A UNITED STATES DEPARTMENT OF COMMERCE

PUBLICATION

NftT I iNSl OF SrANO & TECH R.I C

AlllDM DSltiSS

NIST

PUBLICATIONS

NBS MONOGRAPH 114

U.S.

EPARTMENT

OF

COMMERCE

National

Bureau

of

Standards

Survey of

Micromanometers
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards ' was established by an act of Congress March 3, 1901. Today,

in addition to serving as the Nation's central measurement laboratory, the Bureau is a principal

focal point in the Federal Government for assuring maximum application of the physical and

engineering sciences to the advancement of technology in industry and commerce. To this end

the Bureau conducts research and provides central national services in four broad program

areas. These are: (1) basic measurements and standards, (2) materials measurements and

standards, (3) technological measurements and standards, and (4) transfer of technology.

The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the

Institute for Applied Technology, the Center for Radiation Research, the Center for Computer

Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and

uniform physical measurements throughout the Nation's scientific community, industry, and commerce. The Institute consists of an Office of Measurement Services and the following technical

divisions:Applied Mathematics—Electricity—Metrology—Mechanics—Heat—Atomic and Molecular Physics—Radio Physics -—Radio Engineering -—Time and Frequency -—Astrophysics -—Cryogenics.

THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to im- proved methods of measurement standards, and data on the properties of well-characterized

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provides technical services designed to aid Government agencies in the selection, acquisition,

and effective use of automatic data processing equipment; and serves as the principal focus

for the development of Federal standards for automatic data processing equipment, techniques,

and computer languages. The Center consists of the following offices and divisions: Information Processing Standards—Computer Information — Computer Services — Sys- tems Development—Information Processing Technology.

THE OFFICE FOR INFORMATION PROGRAMS promotes optimum dissemination and

accessibility of scientific information generated within NBS and other agencies of the Federal Government; promotes the development of the National Standard Reference Data System and a system of information analysis centers dealing with the broader aspects of the National Measure- ment System, and provides appropriate services to ensure that the NBS staff has optimum accessibility to the scientific information of the world. The Office consists of the following

organizational units:

Office of Standard Reference Data—Clearinghouse for Federal Scientific and Technical Information ' —Office of Technical Information and Publications—Library—Office of Public Information—Office of International Relations.

^ Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234.

- Located at Boulder. Colorado 80302.

^ Located at 5285 Port Royal Road, Springfield. Virginia 22151.
UNITED STATES DEPARTMENT OF COMMERCE • Maurice H. Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Director

Survey of Micromanometers

W. G. Brombacher

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

National Bureau of Standards Monograph 1 14

Nat. Bur. Stand. (U.S.), Monogr. 114, 62 pages (June 1970) CODEN: NBSMA

Issued 1970

For sale by the Superintendent of Documents, U.S. Goveniment Printing Office, Washington, D.C. 20+02

