change is made from one oil to another.

Gas piston gages will not function properly when dirty and if

forced to operate under such conditions, damage to the piston and

cylinder is likely.

To obtain the highest performance from a gas piston gage, a

good cleaning technique is essential. One method is to use mild

soap and warm water. The piston and cylinder should be scrubbed

thoroughly, rinsed with warm water, air blasted to remove the water

droplets and finally polished with lens tissue. Before assembling

the piston and cylinder, dry, clean air (or nitrogen) is used to

remove lint particles. The important points in a good cleaning

technique are: (1) remove all foreign material, such as dirt,

grease, and fingerprints, (2) leave no residue, (3) polish,

(4) remove all remaining lint before assembling. It may be

necessary to repeat the cleaning procedure to obtain satisfactory

results. The only way to judge how clean is "clean enough" is by

the performance of the gage. If the gage is clean, floating, and

rotating (by hand) on the order of 30 revolutions per minute, it

should take a few minutes to coast to a gradual stop. It is also

important that the remaining plumbing be clean.

Where the removal of the cylinder is difficult or undesirable.

50
it must be cleaned in place. Water should be used with extreme

care. It is far safer to use a solvent that will evaporate fairly

rapidly.

The piston gage operator should be able to determine from the

behavior of the instrument (spin time, sensitivity, etc.) whether

the instrument is functioning properly. Proper operating

specifications should be available from the operators manual

provided by the manufacturer.

E. Rotation.

In most piston gages an electric motor is provided to rotate

either the piston or the cylinder to relieve friction and to

maintain a continuous film of gas or oil between piston and

cylinder. Heat given off by some drive motors may increase the

temperature of the piston and cylinder above the nominal room

temperature over a period of several hours. Under these conditions

it is difficult to measure the temperature of the piston and

cylinder accurately. Shielding the motor or moving it to a different location may mitigate the problem.

Some commercial units have drive motors which rotate the

piston assembly much faster than is necessary. High speed

rotation of a gas gage can increase the danger of damage. Some

manufacturers recommend the application of a thin film of oil to

the piston and cylinder to prevent galling and to reduce excessive

fall rates. While this procedure may lead to an acceptable fall

rate, it will increase friction and reduce sensitivity. Some

piston assemblies are rotated by threads attached to a drive

mechanism. Unknown vertical forces will be applied to the piston

if these threads are not kept horizontal when the gage is in

operation. Hand rotation of the piston and weight stack is quite

satisfactory since the optimum speed of rotation can be achieved

for each instrument. A rate of 15 to 20 revolutions per minute is

adequate for most gages.

P. Data evaluation.

We determine the effective area and the coefficients of the

test gage by fitting eight equations to the calibration data and

51
then selecting that which is most appropriate. These equations are

variations of eq (23) and are given below.

(27 . 1)

= \

- t/p (27 . 2)

= A,(l + b^p) (27 . 3)

= A^d + b^p) •- t/p (27 . 4)

= Aod + b^p + bjP^) (27 . 5)

= AJl + b^p + b2P^) - t/p (27 . 6)

= A„(l + b^p^) (27 . 7)

= AJl + b^p^) - t/p (27 . 8)

t may be either a tare error in the data that requires

investigation or a coefficient necessary to characterize the

behavior of the gage. At low pressures, the terms involving the

pressure coefficients b^ and b2 are usually insignificant and either

eqs (27.1) or (27.2) is used to characterize the gage. At high

pressures the coefficient b^ and occasionally also b2 become

significant and must be included in the function fitted to the

data. In some cases, the coefficient b^ is insignificant while

is significant.

The computer program used for these computations provides, in

addition to the coefficients, the standard deviations of the

coefficients, the residuals, the standard deviations of the

residuals, and the standard deviations of the predicted values. A

plot of the residuals as a function of pressure will show whether

any gross errors have been made in recording and entering the data

and is a valuable aid in judging which equation is appropriate.

One may also separate the data according to the direction of

rotation of either gage and check for effects depending on the

direction of the rotation.

Selecting the proper fit is a matter of judgment based on the

52
residuals, the standard deviations of the residuals, the standard

deviations of the coefficients, and the standard deviations of the

predicted values of the coefficients. The technique is to find the

fit having no evident systematic structure in the plot of the

residuals as a function of pressure, having the minimum standard

deviation of the residuals, having the minimum standard deviation

of the predicted values of the coefficients, and having no

coefficient that is smaller than its corresponding tripled standard

deviation. When these conditions do not exist for the same fit,

then it is a matter of judgement and compromise. If two fits

represent the data equally well, we would choose the simpler

equation

Our practice is to express the total uncertainty of the

effective area for the test gage as three times the sum of the

standard deviation of the predicted values for the chosen fit plus

the estimated uncertainty (3 a) of the effective area of the

standard

An example of a typical calibration report is in the Appendix.

IV. INTERNATIONAL INTERCOMPARISONS

A primary pressure standard must be characterized in terms of

the fundamental units of mass, length, time and temperature, in

contrast to a secondary standard or transfer standard that is

calibrated through pressure measurements using the primary

standard. An excellent way to test the quality of the

characterization of a primary standard is by comparing it by direct

pressure measurement with primary standards characterized by other

personnel in other laboratories.

Two international intercomparisons of current NIST primary

pressure standards have been done which include a bilateral

intercomparison of gas gages with Istituto de Metrologia "G.

Colonnetti" (IMGC)[15] and a round-robin intercomparison of oil

gages sponsored by Bureau International des Poids et Mesures

(BIPM) [ 13 , 16]

A. IMGC

53
Intercomparisons of pressures generated by a primary standard

gas piston gage (IMGC5) of the Istituto di Metrologia "G.

Colonnetti" were made with pressures generated by a transfer gas

piston gage (PG23) of NIST and a primary standard gas piston gage

(PG24) of NIST. PG 24 has since been retired.

IMGC5 is a simple piston and cylinder in which the area at

atmospheric pressure (determined from the average of the areas of

the piston and of the cylinder) was obtained from direct

dimensional measurements of the diameters. The pressure

coefficient of the area was determined by IMGC by comparison with

another IMGC simple piston and cylinder gas piston gage of 2 MPa

range whose pressure coefficient had been calculated theoretically.

PG23 has a pressure range of 0.7 to 17.2 MPa and was calibrated

against the primary standard PG24, but only over the range of 0.7

to 1.9 MPa. PG24 was a primary standard gas-operated,

controlled-clearance piston gage with the area derived from

dimensional measurements of the piston only, with an empirically

determined correction based on extrapolation of jacket pressure

required to close the cylinder on the piston, and a theoretical

pressure coefficient applied to the deformation of the piston only.

A total of 21 comparisons at 10 different pressures was made

between IMGC5 and PG23. Nitrogen was the pressurizing fluid for

all of the measurements. All of the measurements were done in the

gage mode. One method of evaluating the data was to regard PG2 3 as

the standard and IMGC5 as a test gage to be calibrated and apply

the usual NIST computer program to determine the areas of IMGC5.

This program determines the effective area and the pressure

coefficient of the test gage in terms of those of the standard.

The lowest order equation, eq (27.1), was selected and gives

an effective area of the IMGC gage of 2.000661x10"^ m^ at 23 °C with

a standard deviation of the area of 0.6 ppm. The area of the IMGC

gage given by IMGC is 2.000662x10'^ m^ at 23 °C. The areas are seen

to differ by 0.5 ppm which is less than one standard deviation.

Another method of evaluating the intercomparison was to

calculate the pressure generated by each piston gage according to

the method used by the respective laboratories. The pressures were

referenced to the base of the IMGC piston to account for head

54
corrections. The average of the pressures calculated by IMGC minus

the pressures calculated by NIST is -12.7 Pa with a standard

deviation of the mean of 2 . 0 Pa . The average of the pressures

calculated by IMGC minus the pressures calculated by NIST divided

by the NIST pressure is -5.4 ppm with a standard deviation of the

mean of 1.0 ppm.

Sixteen comparisons were made between IMGC5 and PG24 at five

different pressures. The same equation (eq (27.1)) was selected

for this pair of gages. It gives an effective area of the IMGC

-4 2 . . . gage of 2.000649x10 m at 23 " C with a standard deviation of the

area of 0.6 ppm. The difference in area of the IMGC gage determined

by PG24 in this comparison with that given by IMGC is -6.5 ppm.

The second method of evaluating the intercomparisons was also

applied to this pair of gages. The average of the pressure

calculated by IMGC minus the pressures calculated by NIST is

-6.8 Pa with a standard deviation of the mean of 1 . 1 Pa . The

average of the pressures calculated by IMGC minus the pressures

calculated by NIST divided by the NIST pressures is -6.5 ppm with

a standard deviation of the mean of 0.6 ppm.