(Order by SD Catalog No. C 13. +4:114), Price 60 cents
I

Library of Congress Catalog Card No. 76—603901

II
Contents

1. Introduction 1

2. U-tube micromanometers 2

2.1 General considerations 2

2.2 Index point detectors 3

2.2.1. Index adjustable _ 3

2.2.2. Indices fixed _. 4

2.2.2.1. Rayleigh micromanometer 4

2.2.2.2. Pearson micromanometer 4

2.3 Float detectors 4

2.3.1. Ploat displacement measured directly __ 5

2.3.2. Float displacement multiplied 5

2.4. Visual and optical detectors _. 6

2.4.1. Column height measured by a scale 6

2.4.2. Column height measured by a

precision screw _ _ 6

2.4.3. Photocell detectors 7

2.4.4. Optical reflection detectors 7

2.5. Optical interferometer designs 7

2.5.1. Interference fringes counted 8

2.5.2. Interferometric mercury surface

detectors 8

2.6 Electrical transducers 9

2.6.1. Capacitance transducers 9

2.6.2. Inductance transducers 10

2.6.3. Resistance transducers — 12

2.7. Ultrasonic transducer 12

2.8 Linear amplifiers of column height 12

2.8.1. Gas bubble designs 12

2.8.2. Puddington manometer 13

2.9. Two-liquid designs _ 14

2.10. Inverted bell and cartesian diver 15

2.11. Force balance designs 16

2.11.1. Hickman gage 16

2.11.2. Kemp gage 16

2.11.3. Ring gage 16

2.11.4. Weighing barometers 16

3. Gas column manometers 17

4. Elastic element micromanometers 17

4.1. Primary elastic elements 17

4.1.1. Diaphragms 18

4.1.2. Bourdon tubes 18

4.1.3. Bellows 19

4.1.4. Performance criteria 19

4.2. Secondary elastic elements 20

4.3. Sensor deflection measured mechanically 20

4.3.1. Deflection amplified mechanically 20

4.3.2. Deflection not amplified 20

4.3.3. Force balance systems 21

4.4. Optical transducer 21

4.4.1. Light beam transducer 21

4.4.2. Interferometric 23

4.4.3 Photoelectric 24

4.5 Capacitance transducer 24

4.5.1. Theory 24

4.5.2. Electrodes and pressure-sensitive elements 26

4.5.3. Measurement circuits 26

4.5.3.1. Capacity bridge balanced, change in capacitance measured 27

4.5.3.2. Capacity bridge unbalanced 27

4.5.3.2.1. Current measured 27

4.5.3.2.2. Voltage measured 27

4.5.3.3. Resonant capacity circuit, resonance maintained 28

4.5.3.3.1. Capacitance measured .— 28

4.5.3.3.2. Frequency change measured 28

4.5.3.3.3. Beat frequency measured 28

4.5.3.4. Resonant capacity circuit; unbalanced current measured 28

4.5.3.5. Electic element null restored 29

4.5.3.5.1. Electrostatic voltage restores null 29

4.5.3.5.2. Pressure restores

null - 30

4.5.3.5.3. Spring force

restores null 30

4.5.4. Performance factors 31

4.5.4.1. Sensitivity, linearity, and

stability 31

4.5.4.2. Temperature effect 31

4.5.4.3. Gas composition 32

4.5.4.4. Gas adsorption 32

4.5.4.5. Ionization of gases 32

4.5.4.6. Variation of null with pressure 32

4.5.4.7. Stray capacitances 32

4.5.4.8. Overpressure 32

4.6. Inductance transducers 33

4.6.1. Differential transformer transducer 33

4.6.2. Mutual inductance transducer _ 33

4.6.3. Variable reluctance transducer 34

4.7. Strain gage transducers 35

4.7.1. Unbonded strain gage micromanometers 35

4.7.2. Bonded strain gage micromanometers 36

4.8. Electrical conductance manometer 36

4.9. Microwave null detector 36

4.10. Vacuum tube transducer . _ 37

4.11. Microphone micromanometers 37

4.12. Vibrating wire gage 37

5. Piston gages 38

5.1. Tilted, air-lubricated piston gages 38

5.2. Vertical piston gages 39

5.3. Piston-type pressure amplifier 40

6. Vane gages . — 40

6.1. Deflection of vane measured — 40

6.2. Force on vane balanced 41

6.3. Torsion vane gages _ 42

7. Centrifugal micromanometers 43

8. Special-purpose gages _ 43

8.1. Dynamic pressure measurement _ 44

8.1.1. Theory 44

8.1.2. Piezoelectric gages 44

8.1.3. Frustrated internal reflection gage 45

8.1.4. Frequency response of gages 45

8.2 Atmospheric pressure oscillations 46

8.2.1. Microbarographs 46

8.2.1.1. Elastic element microbarographs 46

8.2.1.2. Liquid column microbarographs 47

8.3. Elevation from pressure measurement 49

8.4. Low vapor pressure 49

8.4.1. Effusion—weight method 49

8.4.2. Effusion—torque method 50

8.4.3. Dewpoint pressure divider 51

8.4.4. Optical transmission gage 51

8.5. Low differential pressure at high pressure 52

8.6. Corrosive gases 52

8.7 Distant indication .—_ 52

8.8. Miniature pressure cells . 52

8.9. Oxygen partial pressure 53

9. Calibration techniques 53

9.1. Static calibration 53

9.1.1. U-tube micromanometer _ 54

9.1.2. McLeod gage 54

9.1.3. Piston gage 54

9.1.4. Gas column manometers 54

9.1.5. Gas volume expansion 54

9.1.6. Vapor pressure . 54

9.1.7. Centrifugal micromanometer 54

9.1.8. Elastic element gage 54

9.2 Dynamic Calibration 55

9.2.1. Pressure step produced 55

9.2.2. Fluctuating pressures produced 55

10. References 56

III

Survey of Micromanometers

W. G. Brombacher

This survey is concerned with instrumentation for measuring pressures from about 0.001 to 50 mm of mercury (0.13 to 6650 Nm"^), described in publications during the years 1900-1968. U-tube micromanometers and diaphragm-capacitance gages are treated in considerable detail. Other in- strumentation described includes gas column manometers; elastic element micromanometers with

optical, inductance, resistance wire, strain gage, and vacuum tube transducers; piston gages; vane

gages; and centrifugal micromanometers. The measurement of dynamic pressure, atmospheric

pressure oscillations, low vapor pressure, and calibration techniques are discussed. Only technical

periodicals, books, and government or university laboratory serials were used as sources of information. Details of electrical measurement circuits, amplifiers, and recorders have been omitted. Schematic diagrams of approximately 70 instruments are included. References to the sources of information and available performance data are given. Key words: Calibration techniques; capacitance pressure gages; gas column manometers; manometers; meteorographs; micromanometers; piston gages; pressure measurement; vane gages; vapor

pressure measurement.

1. Introduction

Micromanometers are here defined as instrumentation used to measure gas pressure, either absolute or

differential, in the range from about 0.001 to 50 mm of mercury (0.13 to 6650 N/m~^). Gages primarily used

to measure pressures below about 10~^ mm of mercury

are not discussed. This eliminates McLeod gages, radioactive ionization gages, thermocouple-type thermal conductivity gages, radiometer gages, and viscosity gages, although all can be used to measure pressures in the micromanomater range. On the whole, the discussion has been limited to in- strumentation which has been described in technical

periodicals, books, and government or university lab- oratory serials for the years 1900-1968. Patents, cata- logs and, to a large extent, progress reports on govern- ment contracts have not been searched or referenced. The emphasis in the descriptions has been on the measuring element or method of measurement, and a summary of performance. Electrical or electronic cir- cuits required for electrical transducers have been for the most part indicated by block diagrams in the fig- ures; details of these circuits have been omitted as not germane to this survey. The principal objective was to review the major sensing elements of the multiplicity of designs which have beei* developed. Details of mechanical design have been omitted, and in some cases performance data are lacking.

For micromanometers, the unit of pressure com- monly used is either the millimeter of mercury, the millimeter of water, or the inch of water. A unit com- monly used in vacuum and low-pressure technology is the torr, which is frequently quoted herein. A pressure

of one atmosphere equals 760 mm of mercury or 760

torr; 101,325 newtons per square meter (N/m^) ; 1013.25 millibars (mbar) ; 10350.8 mm of water; and

407.513 in of water. All of the liquid columns are pre- sumed to be subjected to standard gravity, 980.665

cm/s^. The density of mercury assumed is that at 0 °C,

13.5951 g/cm^. The density of water is that at 20 °C,

0.998207 g/cm^. In the pressure range here of interest,

1 torr equals 1 mm of mercury. One torr equals 133.322

N/m- and 1 N/m2 equals 0.0075006 torr. See [6009] ^ for additional details. A gas pressure in the micromanometer range may be

measured in four iundamental ways. These are: (a)

by means of a balancing liquid or gas column; (b) by

the strain produced in an elastic element; (c) by a balancing gravitational force; and (d) by a balancing

centrifugal force. Other methods of measuring pressure

in the micromanometer range, such as thermal conductivity, viscosity, radiation, and ionization, are more

applicable to the higher vacuum ranges and are not dis- cussed here. The large variety of instrument designs which use

these four primary methods for sensing pressure in- volve the amplification or conversion of the primary

signal. Thus the small heights of a liquid column have

been amplified by mechanical means (including force balances), by optical devices such as the optical lever and interferometers, and by the various forms of elec- trical transducers. Gas columns have not been widely

used, and then only to produce a balancing pressure.

Elastic element deflections have been amplified mechanically in a large variety of designs, at present to a

liv.iited extent by optical means and to a greater extent by a variety of equipment utilizing electrical trans- ducers. In the latter case the transducers have been

principally electrical capacitance, electrical inductance, or wire strain gages. Of limited application have been

electrical conductance, microwave frequency, and mechanical control of the output of a vacuum tube. The

pressure acting on an elastic element has been bal- anced by a mechanical force, supplied either' by a spring or a torsion wire, or by electrostatic force, the

' Figures in brackets indicate the literature references at the end of this Monograph.

1
latter now being favored. Also, the deflection of the transducer itself can be tracked or followed by feed- back.

Gravitational force balances include the familiar

piston gage, now being applied to measure pressures in the micromanometer range, and vane elements used

principally to measure low vapor pressures. The development and application of centrifugal micromanometers have been quite limited up to the

present.

The diversity of the designs found is due (a) to the unique requirements of the variety of applications;

(b) to the lack of commercially available instruments

for many applications; and (c) to the unique training

and experience of the many experimenters who have

designed and built instruments for their own use. The principal laboratory applications for micromanometers have been in investigating gas reactions, in making chemical analyses, in measuring low vapor

pressures, atmospheric pressure fluctuations, low gas

velocity by impact pressures, and low differential pres- sures at high pressures. Their principal industrial application appears to be in petroleum refining.

The sensitivity of an instrument is here defined as the smallest change in pressure which can be measured.

It will vary with pressure in many cases. The reader is referred to section 10 for information on the procedure used in numbering the references.

2. U-Tube Micromanometers

2.1. General Considerations

This section will cover micromanometers which de- pend upon the change in height of a liquid column.

Essentially, all of these designs are based upon the use of a U-tube, which differ in the means used for detecting the liquid surface and for measuring the column height.

The pressure or differential pressure can be ex- pressed in terms of the column height, generally milli- meters of water or mercury, or converted to dynes per square centimeter by multiplying by the density of the

liquid and ambient gravity. When the height of the column is used as the unit of pressure measurement, re- duction of the readings to standard conditions of temperature and gravity is theoretically necessary. Unless the accuracy obtainable is better than 0.5 percent

(not easily secured in making measurements at pres- sures below one torr), the corrections can safely be

neglected.

Ordinarily, only ^he difference in the column height

in U-tube micromanometers is recorded. Recorders

may be devised utilizing an optical lever, so that the

position of the light beam on the scale can be photographed, or an electrical transducer, the output of which can be passed into an electrical recorder. The

optical interferometer, to be of any practical use, re- quires a recorder, on which discussion will follow in section 2.5. In general, the U-tube micromanometer measures a

differential pressure, which becomes an absolute pres- sure if the pressure in one leg is well below the sensitivity of measuring the column height. Mercury is the

liquid commonly used in U-tube micromanometers for both absolute and differential pressure measurements;

water or an oil ordinarily only for differential pressure measurements. However, oils are now available which

have a vapor pressure below that of mercury, so that vapor pressure is not a problem in their use in making

absolute measurements. For comparative performance

data on 12 liquids see Smith and Murphy [5534]. The

primary problem here is that all known oils absorb

significant amounts of gases, in contrast to non-absorption by mercury. The customary procedure is to out- gas the oil by heating it under vacuum and then to maintain continually a vacuum over it insofar as possible. Other methods of degassing are also used. Thomas,