Figure 17 is a plot of the differences in pressure calculated

from the characteristics of the gages versus pressure, and

figure 18 is a plot of the relative difference in pressure

calculated from the characteristics of the gages versus pressure.

While a systematic difference in pressure is evident in the data,

it is small compared to the estimated systematic uncertainties.

Both methods of expressing the results of the intercomparisons

show significantly better agreement between the gages (1 to 7 ppm)

than the estimated systematic uncertainty of each of the gages

(IMGC5, 24 ppm; PG23, 30 ppm; and PG24, 28 ppm).

The differences observed between IMGC5 and PG24 (the primary

standard), 6.8 ppm by area comparison and 6.5 ppm by pressure

comparison, indicate that the two different methods of calculating

areas are well verified at this pressure range. The differences

observed between IMGC5 and PG23 (the transfer standard) , 0.5 ppm by

area comparison and 5.4 ppm by pressure comparison, indicate that

the latter gage serves very well as a transfer standard in the

given pressure range.

55
o

00.. cn<

Q.

in

•-^ o

Z3

Q. o

LU

u- O

O 1 0

X-feS-PG24

3 4

PRESSURE. MEGAPASCJkL

Figure 17. Difference in pressure (Pa) versus pressure (MPa) for IMGCS

against PG23 and IMGC5 against PG24. The numbers "2" and "3"

represent the number of replicate data for IMGC5 against PG24

plotted at the same point.

56
o

UJ

crCO

cnUJd

CL S 2

i

•

cnc

c

o LU ru

o

I 0 3 4

PRESSURE. HEGAPASCAL

IHGC5 YS

Q-NBS-PG23

X-^eS-PG24

Figure 18. Difference in pressure divided by pressure (ppm) versus pressure

(MPa) for IMCG5 against PG23 and IMGC5 against PG24. The numbers

"2" and "3" represent the number of replicate data for IMGC5

against PG24 plotted at the same point.

57
B. BIPM

The Working Group on High Pressure of the Comite Consultatif

pour la Masse et les Grandeurs Apparentees of the Bureau

International des Poids et Mesures (BIPM) organized an

intercomparison of the primary standard piston gages of 13 nations

in the range of 20 to 100 MPa [13, 16]. The intercomparison was

accomplished by circulating a transfer standard piston gage among

the participating laboratories where each calibrated it using their

primary standard. The data was then sent to the pilot laboratory

for analysis. This was done in three phases. The participants on

the first phase were Laboratoire National D'Essais (LNE) , Paris,

France, which is also the pilot laboratory; Istituto di Metrologia

"G. Colonnetti" (IMGC) , Torino, Italy; Physikalisch-Techniche

Bundesanstalt (PTB) , Braunschweig, West Germany; National Physical

Laboratory (NPL) , Teddington, United Kingdom; and National Bureau

of Standards (NBS, now National Institute of Standards and

Technology, NIST) , Gaithersburg , MD, USA. The results of the first

phase shown in figure 19 are very instructive. This is a plot of

the relative change of area of the transfer standard as a function

of pressure as determined by each laboratory and compared to a reference value determined by the pilot laboratory. The curve for

NIST is 14 ppm lower than that published in references. 13 and 16

due to improved thermal expansion data for the piston that was not

available earlier. .

Three features of figure 19 to note are:

1. The maximum spread in the data is 78 ppm which occurs at

the maximum pressure. This is within the combined uncertainties of

the laboratories and is very good agreement.

2. The area of the transfer standard increased by nearly

25 ppm during the year required for these measurements as indicated

by the difference on the curves LNEl and LNE2 obtained before and

after circulation to the other laboratories. The transfer standard

has a steel piston and a tungsten carbide cylinder. If we assume

the total change was in the piston, then the corresponding change

in the radius is 60 nm. It has been suggested that the increase in

area is due to relaxation of stresses due to manufacture.

Reference 13 is the first published report of this phenomenon. It

requires further study to be understood. It should not be ignored.

58
50

PPM

A

59
3. The slopes of the curves are different which means that

the various national laboratories do not agree on how the effective

area of the transfer standard changes with pressure.

The differences in the results from various laboratories are

better shown by fitting an equation of the form

^ Aq{1 + hp) (28)

to the data from each laboratory and plotting the residuals as a

function of pressure as has been done in figure 20. Three of the

curves, NPL, PTB, and IMGC are concave upward. NPL determined the

pressure coefficient of their standard using the "similarity"

method [17] wherein two gages of identical geometry, but made of

material having different known elastic moduli are cross-floated,

providing data from which the distortion coefficient was

calculated. Both PTB and IMGC calculated the distortion

coefficient using elasticity theory. The three curves LNEl, LNE2

,

and NIST are concave downward. Both of these laboratories use

controlled-clearance piston gages as their primary standards,

figure 20 implies that there is a fundamental disagreement between

calculational or similarity methods and the controlled-clearance

method

.

All of the methods depend upon assumptions that are open to

question. The controlled-clearance technique utilizes an

auxiliary pressure on the outside of the cylinder to control the

clearance between the piston and the cylinder. It is assumed that

the auxiliary pressure is a linear function of the cube root of the

rate at which the piston falls into the cylinder while the gage is

operating for all loads on the piston. It is necessary also to

extrapolate out of the range of these fall-rate measurements to

obtain values used in the cylinder distortion term. The distance

one must extrapolate is greatly influenced by the roundness of the

piston and cylinder. In the derivation of the equation used in the

calculation method, it is assumed that the pressure in the annulus

is uniform when, in fact, there is a steep pressure gradient. It

is also assumed that there are no shear stresses between planes

passed through the cylinder normal to the cylindrical axis. The

similarity method requires the radial separations between the

pistons and cylinders at zero applied pressure be adjusted as

60
Figure 20. Residuals from fitting straight lines to the area data of the

transfer standard provided by each laboratory and plotted as a function of pressure.

61
closely as possible to be in inverse ratio to the elastic moduli.

Then it is assumed that as the pressure is increased, the pressure

distribution between the pistons and cylinders of the two gages

will be the same. Further research is needed to understand and

reconcile the differences.

62
V. REFERENCES

[I] L. A. Guildner, H. F. Stimson, R. E. Edsinger, and R. L.

Anderson, Metrologia 6, 1 (1970).

[2] L. A. Guildner and R. E. Edsinger, J. Res. Natl. Bur. Stand.

(U.S.) 80A, 703 (1976)

[3] J. F. Schooley, Proceedings of the 1988 Workshop and

Symposium of the National Conference of Standards Laboratories, p.

50-1, August 14-18, 1988.

[4] R. E. Edsinger, and J. F. Schooley, Metrologia 26, 95 (1989) .

[5] P.L.M. Heydemann and B. E. Welch in Experimental

Thermodynamics , Volume II, edited by B. LeNeindre and B. Vodar

(Butterworths, London, 1975), pp. 147-201.

[6] D. R. Tate, J. Res. Nat. Bur. Stand. (U.S.) 72C (1968).

[7] Handbook of Chemistry and Physics , F9 (52nd Edition),

Chemical Rubber Publishing Company, Cleveland, OH (1971).

[8] Precision Measurement and Calibration , U.S. Nat. Bur. Stand.

(U.S.) Handb. No. 77, Vol. Ill, Government Printing Office,

Washington, DC (1961) .

[9] R. M. Schoonover, J. Res. Nat. Bur. Stand. (U.S.) 8^, 341

(1980)

[10] B. E. Welch and V. E. Bean, Rev. Sci. Instrum. 5^, 1901

(1984) .

[II] D. P. Johnson, J. L. Cross, J. D. Hill and A. H. Bowman,

Industr. Engng. Chem. 49, 2046 (1957)

[12] B. E. Welch, R. E. Edsinger, V. E. Bean, and C. D. Ehrlich,

Observations of Gas Species and Mode of Operation Effects on

Effective Areas of Gas-Operated Piston Gages, in High Pressure

Metrology . G. F. Molinar, ed., Bureau International des Poids et

Mesures, Monographie 89/1, (1988), p. 81.

63
[13] J. C. Legras, V Bean, J. Jager, S. L. Lewis, G. F. Molinar,

J. Phys. E. Sci. Instrum. , 18, 361 (1985).

[14] W. Markus, Rev. Sci. Instrum. 41, 158 (1972).

[15] J. C. Houck, G. F. Molinar, and R. Maghenzani, J. Res. Nat.

Bur. Stand. (U.S.) 88 253 (1983).

[16] J. C. Lagras, S. L. Lewis, and G. F. Molinar, Metrologia,

25, 21, (1988)

.

[17] R. S. Dadson, in High Pressure Measurement Techniques , edited by G. N. Peggs (Applied Science Publishers, London, 1983),

pp. 39-43.