Johnson, and Little [62103] vacuum-distilled the oil into their manometer and continually maintained a vacuum over the oil. Holmes and Jones [63347] mechanically agitated the liquid to facilitate the flow of gas up to the liquid surface by using a magnetic paddle

rotated by an external rotating magnet. Tekippe and

Ramanathan [6715] reviewed critically the various

existing procedures. They described a preferred pro- cedure in which the manometer liquid was alternately

frozen by a dry-ice bath and thawed while pumping.

It will be seen in the sections in which particular

instruments are described that the best vacuum micromanometers designed before about 1950 had a precision of measurement limited to about 0.001 torr. Since

then the sensitivity has been increased by an order of magnitude and more. The best differential pressure micromanometers (using water or oil) have a sensitivity of the order of 0.0001 mm of water (0.00007

torr)

.

The mercury barometer was originated in the last half of the seventeenth century. During the last 300

years its various forms have incorporated most of the means used in U-tube micromanometers for both de- tecting a liquid surface and measuring the height of a liquid column. This cdurse of development has been

ably presented by Middleton in his "History of the Barometer" [B641].

Literature on manometers and micromanometers pre- vious to about 1900 has not been searched, so that it may well be that the earliest reference given here for a given design does not necessarily fix its originator.

As will be seen, the fundamentals of some designs ap- pear to have been presented as new, every 20 years or so. In classifying micromanometers into types, a number of them could come under at least two groups; their location in the survey is thus largely an arbitrary

choice.

2
2.2. Index Point Detectors

One of the simplest, and quite sensitive, detectors of the level of a liquid surface is an index point. This is a pointed rod of metal, glass, or ivory adjusted so that

its tip just touches the liquid surface. The index rod can be fixed to the U-tube and the liquid level adjusted

to the touching level, or the index point moved, us- ually by a micrometer. When the manometer liquid is mercury, the index is above the liquid surface; when

it is oil or water, the index point is usually below the

liquid surface. One form of the latter is the well-known

hook gage. When the index point is used to detect the level of

a mercury surface, the sensitivity is greatly improved

by proper illumination of the mercury surface and by

securing the reflection of a series of parallel black

lines on a white background. Disappearance of the dimple in the mercury, as indicated by the reflected lines becoming parallel, indicates that the point just touches

the mercury surface. The point of contact can be de- termined to 0.001 mm by the above procedure if the mercury surface is bright and clean; cf. Stillman

[1408].

An ivory index point is superior to one of metal

since there is less sticking of the mercury to the point.

Glass index points are also used, generally when the index is in a fixed position.

Readings can be secured more rapidly and the mercury level controlled automatically when the point of contact with the mercury surface is indicated by the make and break of an electric circuit. Here the index

point must be a metal and the current through the contact be very small. This method has been little used in micromanometers.

Use of index points in barometers dates back to 1726

[B641] ; the Fortin barometer employing a fixed index

point in the cistern, back to 1809.

2.2.1. Index Adjustable

The design of a micromanometer with adjustable

point indices is shown schematically in figure 1. Here

A and B are the cisterns connected by tube C; PI is a reference pressure (which may be a vacuum) and P2

is the pressure to be measured. £ is a micrometer to which the point index is attached; for our purposes

here, F is a duplicate of E, and reservoirs D and / are, for the moment, not pertinent.

When a difference in pressures PI and P2 is applied,

both micrometers are readjusted so that the point in- dices just touch the liquid surface. The sura of the changes in reading of the micrometers is the column

height. Threlfall [0401] described this design in 1904 using

colored water as the liquid. He measured differences down to 0.01 mm of water. Hering [0604] in 1906 modified the design so that absolute pressures could be measured. A vertical tube

G was attached to tube C in figure 1, which extended

downward and terminated in reservoir D of mercury

open to the atmosphere. The height of the mercury

^

Figure 1. Index point manometers. A and B, cisterns; C, G, and H, connecting tubing; D and J, auxil- iary reservoirs; E, micrometer with a point index; F, a point index; Pi and P2, applied pressures.

column from the liquid surface in A to the liquid sur- face in the auxiliary reservoir D balanced the atmospheric pressure. A fixed index F was installed in cistern A and a micrometer-index combination E in cistern B. The auxiliary reservoir / was adjustable vertically by

a screw to bring the mercury level in cistern A into contact with the fixed index F. Readings on micrometer

E gave the column height. To avoid, to a large extent, capillary difficulties, cisterns A and B were 25 mm in diameter. Pressures down to 5 X 10~^ torr were

measurable.

Muendel [1306] modified the Hering design in two

ways. First, cisterns A and B were 40 mm in diameter.

Second, a micrometer-index was also installed in cis- tern A, so that both micrometers were read in measuring a pressure. A mercury seal was used for the micrometer cistern joint. The index points were viewed

with a microscope. The micrometer sensitivity was

7 X 10~* mm per scale division. The accuracy

claimed was 10~^ torr. The development of vacuum pumps made both Hering's and Muendel's designs obsolete. Cisterns A and B

connected by tubing C, figure 1, are all that is needed.

A vacuum pump connected at PI can produce a refer- ence pressure significantly below P2. Gerard [6603]

describes this micromanometer design in which cisterns A and B were 25 mm in diameter. The accuracy ob- tained was 10 ~- torr. Thomas and Cross [6701] describe a design with

U-tube cisterns 50 mm in diameter, capable of measuring a column height of 4 in and pressures from 10~-

to 100 torr. Mercury, silicone oil, and water were used

as the filling liquids. The index points were brought

up from below to touch the liquid surface when water

or oil was the liquid. The various sources of uncertainty were investigated and were found for full scale readings to total 6.7 X 10~^ torr for mercury, 0.60 X

10~^ torr for water, and 0.83 X 10~^ torr for silicone

oil. For pressures below about 0.1 torr, these errors would be cut in half. It is believed further development

would reduce the xmcertainty in the measured pressure with the oil manometer to 1 X 10"* torr.

3
Ruska, Kao. Chuang, and Kobayashi [6816] modified the above described design to measure differential pressures up to 96 torr at pressures up to 800 kg/cm^

(roughly 800 atm). A stainless steel U-tube, 16 mm

in bore, had two adjustable micrometers installed as shown at E and F in figure 1. A shaped teflon guide

floated on the mercury surface. A stainless steel nail shape pierced the teflon float to extend into the mercury. The micrometers were adjusted manually so that

their tips made electrical contact with the nail head,

whereupon valid readings were made. The temperature

of the manometer was controlled at 40 ± 0.2 °C. The

accuracy claimed was ±0.002 torr. A digitized barometer depending on a micrometer

probe was designed by Brini, Galli, and Gandolfi

[6631]. The contact of the probe with the mercury

surface was detected electrically and maintained auto- matically by a suitable electrical circuit. A disk with

20 holes on its periphery was mounted on the micrometer. A photocell picked up light passed through one

of the holes. The output from the photocell was digit- ized. The sensitivity was 1/30 mbar (0.022 torr).

2.2.2. Indices Fixed

2.2.2.1 Rayleigh Micromanometer

The classical mercury micromanometer is that de- signed by Lord Rayleigh [0101]. Referring again to figure 1, cisterns A and B, bore 25 mm, were equipped

with two fixed indices, the points of which were in the same horizontal plane. Reservoir /, together with

appropriate pinch-clamps in tubing H, was required to adjust the volume of mercury in A and B so that both

indices just touched the mercury at zero differential pressure. Glass tubes, not shown in figure 1, extended

upward from cisterns A and B, culminating in two

domes for cistern A and one for cistern B. These were

the supports for an optical lever. The micromanometer

as a whole was mounted on a wooden frame, supported

at two points, one midway above the two cisterns which

served as a fulcrum, and the other some centimeters

away in the plane of figure 1. The latter support was

a micrometer screw, the operation of which tilted the whole manometer; the amount of tilt was measured by

the optical lever, since the wooden support made use

of the micrometer unreliable. When a differential pres- sure was imposed, the micromanometer was tilted to return the index points back to the mercury-touching

position. Absolute pressures were measured, so that PI

had to be maintained at a pressure significantly below

that measured. The design was such that one torr of

differential pressure produced 231 mm deflection on

the scale of the optical lever. Rayleigh used the instru- ment to measure pressures in the range 0.01 to 1.5 torr. Scheel and Heuse [0903] used Lord Rayleigh's de- sign for pressure measurements up to 5 torr. For

greater pressures they modified Rayleigh's design by

returning one index to the mercury-touching position

by moving one cistern vertically and measuring the motion with a micrometer screw. The required flexi- bility in glass tube C, figure 1, was obtained by shaping

this tube in the form of an elongated horizontal U. The pressure range extended to 30 torr.

2.2.2.2. Pearson Micromanometer

Pearson [3106] developed a design in which the ad- justment of the mercury level to the fixed index point

is made by lowering an auxiliary mercury column and

measuring the volume change in mercury level. In

figure 2, A and B are the cisterns of the U-tube. The

fixed index point / is in B, which is kept at zero pressure. The U-tube is connected to tubes C and D. Space

G contains a fixed amount of dry gas at some pressure below atmospheric. Tube D and cistern E contain mercury. A pressure applied to cistern A causes the mercury in B to rise; cistern E is lowered to restore the mercury level in B to the null position. The vertical displacement h of mercury in tube C is measured on a

suitable scale. The pressure P in terms of column

height is given by the ratio of the bore areas of C/B

times the observed value of h. The amplification B/C

obtainable is at best about 100.

P = 0

G

D

Figure 2. Pearson manometer. A and B. cisterns subjected to pressures P; C and D, connecting

tubing; E, an auxiliary reservoir; and G, a gas.