64
VI. APPENDIX: SAMPLE CALIBRATION REPORT

65
Nisr UNITED STATES DEPARTMENT OF COMMERCE

National Institutse of Standards and Technology

Gaithersburg. Marvland 20893-0001

P-OOOOA

Thermophics Division

A- 55 Metrology Building

Requester

Any One Testing

1234 Some Raod N. E. Pick-a-City, Pick-a-State 12345-1234

Test Instrument Data:

Manufacturer: X Y Z Instrument Corporation

Model: Pr 1111

Serial Number: Zlll

Piston Number: Zlll

Cylinder Number: ZC-ZOOO

Pressure Range: 1.38 MPa To 6.89 MPa

Cylinder Type: Simple

Thermal Expansion Coefficient of Piston: 4.55xlO'V°C

Thermal Expansion Coefficient of Cylinder: 4.55xlO'V°C

Nominal Piston Area: 1.39x10"^ m^

Test Record Data:

Purchase Order Number and Date: TPO87654-43210 Dated 9/21/93

NIST Identification Number: P-OOOOA

NIST Test folder Number: TN-912543-93

Date Instrument was Received: November 31, 1993

Date Test was Completed: December 31, 1993

Test Conditions:

NIST Standard and Calibration Reference: PG 42, August 1988

Reference Temperature: 23°C

Pressure Fluid: Spinesso 22

Pressure Range of Calibration: 1.4 MPa To 6.9 MPa

Surface Tension of Fluid: 3.09E-2

Rotation of Weights: Manual

Test Gage Weights Provided by: NIST

The test gage was leveled so that the axis of rotation was vertical.

Reference level of test piston: The reference level is 0.073 meter below

the uppermost surface of the piston. The gage was operated at mid-stroke.

The suggested fit for the effective area of the test gage is

Area = 1.422481x10"'' * [ 1 + (-1.481e-12 * P) ]

where P is the nominal pressure in Pa and the area is given in square jneters.

The total uncertainty is 66 ppm based on the approximate triple standard deviation.
The test gage was cross - floated against the NIST standard. The calibration data are given

in Table I. The pressures P are at the reference level of the test gage as determined by the

NIST standard gage. The temperature corrected forces F on the test gage were calculated

using the expression

F =

1 + (ap + a,)(T - 23)

where are the masses of the piston, weight hanger and weights corresponding to P,

Pa is the density of the ambient air,

Pn, is the density of the material from which the weights are made,

g is the local acceleration due to gravity,

7 is the surface tension of the pressurizing fluid,

C is the circumference of the piston in the test gage,

ttp and Qc are the linear thermal expansivities of the piston and cylinder,

and

,

T is the temperature in degrees C of the test gage when operating at

pressure P.

Also listed in Table I is the area of the test gage at each pressure calculated using the

expression

A = F/P

To obtain an expression for calculating the area at any pressure, the P and A data have been

fitted to the following eight equations

F = [AJP (1)

F = [Ao]P t (2)

F = [Aod + bP)] (3)

F = [Aod + bP)]P - t (4)

F = [Aod + bP + cp2)]P (5)

F = [Aod + bP + cp2)]P - t (6)

F = [Aod + cp2) ]P (7)

F = [Aod + cp2)]P - t (8)

where the term in brackets is the area as a function of pressure, Ao is the extrapolated area

at zero applied pressure and at 23 °C, b and c are the first and second order pressure

coefficients for the area and t allows for the possibility of a tare. These coefficients and

the tripled standard deviation associated with each coefficient are listed in Table III.

-2-
The test gage was cross - floated against the NIST standard. The calibration data are given

in Table I. The pressures P are at the reference level of the test gage as determined by the

NIST standard gage. The temperature corrected forces F on the test gage were calculated

using the expression

F = ^i^i^^ - ^a/^m>S ^ 7C

1 + (ap + Q,)(T - 23)

where are the masses of the piston, weight hanger and weights corresponding to P,

Pa is the density of the ambient air,

is the density of the material from which the weights are made,

g is the local acceleration due to gravity,

7 is the surface tension of the pressurizing fluid,

C is the circumference of the piston in the test gage,

Qp and are the linear thermal expansivities of the piston and cylinder,

and

,

T is the temperature in degrees C of the test gage when operating at

pressure P . ^

Also listed in Table I is the area of the test gage at each pressure calculated using the

expression

A = F/P

To obtain an expression for calculating the area at any pressure, the P and A data have been

fitted to the following eight equations

A = A„ (1)

A = A„ - t/P (2)

A = A,(l + bP) (3)

A = A„(l + bP) - t/P (4)

A = A„(l + bP + CP2) (5)

A = A,(l + bP + cp2) - t/P (6)

A = AJI + cp2) (7)

A = A„(l + cp2) - t/P (8)

where the term in brackets is the area as a function of pressure, A^ is the extrapolated area

at zero applied pressure and at 23 °C, b and c are the first and second order pressure

coefficients for the area and t allows for the possibility of a tare. These coefficients and

the tripled standard deviation associated with each coefficient are listed in Table III.

-2A-
P-8465

TABLE I. CALIBRATION DATA

OBS. P F F/P

NO. PRESSURE FORCE ON TEST GAGE EXP. AREA

(MPa) (N) (m^)

1.0 1.427626E+00 2.030777E+02 1.422485E-04

2.0 1.427626E+00 2.030777E+02 1.422485E-04

3.0 2.805465E+00 3.990692E+02 1.422471E-04

4.0 4.872209E+00 6.930563E+02 1.422468E-04

5.0 6.939003E+00 9.870519E+02 I.422469E-04

6.0 6.939003E+00 9.870519E+02 1.422469E-04

7.0 6.250043E+00 8.890501E+02 1.422470E-04

8.0 4.183310E+00 5.950625E+02 1.422468E-04

y.O 4.183310E+00 5.950622E+02 1.422467E-04

10.0 2.116515E+00 3.010678E+02 1.422470E-04

9.0 7.629016E+01 1.281849E+03 1.680228E-05

10.0 3.493786E+01 5.870947E+02 1.680397E-05

TABLE II. COEFFICIENTS AND TRIPLED STANDARD DEVIATION OF THE COEFFICIENTS

FROM FITS ACCORDING TO FORCE

FIT

NO. A„ ± AAq, b ± Ab, (Pa)"^ c ± Ac, (Pa)'^ t ± At, N

1 1.422470E-04 0 . OOOOOOE+00 O.OOOOOOE+00 O.OOOOOOE+00

2.415865E-10 O.OOOOOOE+00 0 . OOOOOOE+00 O.OOOOOOE+00

2 1.422466E-04 O.OOOOOOE+00 O.OOOOOOE+00 - 1 . 556432E-03

4.535476E-10 O.OOOOOOE+00 0 . OOOOOOE+00 2.081027E-03

3 1.422472E-04 -2 . 721360E-13 O.OOOOOOE+00 0 . OOOOOOE+00

1.007865E-09 1.192742E-12 O.OOOOOOE+OO O.OOOOOOE+00-

4 1.422447E-04 1.635692E-12 O.OOOOOOE+00 -4 . 680329E-03

1.397966E-09 1.152939E-12 O.OOOOOOE+OO 2.495582E-03

5 1.422488E-04 - 5 . 644814E- 12 5.434030E-19 O.OOOOOOE+OO

1.880300E-09 5.639562E-12 5.637140E-19 O.OOOOOOE+OO

6 1.422407E-04 9.370780E-12 - 6 . 158568E- 19 -8 . 718216E-03

5.103034E-09 9.613867E-12 7.621957E-19 5.352064E-03

7 1.422470E-04 O.OOOOOOE+OO -1 . 422632E-20 O.OOOOOOE+OO

6.618505E-10 O.OOOOOOE+OO 1.217329E-19 O.OOOOOOE+00

8 1.422456E-04 O.OOOOOOE+00 1.239066E-19 -3 . 716186E-03

8.983719E-10 O.OOOOOOE+00 1.011768E-19 2.190966E-03
P-8465

TABLE III. COEFFICIENTS AND TRIPLED STANDARD DEVIATION OF THEC COEFFICIENTS

FROM FITS ACCORDING TO AREA

FIT

NO. Aq ± AA„, b ± Ab, (Pa) -1 c ± Ac, (Pa) t ± At, N

1.422472E-04

6.563554E-10

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

1.422463E-04

6.179310E-10

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

0 . OOOOOOE+00

2.819330E-03

1.566954E-03

1.422481E-04

1.192298E-09

1.481821E-12

1.826769E-12

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

O.OOOOOOE+00

1.42244IE-04

1.662107E-09

2.194630E-12

1.597867E-12

O.OOOOOOE+00

O.OOOOOOE+00

5.631232E-03

2.238437E-03

1.422498E-04

1.612764E-09

8.910301E-12

6.351027E-12

8.864457E-19

7.450572E-19

O.OOOOOOE+00

O.OOOOOOE+00

1.422401E-04

5.268654E-09

1.058918E-11

1.083068E-11

•7.183443E-19

9.206452E-19

9.268421E-03

4.978454E-03

1.422477E-04

9.297143E-10

O.OOOOOOE+00

O.OOOOOOE+00

1.411765E-19

2.397935E-19

O.OOOOOOE+00

O.OOOOOOE+00

1.422452E-04

1.049333E-09

O.OOOOOOE+00

O.OOOOOOE+00

1.757731E-19

1.531932E-19

4.561128E-03

1.829370E-03

-4-
P-OOOOA

The suggested fit based on the calibration data is fit 3, yielding

for the effective area

Area = [l+(bi P)

where P is the nominal pressure in Pa and the area is in square meters,

chosen from the area fit.

The random uncertainty due to the calibration process can be expressed as the tripled approximate standard deviation of the predicted values of the

area is 6.4 ppm. A measure of the total uncertainty of the area is then

obtained by adding this value to the three sigma estimated systematic

uncertainty of the NIST standard used which is 60 ppm. Thus, the total

uncertainty of the effective area is 66 ppm. Note that this uncertainty is

applicable only over the stated range of calibration, and furthermore is valid

only for the specific operating conditions of this calibration, given on page 1.

NOTE: The mass used for the piston assembly was .0838687 kg, based on a density of 15.40 g/cm^ , as reported by X Y Z Instrument Corp.

For the Director,

National Institute of Standards

and Technology

Charles D. Ehrlich, Physicist

Group Leader, Pressure Group

Thermophysics Division

Center for Chemical Technology

-5-
CE/DW/VB

POOOOA

TN 912543

838/8384607

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS & TECHNOLOGY

CHEMICAL SCIENCE & TECHNOLOGY LABORATORY

GAITHERSBURG, MD 2 0899

Calibration Report Appendix

ONE DOUBLE RANGE DEAD WEIGHT PISTON GAGE

SUBMITTED BY

ANYONE TESTING

12 3 4 SOME ROAD N. E.

PICK-A-CITY, PICK-A-STATE 12345-1234

INSTRUMENT RECEIVED: NOVEMBER 31, 1993 TEST COMPLETED: DECEMBER 31, 1993

REFERENCE: THE PURCHASE ORDER NO.

TPO87654-43210 DATED SEPTEMBER 21, 1993

NIST IDENTIFICATION NO.: P1234

MANUFACTURER: X Y Z INSTRUMENT CORPORATION

MANUFACTURER'S SERIAL NO.: Zlll

MANUFACTURER'S TYPE NO.: 2345-432

WEIGHTS WERE NOT RECEIVED WITH THE INSTRUMENT.

NOMINAL SIZE: 1.4E-4 SQ. METER

REFERENCE TEMPERATURE: T(S) = 23.0 °C.

The instrument was leveled so that the axis of rotation of the piston was

vertical

.

Observations were made with manual rotation of the weights on the test gage

The temperature was maintained near 23 °C and corrections were based on

readings of an attached thermometer.

NIST weights Were used in the calibration.

Reference level and piston position: The reference level is

0.073 meter below the uppermost surface of the weight loading

table. The gage was operated with the piston at mid-stroke.

The instrument was calibrated with Spinesstic No. 22 oil

used as the pressure transmitting fluid.

If a tare error is indicated, it should be added algebraically,

in Pa, to the pressure developed by the gage.

DESCRIPTION

PISTON NO. : Zlll

CYLINDER NO.: ZC-ZOOO

PRESSURE RANGE: 1.3 8 MPA TO 6.89 MPA

CYLINDER TYPE: SIMPLE
Page 2

Values of characteristic parameters of the instrument are given in

the following table(s).

To facilitate the detection of errors the weight numbers, gage

temperatures, direction of rotation (l.=CW, -l.=^CCW) and jacket

pressure Pj are listed for all observations. Observation numbers

101 to 199 refer to the standard and 201 to 299 refer to the test

instrument. Mass and density of the weights are listed in the

PROGRAM weight table on pages 3 and 3(a).

(S . NO

.

TEMP "C ROT p. (Pa)

J ^

' WEIGHT NUMBERS

101. 22 . 34 1. 0. 600 . 601

.

602 . 102 . 22 . 34 ' 1. 0. 600. 601. 602 . 103 . 22 . 37 1

.

0. 600 . 601. 602 . 92 . 104 . 22 . 39 1. 0. 600. 601. 602 . 92 . 93 . 105.

105. 22 .41 1

.

0. 600 . 601

.

602 . 9 2 . 93 . 94 . 95.

106. 22.41 1. 0. 600. 601

.

602 . 92 . 93 . 94 . 95 . 107 . 22.43 -1. 0. 600. 601

.

602 . 9 2 . 93 . 94 . 105 . 108 . 22 . 39 -1. 0. 600. 601. 602 . 92 . 93 . 109. 22 . 39 -1

.

0. 600. 601. 602 . 9 2 . 93 . 110. 22 .40 -1. 0. 600 . 601

.

602 . 105 . 201. 22 . 50 1. 0. 603 . 604 . 6 0 5. 606 . 607 . 608 . 609 . 6 3 0. 632 . 464 . 469 . 4 71. 4 / D . 202 . 22 . 50 -1

.

0. 603 . 604 . ^ r\ r' 607 . 608 . 609 . c ^ r\ b J U . 632 . 464 . 469 . 4 / 1 . 4 / o • 203 . 22.51 1. 0. 603 . 604 . r\ r\ r O (J b . 607 . 608 . 609 . 610. 611. 612 . 613 . 627 . 6 3 0. 4 64. 469 . 473 . 474 . 475 . 4 7 6. 632 . 204 . 22 . 51 -1. 0. 603 . 604 . 605. 606. 607 . 608 . 609 . 610 . 611. 612 . 613 . 614 » 615 . 616. 617 . 618 . 619 . 627 . 630 . 464 . 470. 474 . 477 . 632 . 205. 22.51 1. 0. 603 . 604 . 605 . 606 . 607 . 608 . 609 . 610 . 611. 612 . 613 . 614 . 615 . 616 . 617 . 618 . 619 . 620. 621. 622 . 623 . 624 . 625 . 627 . 630.

632 . 464 . 470 . 473 . 477 . 206. 22 . 51 -1. 0. 603 . 604 . 605 . 606 . 607 . 608 . 609 . 610. 611. 612 . 613 . 614 . 615 . 616. 617 . 618 . 619 . 620 . 621. 622 . 623 . 624 . 625 . 627 . 630 . 632 . 464 . 470. 473 . 477 .
PAGE 2 [cont'd]

2 07 . 22.53 1

.

0 . 603 . 604 . 605. 606. 607 . 608 . 609 . 610. 611. 612 . 613 . 614 . 615 . 616 . 617 . 618 . 619 . 620. 621. 622 . 626. 627 . 628 . 631. 632 . 461. 466 . 468 . 470 . 472 . 2 08 . • 22.48 1. 0. 603 . 604 . 605. 606 . 607 . 608 . 609 . 610. 611. 612 . 613 . 614 . 615 . 616 . 617 . 627 . 630. 632 . 464 . 469.

476.

209. 22.48 -1. 0. 603 . 604 . 605 . 606. 607 . 608 . 609 . 610. 611

.

612 . 613 . 614 . 615. 616 . 617 . 627 . 630 . 632 . 464 . 469 . 477 . 210. 22.48 -1. 0. 603 . 604 . 605. 606 . 607 . 608 . 609 . 610. 611

.

627 . 630. 632 . 464 . 469 . 476.
Page 3

Weights not listed in the Program Weight Table are assigned numbers

600 to 699. Those used in this run ARE listed on this page. They

include piston, weight hangers etc. of the instrument under test.

DENSIT^

(g/cm ) 600

.

0 . 083868700 15 . 400

601

.

0 . 344963100 .J T T \J ~J _i. \J \J 7 . 800

602 . 11

.

799716000 7 . 800

603 . 0 . 081155840 8 . 400

604 . 0 . 1 74999565 8 . 400

605

.

1

.

013779200 7 . 800

606 . 0 . 804402000 7 .800

607 4 , 999401 500 7 .800

\J \J • R • 00024 5000 7 .800

609 . 5 . 00028 ] 000 7 . 800

610 . 5 . 000102000 \J \J \J ^ \J \j \J \J 7 . 800

611

.

5 . 000275000 7 . 800

612 . 4 . 999945000 7 . 800

613 . 5 . 000188000 \J \J \J -1- W \J \J \J 7 . 800

614 . 5 . 00003 5000 7 . 800

615 . 5 . 000232000 \J V-* \J £-1 €-1 \J \J \J 7 . 800

616 . 5 . 000163000 7 . 800

617 . 5 . 000203000 7 . 800

618 . 5 . 000297000 7 . 800

619 . 5 . 000316000 7 .800

620 . 5 . 000114 000 7 .800

6? 1 4 qqqqQnOOO 7 . 800

622 . 5. 000261000 7 .800

623 . 5. 000019000 7 .800

624 . 5 . 000220000 7 .800

625. 5. 000194000 7 .800

626. 3 . 000027000 7 .800

627 . 3 . 000075000 7 .800

628 . 2 . 000027000 7 .800

629 . 0. 999983000 7 .800

630. 0 . 500019700 7 .800

631. 0. 300001000 7 .800

632 . 0. 099997800 8 .400
Page 3 [cont'd]

Listed are the characteristics of the standard used in this test

and available data for the instrument under test.