Slavianskii [5257] improved Pearson's design in

details such as providing temperature control and vi- bration protection. The pressure range of his instru- ment was 0.01 to 1.5 torr; the sensitivity is 2 X

10""^

torr, a value indicating a magnification of about 50. LeRoy [4514] made the fixed index point of tungsten and detected the point of contact with the mercury

surface electrically. The adjustment of the mercury

level was secured automatically by a solenoid valve which controlled a slow leak into or out of the vacuum

system. The necessity for close control of the manometer temperature was discussed. The mercury column

height measured was at a maximum about 100 times

the pressure in terms of column height. The objective was to achieve an accuracy of 0.01 torr.

2.3. Float Detectors

A float in both mercury and other liquids has been

often used as a liquid surface level detector in combination with various schemes for measuring the col- umn height. Some form of guide to insure float verti4
cality is required. The float position will be seriously

affected by any change in surface tension of the liquid.

If the liquid wets the surface of the float, some creep- ing of the liquid over the surface of the float will occur; presumably this can be prevented by a nonwetting surface coating on the float. The float clearance between float and cistern walls must be adequate to avoid interfering menisci. The use of a float is attrac- tive in comparison with index points, in that readings

of pressure can be obtained directly without the need

for any intermediate operations.

2.3.1. Float Displacement Measured Directly

A simple design of a micromanometer using a float

is that developed by Betz [3111] for measuring pitotstatic pressures in wind tunnel operation. A glass scale was attached to a float and extended well below it into a well forming part of a cistern. The position of this

scale, hence of the float, was oL served through a lens

relative to a reference mark. The scale was illuminated

by an electric lamp. The liquid had to be transparent.

The sensitivity was 0.2 to 0.3 mm of the liquid column.

The above design requires modification if the manometer liquid is mercury. The scale attached to the float must rise above the mercury column. However, the

precision obtainable is low compared to other detectors.

It should be mentioned that installing a magnet in the float and a detector of the magnetic field outside

of the tube has been successfully used in barometers.

While the sensitivity of such a design is not as good

as that of index points, it offers one possibility for obtaining readings without manual manipulation of the output signal, if the external detector adjusts to its equilibrium position automatically and its displacement

is indicated. This single advantage seems thus far not

to warrant its application in micromanometry.

2.3.2. Float Displacement Multiplied

In all of the designs to be described, changes in the

float position have been multiplied by using an optical

lever. This simple device for magnifying a linear or angular motion had been widely used by physicists up

to the time when electronic devices became available. Lord Rayleigh used it in 1901 in his device to measure

low vapor pressures: usually he is credited with being

the first to do so. but undoubtedly the optical lever is much older and may have been used earlier in pressure- measuring instruments.

A modern design, due to Eichhorn and Irvine

[5810], will be described first. In figure 3. A and B

are the U-tube cisterns. The float F is pivoted eccentrically and in effect deflects angularly as the liquid column

in cistern B rises or falls due to a change in pressures Pi or P2. A mirror M mounted on float F turns with

the float and deflects a light beam focused upon a scale. The light beam enters and leaves by the glass top G

of the cistern and is rotated 90° by mirror R.

Oil was the manometer liquid, but design modifications to use mercury would not be difficult. A plunger

C is provided for use in calibrating the manometer. Its insertion into the liquid raises the column height a

't

PI

:ll —1

1

1 JL

G P2 M r-v F

I.J B

A

Figure 3. Float micromanometer. A and B, cisterns, subjected to pressures Pi and P2; C, a plunger

used for calibration; F, a pivoted float; G, window; M and R, mirrors.

computable amount. In the instrument constructed, the

sensitivity was 1 nmi deflection of the light beam on

the scale for 3.15 X 10~^ in of liquid column.

The earliest design of the float-optical lever combination appears due to Shrader and Ryder [1901]. Here

the U-tube cisterns were separated, as shown in figure

1. and the optical lever was installed above one of the mercury columns. The float, a glass bead, was fastened

to one leg of the optical lever and the mirror to the other leg. Two knife edges, supported by wire loops,

supported the optical lever. The range of measurable

pressures was 0.001 to 3 or 4 torr: the sensitivity, 0.001 torr. Carver [2301] improved the Shrader-Ryder design

in several particulars. He used a steel float with sharp

edges in contact with the mercury surface to prevent

wetting. The cistern of the U-tube containing the float was enlarged to a bore of 44 mm, reducing the effect of changes in capillarity. The design of the optical lever was refined to reduce uncertainties in position

equivalent to 10~* mm Hg. Finally, because ripples on the mercury surface caused by earth tremors were

troublesome, producing several centimeters of oscilla- tion of the light beam on the scale, these were prevented

by a rigid, massive mounting attached to a concrete

pillar. The sensitivity achieved was 10~* torr; ac- curacy. 2 X 10~* torr; pressure range, 5 X 10~^

to 1 torr. Johnson and Harrison [2901] redesigned the Shrader-Ryder optical lever with a view of obtaining

greater ease in construction. A system of platinum

ribbons and a fine glass rod composed the optical lever. The float had a flat bottom which diminished the ef- fect of the inescapable ripples on the mercury surface. The sensitivity obtained was 9 X 10~* torr per mifli- meter deflection of the light beam on the scale; the pressure range was 2 X 10~* to 0.5 torr. Newbury and Utterback [3201] constructed a manometer which differed notably from designs previously

discussed only in the design of the optical lever. An

iron ribbon attached to the iron float turned a hori- zontal rod as the float moved upward. This rod had

jewel bearings. The mirror was attached to the rod.