CHARACTERISTICS OF THE STANDARD

1 . 4200000E+02

8 . 4021380E-05

•2 . 4000000E-12

0 . OOOOOOOE+00

0 , OOOOOOOE+00

3 . 2480000E-02

0 . OOOOOOOE+00

4 . llOOOOOE-06

4 . llOOOOOE-06

0 . OOOOOOOE+00

2 . 3000000E+01

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

8 . 6000000E-05

2 . 4000000E-12

0 . OOOOOOOE+00

Standard

^ Area in m

Pressure Coefficient '1 in Pa

Pressure Coefficient in Pa

Circumference of Piston ip m

Oil Buoyancy (volume in m ) Correction Above Cylinder

Thermal Expansivity of Piston °C

^ Thermal Expansivity of Cylinder °C

Reference Temperature of Standard °C

(Pa)

S^ (Pa'N'^)

Qz (Pa N"^)

D (Pa' ) E (Pa N ) F (Pa N )

3 Sigma A/A

Zero Clearance Jacket Pressure (Coeff)

Jacket Pressure Distortion (Coeff)

Sigma b^

Sigma bCHARACTERISTICS OF INSTRUMENT UNDER TEST

2 . OOOOOOOE+02

1 . 4200000E-04

0 . OOOOOOOE+00

0 . OOOOOOOE+00

0 . OOOOOOOE+00

4 . 2400000E-02

0 . OOOOOOOE+00

4 . 5500000E-06

4 . 5500000E-06

1 . 6300000E-01

2 . 3000000E+01

8 . 5780000E-01

0 . OOOOOOOE+00

3 . 0930000E-02

Instrumen|: Under Test

Area in m

Pressure Coefficient b From Previous Calibration in Pa

-1

-1 Circumference of Piston ip m

Oil Buoyancy (volume in m ) Thermal Expansivity of Piston °C

Thermal Expansivity of Cylinder °C

Difference in Reference Levels in m

Reference Temperature of the Insti^ument Under Test

Density of Pressure Fluid in g/cm

^ Pressure Coefficient of Density in Pa

^ Surface Tension of Pressure Fluid in N m
Page 3(a)

Masses listed in the Program Weight Table are assigned

numbers 001 to 599, and 701 to 2000.

Those used in this calibration are listed on this page.

* File 6tab81.tab MASS TABLE VALUES AS OF 09/91

Air Density used 0.00118 q/cia Local Gravity is 9.801010 m/s^

NUMBER MASS DENSITY

kg g/cm

92 . . 118133230E+02 0. 840E+01

93 . . 118132960E+02 0 . 840E+01

94 . . 118130970E+02 0. 840E+01

95. . 118132870E+02 0. 840E+01

105. . 590641670E+01 0. 840E+01

461. . 226798910E+00 0. 780E+01

464 . . 453600990E-01 0. 780E+01

466. . 136078170E-01 0. 780E+01

468 . . 453596910E-02 0. 780E+01

469. . 226802130E-02 0. 780E+01

470. . 136066550E-02 0. 780E+01

471. . 907253680E-03 0. 780E+01

472 . . 453621850E-03 0. 166E+02

473 . . 226796410E-03 0. 166E+02

474 . . 136055750E-03 0. 166E+02

475. . 907930890E-04 0. 166E+02

476. . 454732690E-04 0. 166E+02

477 . .227166310E-04 0. 270E+01
Page 4

This table lists the force generated by the load on the standard

instrument. An air buoyancy correction has been applied. Also listed

are the corrections for surface tension, temperature, jacket pressure

and pressure coefficient of the standard.

FORCE SURFACE TEMPERATURE JACKET PRESS. FRACTIONAL

NO. STD (N) TENS. (N) CORR . STD PRESSURE COEFF. CHANGE (d)

101. 1.19834E+02

102. 1.19834E+02

103. 2.35600E+02

104. 4.09247E+02

105. 5.82896E+02

106. 5.82896E+02

107. 5.25011E+02

108. 3.51366E+02

109. 3.51366E+02

110. 1.77715E+02

1 . 00461E-03

1 . 00461E-03

1 . 00461E-03

1 . 00461E-03

1 . 00461E-03

1. 00461E-03

1. 00461E-03

1 . 00461E-03

1 . 00461E-03

1 . 00461E-03

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

9 . 99995E-01

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

l.OOOOOE+00 9

99997E-01

99997E-01

99993E-01

99988E-01

99983E-01

99983E-01

99985E-01

99990E-01

99990E-01

99995E-01

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00

0 . OOOOOE+00
Page 5

This table lists the force generated by the load on the instrument

under test. An air buoyancy correction has been applied. Also listed

are the corrections for surface tension, temperature and fluid head

in the connecting lines between the two instruments.

FORCE FLUID BUOY. SURFACE TEMP. CORR. HEAD CORR.

NO. TEST (N) TEST (N) TENS. (N) TEST (Pa)

201. 0. 2030754E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 ^1368504E+04

202 . 0. 2030754E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04

203 . 0. 3990661E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04

204 . 0. 6930518E+03 0 . OOOOOOOE+00 0 . 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04

205. 0. 9870462E+03 0 . OOOOOOOE+00 0 . 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04

206. 0 . 9870462E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999955E+00 -0 . 1368504E+04

207 . 0. 8890450E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999957E+00 -0 . 1368504E+04

208 . 0. 5950584E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04

209. 0. 5950581E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04

210. 0. 3010651E+03 0 . OOOOOOOE+00 0. 1311432E- 02 0 . 9999953E+00 -0 . 1368504E+04
Page 6

After computation of the pressure generated by the standard at the

reference level of the instrument under test, the following functions

are fitted to the data.

FORCE EQUATIONS

FIT 1 F=PAq

FIT 2 F=PAq - t

FIT 3 F=PAq [ 1+ (b^ P) ] FIT 4 F=PAq [l+(b^ P) ]

FIT 5 F=PAo [l+(bi P) + (b2 P ) ] FIT 6 F=PAq [l+(bi P) + (b2 P ) ] FIT 7 F=PAq [l+(b2 P ) ] FIT 8 F=PAq [l+(b2 P ) ] - t

- t

With: F Force on test instrument

P Pressure at Ref Level

^0 Effective Area of test instrument at Zero pressure

b^ and b2 Pressure Coefficients

t Tare Weight (force)

.

This table lists the observation numbers, pressure and the residuals

of the fits converted to the equivalent pressures.

OBS.

NO.