It should be noted that some materials more perfectly

flexible than iron would be preferable for the ribbon;

the iron ribbon, with time, retains to some extent the curvature of the rod. an effect which affects the validity of any calibration. The sensitivity of this manometer

was 10~^ torr per millimeter deflection of the light

5
beam on the scale. It was calibrated in a pressure

interval, from 10^^ to 2 X 10~^ torr. Spalding [5056] designed a water micromanometer

for measuring low air velocities using a pitot tube. He

tried first a design in which two U-tubes were used. A float was installed in one of the cisterns of each

U-tube. The optical lever was operated differentially by

these floats. This design was abandoned because the

floats moved laterally, a difficulty which was reduced

materially by sprinkling powdered chalk on the water. However, there seems no advantage in this more

complicated design over that of one U-tube with a float- optical lever combination in one leg of the U-tube. Spalding's final design was of the latter type. It was

novel in that the mirror was horizontal. The design was

such that differential pressures down to 2 X 10~'^ mm of water could be measured.

Blaha [6609] utilized a float-optical lever detector

in a U-tube with a photocell receiver to indicate equality in the pressure in the two U-tube legs. A servomotor

controlled by the photocell automatically balanced the pressure to be measured by compressing a metal bel- lows connected to one of the U-tube legs. The angular

motion of the servomotor was measured and was pro- portional to the applied pressure difference. A silicone

oil was used in the U-tube. The pressure range was 20

torr with a precision of 10~^ torr.

2.4. Visual and Optical Detectors

This class of micromanometers includes simple

U-tubes in which the eye, aided or unaided by a lens system, is used to detect the level of the liquid surface. The column height may be measured by a simple scale or at best by a precision screw. Interferometers have

also been used simply as detectors; consideration of these will be deferred to section 2.5.

2.4.1. Column Height Measured by a Scale

The practical limit of sensitivity is about 0.02 mm

when a simple scale, vernier, and sighting ring are used

to measure the column height. This is inadequate for many applications. See Brombacher, Johnson, and

Cross [6009].

The first modification to be considered is to slant one leg of the U-tube, using tubing small in diameter

relative to that of the cistern, so as to throw most of the column displacement to the slanted tube. This de- sign has the great advantage of simplicity. Assuming

a slanted tube in which the column displacement along

the slant is ten times the vertical column displacement,

the theoretical sensitivity becomes 0.002 mm in column

height. However, capillary effects cause distortions of the liquid surface, whether water, oil, or mercury,

which reduce the certainty in its placement relative

to the scale. This fact requires that the angle of slant assumed, about 6°, be increased measurably. In any

event, the slanted scale needs a vernier to achieve the

sensitivity needed to compete with other types of micromanometers, which greatly complicates the de- sign and apparently has not been undertaken.

2.4.2. Column Height Measured by a

Precision Screw

The rotation of a screw is a sensitive means of measuring small displacements. Its sensitivity is compatible

with that of a point index detector of a liquid level so that this combination has been often used in micromanometers; see section 2.2. With reasonable care in design, a sensitivity of about 0.005 mm is easily

achieved, with more sensitivity attainable if the effort

is desirable. Two designs using a slanted tube and a precision screw will be described. In Hodgson's design [2910],

a cistern A, figure 4, contains a firmly held plunger C, the vertical position of which is controlled by micrometer M. When a difference in pressures PI and P2

existed, the plunger position was adjusted vertically to bring the liquid level in tube B back to a marked null position, as observed by microscope F, with illumination supplied by light D via mirror E. The height of the column is given by the change in the micrometer reading. The slant tube had a slope of 1/10. The oil meniscus position could be set to 10~* in (2.5 X 10~^ mm)

which, with the tube slant, gave a sensitivity in pressure

of 10~^ in of oil. This required pushing the micrometer

sensitivity to the limit, from which some improvement was obtained by making the plunger area less than that of the free surface of the liquid.

The second design was devised by Parkin in 1921

and is described by Ower [B496]. In principle, the design is simple. A short length of slant tube ST, figure

5, is connected by flexible tubing T to a fixed cistern. The slant tube was movable vertically by means of a micrometer MI so that the liquid surface can always be

brought to a fixed mark M on the tube ST. The vertical

Figure 4. Plunger micromanometer.

A, cistern; B, leg of manometer; C, plunger, vertically controlled by

micrometer M; D, light source; E, mirror; F. microscope; P2-P1, dif- ferential pressure.

Figure 5. Null micromanometer.

M, null mark; MI, micrometer; P—Po, differential pressure; ST, slant

tube; T, flexible tubing.

6
motion, measured by the micrometer, is proportional to the height of the liquid column. This design has mainly

been used to measure differential pressures with a sensitivity of the order of 0.01 mm of water. To avoid one

source of error, the design must be such that changes

in internal volume in the flexible tubing with changes

in pressure or position are insignificant.

Smith and Murphy [5534] modified the above de- scribed gage. For the differential pressure interval 0

to 0.8 in of water, they used a dial gage to measure

the vertical motion of the cistern, and for greater

differential pressures, a simple scale and vernier, the

latter attached to the cistern. The slant tube had a 10° slope. They investigated 12 possible liquids (not

mercury) and concluded that silicone oil DC200, visc- osity 0.65 cSt, gave the most stable repeatable meniscus.