PRESSURE

kPa

RESIDUALS

FIT l,Pa

RESIDUALS

FIT 2, Pa

RESIDUALS

FIT 3, Pa

RESIDUALS

FIT 4, Pa

0 0. OOOOOOE+00 0. OOOOOE+00 - 0. 10942E+02 0. OOOOOE+00 -0. 32903E+02

1 0. 142763E+04 0 . 15982E+02 0 . 80931E+01 0. 14300E+02 0. 23669E+01

2 0. 142763E+04 0 . 15982E+02 0. 80931E+01 0. 14300E+02 0. 23669E+01

.0 0 . 211651E+04 -0 . 61656E-01 - 0. 64775E+01 •-0. 21580E+01 -0. 67546E+01

3 0. 280547E+04 0 . 21611E+01 - 0 . 27815E+01 -0. 91617E-01 0. 83833E+00

8 0 . 418331E+04 -0 . 44270E+01 - 0 . 64232E+01 •-0. 62175E+01 0 . 33221E+00

9 0 . 418331E+04 -0 . 59954E+01 - 0 . 79916E+01 -0. 77859E+01 -0. 12362E+01

4 0. 487221E+04 -0. 47538E+01 - 0. 52769E+01 •-0. 59258E+01 0. 71743E+00

7 0. 625004E+04 0. 36083E+01 0. 60315E+01 0. 44484E+01 0 . 58459E+01

5 0. 693900E+04 -0. 53004E+00 0. 33665E+01 0. 17036E+01 -0. 22384E+01

6 0. 693900E+04 -0. 53004E+00 0. 33665E+01 0. 17036E+01 -0. 22384E+01

)BS. PRESSURE RESIDUALS RESIDUALS RESIDUALS RESIDUALS

NO. kPa FIT 5, Pa FIT 6, Pa FIT 7, Pa FIT 8, Pa

0. 0 . OOOOOOE+00 0 . OOOOOOE+00-0 . 612893E+02 0. OOOOOOE+00 -0. 261249E+02

1. 0 . 142763E+04 0 . 689423E+01 0. 464599E+00 0. 153068E+02 0. 302773E+01

2 . 0 . 142763E+04 0. 689423E+01 0. 464599E+00 0. 153068E+02 0. 302773E+01

10. 0 . 211651E+04 -0 . 811235E+01-•0. 397241E+01 -0. 989297E+00 -0 . 730094E+01

3 . 0 . 280547E+04 -0 . 276921E+01 0. 467506E+01 0. 106687E+01 -0. 109428E+00

8 . 0 . 418331E+04 -0 . 113204E+01 0. 219682E+00 -0. 548556E+01 0. 267605E-01

9. 0 . 418331E+04 -0. 270047E+01-•0. 134875E+01 -0. 705400E+01 -0. 154167E+01

4 . 0 . 487221E+04 0. 151389E+01-0. 198239E+01 -0. 555432E+01 0. 969509E+00

7 . 0 . 625004E+04 0. 821196E+01 0. 278647E+01 0. 394397E+01 0. 647049E+01

5. 0 . 693900E+04 -0. 269595E+01-•0. 653431E+00 0. 739648E+00 -0. 228509E+01

6. 0 . 693900E+04 -0. 269595E+01-•0. 653431E+00 0. 739648E+00 -0. 228509E+01
PAGE 6A

This table lists the observation numbers, pressure and the standard

deviations of the predicted values, expressed in Parts Per Million

(ppm)

.

)BS. PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PRED

NO. KPA FIT l,ppm FIT 2, ppm FIT 3, ppm FIT 4, ppm

0. 0. OOOOOOE+00 0. OOOOOOE+00 0. 693676E-03 0. OOOOOOE+00 0 . 831861E-03

1. 0. 142763E+04 0. 169834E+01 0 . 752192E+01 0. 545154E+01 0. 510055E+01

2 . 0. 142763E+04 0. 169834E+01 0. 752192E+01 0 . 545154E+01 0 . 510055E+01

10. 0. 211651E+04 0 . 169836E4-01 0. 429170E+01 0 . 468090E+01 0 . 242395E+01

3 . 0. 280547E+04 0 . 169836E+01 0 . 274598E+01 0 . 393084E+01 0. 179695E+01

8 . 0. 418331E+04 0 . 169836E+01 0 . 154878E+01 0 . 256607E+01 0 . 143516E+01

9. 0. 418331E+04 0 . 169836E+01 0 . 154878E+01 0 . 256608E+01 0 . 143516E+01

4 . 0 . 487221E+04 0 . 169836E+01 0 . 141854E+01 0 . 204377E+01 0 . 118026E+01

7 . 0. 625004E+04 0 . 169836E+01 0. 150345E+01 0 . 184729E+01 0 . 848793E+00

5. 0. 693900E+04 0 . 169836E+01 0 . 159854E+01 0. 224855E+01 0 . 106683E+01

6. 0. 693900E+04 0. 169836E+01 0. 159854E+01 0. 224855E+01 0. 106683E+01

)BS. PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PRED

NO. KPA FIT 5, ppm FIT 6, ppm FIT 7, ppm FIT 8, ppm

0. 0. OOOOOOE+00 0. OOOOOOE+00 0 . 178402E-02 0. OOOOOOE+00 0 . 730322E-03

1. 0. 142763E+04 0 . 666613E+01 0 . 424899E+01 0 . 442474E+01 0 . 552048E+01

2 . 0. 142763E+04 0 . 666613E+01 0 . 424899E+01 0 . 442474E+01 0 . 552048E+01

10. 0. 211651E+04 0. 446395E+01 0 . 247184E+01 0. 415465E+01 0. 269989E+01

3 . 0. 280547E+04 0 . 300438E+01 0 . 218358E+01 0. 378619E+01 0. 188354E+01

8 . 0. 418331E+04 0. 224036E+01 0. 110234E+01 0 . 280796E+01 0 . 158784E+01

9. 0. 418331E+04 0. 224036E+01 0. 110234E+01 0 . 280796E+01 0. 158784E+01

4 . 0. 487221E+04 0. 216431E+01 0. 113640E+01 0 . 227432E+01 0 . 137160E+01

7 . 0. 625004E+04 0. 147214E+01 0. 889763E+00 0. 184583E+01 0, 940994E+00

5. 0. 693900E+04 0. 175083E+01 0. 866464E+00 0. 237642E+01 0 . 119983E+01

6. 0. 693900E+04 0. 175083E+01 0. 866464E+00 0. 237642E+01 0 . 119983E+01
I

I Page 7

In order to detect any effect due to the rotational direction of the ' pistons, the residuals from FIT 6 are separated with respect to the

direction of rotation of the pistons and tabulated.

)BS . PRESSURE 1 = CW TEST TEST 1=CW STD. STD.

NO. kPa 1=CCW CW, Pa CCW,Pa - 1=CCW CW, Pa CCW,Pa

0. 0 . OOOOE+00 0. 0. OOOOE+00 0 . OOOOE+00 0. 0 . OOOOE+00 0. OOOOE+00

1. 0 . 1428E+ 04 1. 0. 4646E+00 0 . OOOOE+00 1. 0 . 4646E+00 0. OOOOE+00

2 . 0 . 1428E+04 -1. 0 . OOOOE+00 0 . 4646E+00 1. 0. 4646E+00 0. OOOOE+00

10. 0 . 2117E+04 -1. 0. OOOOE+00 3972E+01 -1. 0. OOOOE+00 3972E+01

3 . 0 . 2805E+04 1

.

0 . 4675E+01 0. OOOOE+00 1. 0. 4675E+01 0 . OOOOE+00

8 . 0 . 4183E+04 1. 0. 2197E+00 0. OOOOE+00 -1. 0. OOOOE+00 0. 2197E+00

9 . 0 . 4183E+04 -1. 0. OOOOE+00 1349E+01 -1. 0. OOOOE+00 1349E+01

4 . 0 . 4872E+04 -1. 0. OOOOE+00 1982E+01 1. 1982E+01 0. OOOOE+00

7 . 0 . 6250E+04 1. 0. 2786E+01 0. OOOOE+00 -1. 0. OOOOE+00 0. 2786E+01

5. 0 . 6939E+04 1

.

6534E+00 0. OOOOE+00 1. 6534E+00 0. OOOOE+00

6. 0 . 6939E+ 04 -1

.

0 . OOOOE+00 6534E+00 1. 6534E+00 0. OOOOE+00
PAGE 8

The results of the test, as determined by using the FORCE EQUATIONS,

are compiled in this table. It lists the coefficients and their

tripled standard deviations due to random sources of error and, for

the highest pressure, the uncertainty in pressure due to the

uncertainty in these coefficients.

COEFF, FIT 1 COEFF, FIT 2 COEFF, FIT 3 COEFF, FIT 4

1.422470E-04

0 . OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

1. 422466E-04

0 . OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

1. 422472E-04

2 . 721360E-13

0. OOOOOOE+00

0 . OOOOOOE+00

422447E-04 AREA, M

635692E-12 PRES COEF b

0 . OOOOOOE+00

0. OOOOOOE+00 -1. 556432E-03 0. OOOOOOE+00 -4 . 68 0 3 2 9E-0 3 TARE, N

Pa

-1 OOOOOOE+00 PRES COEF b^ Pa

1. 698359E-06 3 . 188460E-06 7 . 085308E-06 9 . 827898E-06 3 STD DEV

0 . OOOOOOE+00 0. OOOOOOE+00 1. 192742E-12 1. 152939E-12 3 STD DEV

0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 3 STD DEV

0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00

0 . OOOOOOE+00 2 . 081027E-03 0. OOOOOOE+00 2 . 495582E-03 3 STD DEV

2.464246E-02 2.047674E-02 2.540394E-02 1.155705E-02 3 RES STD DEV kPa

A

P

1.698359E-06 5.296785E-06 1.536175E-05 2.035646E-05 3 STD DEV A, /A„ at e ' e

COEFF, FIT 5 COEFF, FIT 6 COEFF, FIT 7 COEFF, FIT 8

1.422488E-04 1

•5. 644814E-12 9

5.434030E-19 -6

422407E-04 1

370780E-12 0

158568E-19 -1

422470E-04

OOOOOOE+00

422632E-20

1.422456E-04 AREA, M

0. OOOOOOE+00 PRES COEF b

0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00 0. OOOOOOE+00

0. OOOOOOE+00 -8 . 718216E-03 0. OOOOOOE+00 -3 . 7 1 6 18 6E-0 3 TARE, N

Pa

-1 1.239066E-19 PRES COEF b. Pa

1. 321839E-05

5. 639562E-12

5. 637140E-19

0. OOOOOOE+00

0. OOOOOOE+00

3 . 587605E-05

9 . 613867E-12

7 . 621957E-19

0. OOOOOOE+00

5. 352064E-03

4 . 652826E-06

0. OOOOOOE+00

1. 217329E-19

0. OOOOOOE+00

0. OOOOOOE+00

6. 315639E-06

0. OOOOOOE+00

1. 011768E-19

0 . OOOOOOE+00

2 . 190966E-03

STD DEV Aq /a

STD DEV b

0 -1

1 STD DEV Pa"^

3 STD DEV T, N

1.833163E-02 8.873121E-03 2.593875E-02 1.279243E-02 3 RES STD DEV kPa

7.949402E-05 1.447085E-04 1.051424E-05 1.340698E-05 3 STD DEV A^ /A^ at

P
\

P(Pa)

0. 14276260E+07

0. 14276260E+07

0 . 28054650E+07

0. 48722090E+07

0. 69390030E+07

0 . 69390030E+07

0. 62500430E+07

0. 41833100E+07

0 . 41833100E+07

0 . 21165150E+07

PAGE

AREA

,

0. 14224854E-03

0 . 14224854E-03

0 . 14224708E-03

0. 14224684E-03

0. 14224694E-03

0. 14224694E-03

0 . 14224704E-03

0. 14224681E-03

0. 14224674E-03

0. 14224696E-03

P(MPa)

0. 14276260E+01

0 . 14276260E+01

0 . 28054650E+01

0 . 48722090E+01

0. 69390030E+01

0 . 69390030E+01

0 . 62500430E+01

0. 41833100E+01

0. 41833100E+01

0. 21165150E+01

2 AREA , mm

0. 14224854E+03

0 . 14224854E+03

0. 14224708E+03

0. 14224684E+03

0. 14224694E+03

0. 14224694E+03

0. 14224704E+03

0. 14224681E+03

0. 14224674E+03

0. 14224696E+03

This data represents the effective area of the

TEST GAGE, determined as the full air buoyancy corrected

force on the test gage divided by the pressure at the

reference level of the test gage. The equations on PAGE 10

are fit to this data.
Area vs Pressure [Data on Page 9)

1.42250E+02 ,

1.42249E+02

E

u

(0 w

L

<

1.42249E+02

I.42248E+02 -

1.4224aE+02

1.42247E+02

1.42247E+02

1,42246E+02

1 2 3 4 5 6 ?

Pressure (MPa)
PAGE 10

After computation of the pressure generated by the standard at the

reference level of the instrument under test the following functions

are fitted to the data.

AREA EQUATIONS

FIT 1 A-Aq

FIT 2 A=An - (t/P)

FIT 3 A=Aq [ 1+ (b^ P) ] FIT 4 A-Aq [l+(b^ P) ] - (t/P)

FIT 5 A-Aq [l+(bi P) + (b2 PJ ] FIT 6 A=Ao [l+(bi P) + (b2 P ) ] - (t/P)

FIT 7 A=Ao [l+(b2 P )

]

FIT 8 A=Aq [l+(b2P)] - (t/P)

With: P Pressure at Ref Level

A Effective Area of Test Instrument at each observation

b^ and b2 Pressure Coefficients

t Tare (force in newtons)

This table lists the observation numbers, pressure and the residuals

of the fits converted to the equivalent pressures.

OBS

.

NO.

PRESSURE

kPa

RESIDUALS

FIT l,Pa

RESIDUALS

FIT 2, Pa

RESIDUALS

FIT 3, Pa

RESIDUALS

FIT 4, Pa

1. 0 . 142763E+04 0. 130298E+02 0 . 272127E+01 0 . 734600E+01 0. 857584E+00

2 . 0 . 142763E+04 0. 130298E+02 0 . 272127E+01 0. 734600E+01 0. 857584E+00

3 . 0. 280547E+04 -0. 324452E+01 -0 . 437363E+01 -0. 868611E+01 0. 255919E+01

4 . 0 . 487221E+04 -0. 138593E+02 -0 . 121910E+01 -0 . 838813E+01 0. 328502E+01

5 . 0 . 693900E+04 -0. 147186E+02 0 . 116912E+02 0 . 143251E+02 -0. 498220E+01

6 . 0. 693900E+04 -0 . 147186E+02 0 . 116912E+02 0. 143251E+02 -0. 498220E+01

7 . 0 . 625004E+04 -0 . 880864E+01 0 . 130111E+02 0. 109705E+02 0. 548043E+01

8 . 0 . 418331E+04 -0. 127313E+02 -0. 468078E+01 -0. 123042E+02 0. 271600E+01

9 . 0 . 418331E+04 -0. 148403E+02 -0. 678980E+01 -0. 144132E+02 0 . 606976E+00

10 . 0 . 211651E+04 -0. 425524E+01 -0 . 997434E+01 -0 . 105213E+02 -0. 639840E+01

)BS. PRESSURE RESIDUALS RESIDUALS RESIDUALS RESIDUALS

NO. kPa FIT 5, Pa FIT 6, Pa FIT 7, Pa FIT 8, Pa

1. 0 . 142763E+04 0 . 291558E+01 0 . 256754E+00 0. 919752E+01 0. 112396E+01

2 . 0. 142763E+04 0 . 291558E+01 0. 256754E+00 0. 919752E+01 0. 112396E+01

3 . 0 . 280547E+04 -0 . 318241E+01 0. 536278E+01 -0. 846554E+01 0. 142916E+01

4 . 0. 487221E+04 0. 744012E+01 -0 . 200112E+01 -0 . 120120E+02 0. 429009E+01

5. 0 . 693900E+04 -0 . 675284E+01 -0. 373053E+00 0. 118264E+02 -0. 504226E+01

6. 0 . 693900E+04 -0 . 675284E+01 -0. 373053E+00 0. 118264E+02 -0. 504226E+01

7 . 0 . 625004E+04 0 . 103418E+02 0 . 244383E+01 0 . 708297E+01 0. 670576E+01

8 . 0. 418331E+04 0. 301154E4-01 0. 698928E-02 -0. 148295E+02 0. 290519E+01

9 . 0. 418331E+04 0. 902523E+00 -0. 2102C3E+01 -0. 169385E+02 0. 796166E+00

10. 0. 211651E+04 -0 . 108392E+02 -0 . 347787E+01 -0. 920735E+01 -0. 734207E+01
PAGE lOA

This table lists the observation numbers, pressure and the standard

deviations of the predicted values, expressed in Parts Per Million

(ppm)

.

BS . PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PRED

NO. KPA FIT l,ppin FIT 2, ppm FIT 3, ppm FIT 4, ppm

1

.

0. 142763E+04 0 . 461415E+01 0. 461149E+01 0 . 615248E+01 0 . 282817E4-01

2 . 0. 142763E+04 0. 461415E+01 0. 461149E+01 0 . 615248E+01 0 . 282817E+01

3 . 0. 280547E+04 0 . 461419E+01 0 . 228254E+01 0. 441376E+01 0. 223057E+01

4 . 0. 487221E+04 0 . 461420E+01 0 . 269055E+01 0. 395981E+01 0 . 169360E+01

5 . 0. 693900E+04 0. 461420E+01 0 . 310396E+01 0 . 635519E+01 0 . 250502E+01

6 . 0. 693900E+04 0 . 461420E+01 0 . 310396E+01 0 . 635519E+01 0. 250502E+01

7 . 0 . 625004E+04 0. 461419E+01 0. 298745E+01 0 . 538369E+01 0. 193579E+01

8 . 0. 418331E+04 0 . 461420E+01 0. 251077E+01 0 . 371208E+01 0 . 193922E+G1

9 . 0. 418331E+04 0 . 461420E+01 0. 251077E+01 0. 371208E+01 0. 193922E+01

10 . 0 . 211651E+04 0. 461420E+01 0. 272312E+01 0 . 520424E+01 0 . 199682E+01

)BS . PRESSURE 3 SD PRED 3 SD PRED 3 SD PRED 3 SD PRED

NO. KPA FIT 5, ppm FIT 6, ppm FIT 7, ppm FIT 8, ppm

1. 0. 142763E+04 0 . 470577E+01 0. 227341E+01 0 . 616617E+01 0 . 315861E+01

2 . 0. 142763E+04 0 . 470577E+01 0 . 227341E+01 0. 616617E+01 0 . 315861E+01

3 . 0. 280547E+04 0. 325791E+01 0. 216203E+01 0 . 521770E+01 0 . 233687E+01

4 . 0. 487221E+04 0. 371623E+01 0. 191900E+01 0 . 420086E+01 0. 201089E+01

5. 0. 693900E+04 0. 478399E+01 0. 213336E+01 0 . 771056E+01 0. 291659E+01

6. 0. 693900E+04 0 . 478399E+01 0 . 213336E+01 0 . 771056E+01 0 . 291659E+01

7 . 0. 625004E+04 0 . 342834E+01 0 . 163487E+01 0 . 599034E+01 0 . 213567E+01

8 . 0. 418331E+04 0. 387989E+01 0 . 172684E+01 0 . 423772E+01 0. 227451E+01

9 . 0. 418331E+04 0. 387990E+01 0. 172684E+01 0 . 423772E+01 0 . 227451E+01

10. 0. 211651E+04 0. 331547E+01 0. 235774E+01 0. 574685E+01 0. 207900E+01
Res i dua Is of Fit 1

cd Q.

(0

cn

-10 -

^ 5 Thousands Pressure C PaD

Res i dua Is of Fit 2

d

a

(du

cr

^ 5 Thousands Pressure CP^D
Res i dua Is of Fit 3

a

m

en

-20

Pressure (Pa^

Res i dua I s of Fit 4

cdu

"D

(D cr

4 5 Thousands Pressure C
Residuals of Fit 5

CO

"D

0]

(U

Thousands Pressure CPaD

Res i dua I s of Fit 6

CO a

w

d

(U

Pressure CP^D
Residuals in ppm C3 Signna Error Bars Applied^ Fit 1 10 I

E

a

a

CO <

(S)

(d

T3m

4 5 Thousands Pressure C^Ps.^
Residuals in ppm C3 Sigma Error Bars App I ( ed^ Fit 3

10 I

12345678 Thousands Pressure C^Pa)
Residuals (n ppm C3 Sigma Error Bars Applied^ Fit 6

3 I

I

I I I I I I 1 2345678 Thousonds Pressure C^Pa])
PAGE 2 3

The results of the test, as determined by using the AREA EQUATIONS,

are compiled in this table. It lists the coefficients and their

tripled standard deviations due to random sources of errors and,

for the highest pressure, the uncertainty in pressure due to the

uncertainty in these coefficients.

COEFF, FIT 1 COEFF, FIT 2 COEFF, FIT 3 COEFF, FIT 4

1. 422472E-04

0. OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

1 . 422463E-04

0. OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

-2 . 819330E-03

1. 422481E-04

•1.481821E-12

0 . OOOOOOE+00

0 . OOOOOOE+00

0 . OOOOOOE+00

1.422441E-04 AREA, m

2.194630E-12 PRES COEF

0. OOOOOOE+00 PRES COEF

0 . OOOOOOE+00

-5. 631232E-03 TARE, N

Pa

Pa"

4 . 614187E-06 4 . 344092E-06 8 . 381819E-06 1

168489E-05 3 STD DEV

0. OOOOOOE+00 0 . OOOOOOE+00 1. 826769E-12 1597867E-12 3 STD DEV

0. OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+00 0. OOOOOOE+00 3 STD DEV

0 . OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+00 0 . OOOOOOE+00

0. OOOOOOE+00 1. 566954E-03 0. OOOOOOE+00 2 . 238437E-03 3 STD DEV T,

Pa

Pa

1. 459134E-05

4 . 614187E-06

7 . 183315E-06

5 . 931598E-06

1. 173177E-05

2 . 105778E-05

4.149265E-06 3 RES STD DEV A/A

2.504029E-05 3 STD DEV A„ /A„ at e ' e

COEFF, FIT 5 COEFF, FIT 6 COEFF, FIT 7 COEFF, FIT 8

1. 422498E-04

8 . 910301E-12

8 . 864457E-19

0 . OOOOOOE+00

0 . OOOOOOE+00

1 . 422401E-04

1. 058918E-11

•7 . 183443E-19

0 . OOOOOOE+00

•9 . 268421E-03

1. 422477E-04

0 . OOOOOOE+00

1. 411765E-19

0 . OOOOOOE+00

0 . OOOOOOE+00

1.422452E-04 AREA, m

O.OOOOOOE+00 PRES COEF

1.757731E-19 PRES COEF

0. OOOOOOE+00

-4 . 561128E-03 TARE, N

Pa

Pa"

-1

1. 133755E-05

6. 351027E-12

7 . 450572E-19

0. OOOOOOE+00

0. OOOOOOE+00

3 . 704057E-05

1 . 083068E-11

9 . 206452E-19

0 . OOOOOOE+00

4 . 978454E-03

6. 535885E-06

0. OOOOOOE+00

2 . 397935E-19

0. OOOOOOE+00

0 . OOOOOOE+00

7 . 376934E-06

0 . OOOOOOE+00

1. 531932E-19

0. OOOOOOE+00

1. 829370E-03

STD DEV Aq /Aq

^ STD DEV b^ Pa

STD DEV b^ Pa

-2

3 STD DEV T, N

7.468447E-06 3.240224E-06 1.312718E-05 4.679866E-06 3 RES STD DEV A/A

9.128167E-05 1.615673E-04 1.808189E-05 1.660652E-05 3 STD DEV A^ /A^ at

Run 01/04/94 11:09:22.45

Pmax

As shown in the Residual Plots in ppm on the preceeding pages the

Maximum uncertainty values in ppm for Fits 1-6 are:

1 2 3 4 5 6

9.1 4.7 6.4 3.0 5.1 2.4
THE SP 250 SERIES ON NIST MEASUREMENT SERVICES*

SP 250-1 Spectral Radiance Calibrations PB871 79883

SP 250-2 Far Ultraviolet Detector Standards PB87227609

SP 250-3 Radiometric Standards in the Vacuum

Ultraviolet PB87227625

SP 250-4 Fricke Dosimetry in High-Energy Electron Beams

PB881 10374 SP 250-5 Alpha-Particle Calibrations PB881 68620

SP 250-6 Regular Spectral Transmittance PB881 08550

SP 250-7 Radiance Temperature Calibrations PB881 23674

SP 250-8 Spectral Reflectance PB881 09905

SP 250-9 Calibration of Beta-Particle-Emitting

Ophthalmic Applicators

PB881 08535

SP 250-10 Radioactivity Calibrations with the "4n" Gamma Ionization Chamber and Other

Radioactivity Calibration Capabilities

PB881 23708

SP 250-1 1 Dosimetry for High Dose Applications

PB88201587

SP 250-12 Neutron Personnel Dosimetry

PB87227617

SP 250-1 3 Activation Foil Irradiation with Californium

Fission Sources PB88217443

SP 250-14 Activation Foil Irradiation by Reactor Cavity

Fission Sources PB882 17435 SP 250-15 Photometric Calibrations PB881 53747

SP 250-16 Calibration of X-Ray and Gamma-Ray

r\/leasuring Instruments PB882 11826 SP 250-17 The NBS Photodetector Spectral Response

Calibration Transfer Program

PB88201595

SP 250-18 Neutron Source Strength Calibrations PB88211818

SP 250-1 9 Calibration of Gamma-Ray-Emitting

Brachytherapy Sources PB89 193858

SP 250-20 Spectral Irradiance Calibrations PB881 23781 SP 250-21 Calibration of Beta-Particle Radiation Instrumentation PB88201579

SP 250-22 Platinum Resistance Thermometer

Calibrations PB881 38367

SP 250-23 Liquid-in-Glass Thermometer

Calibration Service PB89 128888

SP 250-24 Standard Cell Calibrations PB881 23690

SP 250-25 Calibration Service for Inductive Voltage Dividers SP 250-26 NBS Phase Angle Calibration Services PB88225636

SP 250-27 AC-DC Difference Calibrations PB892222616

SP 250-28 Solid-state DC Voltage Standard Calibrations PB881 68703

SP 250-29 Traceable Frequency Calibrations PB881 68364

SP 250-30 GOES Satellite Time Code Dissemination:

Description and Operation

PB881 68760

SP 250-31 Mass Calibrations PB89 153894 SP 250-32 A Calibration Service for 30 MHz

Attenuation and Phase Shift PB88238324

SP 250-33 A Calibration Service for Voltage Transformers and High-Voltage Capacitors

PB882252903

SP 250-34 High Vacuum Standard and Its Use

PB891 93841 SP 250-35 The Calibration of Thermocouples

and Thermocouple Materials PB89209340

SP 250-36 A Calibration Service for Current Transformers PB91216770

SP 250-38 NIST Leak Calibration Service PB92 149772 SP 250-39 NIST Pressure Calibration Service SP 250-40 Absorbed-Dose Calibration of Ionization Chambers in a

^°Co Gamma-Ray Beam

SN003-003-03034-1 S2.00

* Entries containing a stock number (SN003-003-) and price can be purchased from the Superintendent of Documents, U.S. Government

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Entries containing PB numbers can be purchased from the National Technical Information Service, Springfield, VA 221 61 . NTIS will accept

American Express in addition to the payment methods listed for GPO. For more information call (703)487-4650; to place an order call (800) 553-6487. Fax: (703) 321-8547. Be sure to cite the PB number on all orders.

Entries without stock or PB numbers are in preparation.
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