As the pressure is varied, some volume change can be

expected in the flexible tubing necessarily used between

the slant glass tube and the cistern, which introduces an error. This they investigated. They claim an ac- curacy of 2 X 10~^ in of water (5 X 10~^ mm)

for the low range and 10~^ in of water for the high

range. An obvious alternative to the Parkin's design where

the slant tube was movable and the cistern position

fixed is to arrange the reverse. Diedrichs and Andrae

[B301] describe Ensberger's micromanometer, in which an annular cistern could be raised and lowered

by a micrometer to bring the liquid surface to the mark

on the slant tube. A sensitivity of 0.0001 in of mercury

(0.0025 torr) was achieved.

A refinement of the Parkin design was incorporated

by Casella and Company in 1931 [B496]. A cistern with a hook gage (fixed index point below the water

surface) is provided in place of the slant tube. Both

legs of the U-tube are movable vertically for range

adjustment. Motion of the cistern with the index point

from the zero differential pressure to the inde^fchuching

position is measured by a vernier-scale combination.

In view of the sensitivity of the hook gage, the measuremlrJt could be made to advantage by a micrometer

screw. The hook gage is observed through an optical

system including means for illumination of the index.

Maslach [5230] installed two precision screws, one

along each leg of a U-tube made of 10-mm precisionbore tubing. These screws were connected by a differ- ential which was manually operated. The liquid (butyl

phthalate) surface was observed by eye through a lens attached to each screw. Individual hand cranks brought

each lens to the liquid surface level. A five-place counter indicated the difference in the liquid column

height. A precision of 0.001 torr (approximately 0.01 mm in column height) was obtained over a measuring

range from 0.05 to 20 torr.

2.4.3. Photocell Detectors

The next step in the above design would be to substitute a photocell for the eye in detecting a mercury

surface. By feedback from the photocell to a servo- motor, readings can be obtained automatically. The

sensitivity achieved with such an arrangement [5774,

6009, 63250] is now not better than 0.02 mm. Jn vacuum measurement its chief virtue is that readings can be obtained automatically and that it lends itself to the automatic maintenance of a steady value. It has

not been applied to micromanometers, since the greater

precision obtainable by other means does not warrant

the inherent complexity of the design.

A design for measuring small differential pressures, involving an inverted bell on a balance arm with

shutters, one for each of two photocells, is described

briefly by Ower [p. 233, B496].

Robertson [5688] used photocells to detect light

transmitted through butyl phthalate in a U-tube micromanometer. The light so transmitted was focused on the

photocells; the extraneous light was scattered. The

output from the two photocells entered a Wheatstone

bridge and then an electrical recorder. The best sensitivity was 0.25 mm of water per millivolt across the recorder terminals.

2.4.4. Optical Reflection Detectors

While not particularly useful in a micromanometer, the

sensitivity obtainable warrants mention of the primary

standard barometer developed by the National Physical Laboratory [6092]. The U-tube is vertical while

the optical probe is horizontal, a right-angle prism

being used to transmit reflections from the mercury

surface to the probe. Two horizontal tubes, movable

as a unit on a track, have their axes intersect at a

selected angle. A light beam from a lamp at the end

of one tube passes through a grid to the mercury

surface where it is reflected and passes through the second tube and a grid similar to the first. Maximum

illumination is obtained when the axes of the two tubes

intersect at the mercury surface. The accuracy of the

setting is 5 X 10~* mm. In the barometer two such

probes are used, one for each mercury surface. The

U-tubes are 4 in in diameter. The point of maximum

brightness is determined by photocells, together with

appropriate electrical circuits. The optical tubes are mounted on precision ways. Their positions at the point

of maximum brightness are measured by line stand- ards together with optical accessories for viewing.

The merits of somewhat similar optical reflection designs are discussed by Terrien [59192], but these are probably not practical for application to micromanometers.

2.5. Optical Interferometer Designs

For measuring the height of a liquid column, the

best techniques in the order of their accuracy and

sensitivity are the optical interferometer, gage blocks,

and a precision screw. For micromanometers, gage

blocks are impractical. The interferometer, while at- tractive in its accuracy and its function as a detector,

is complex in design and requires careful adjustments.

Only a requirement for high accuracy warrants its application here. Interferometers may be used in two ways. In one.

the interference fringes are counted as the height of

7
the mercury column changes. In the other, the central fringe produced by white light is used only to detect the mercury surface.

2.5.1. Interference Fringes Counted

Prytz [0501] proposed the use of Newton's rings for measuring small pressure differences, but no evidence was found indicating that an instrument was constructed. Barus [2104] experimented with an interferometer

for measuring small differences from atmospheric pressure. The U-tube legs were separated by a metal parti- tion and had covers of optical flats. Half-silvered glass

disks were placed above each mercury surface, so that a single light beam was reflected from each mercury

surface and the resulting interference pattern observed

with a telescope. Ripples on the mercury, reported by

all experimenters as impossible to eliminate from a

free surface, were avoided by placing thin glass disks on the mercury surface. The mercury depth was made

small, further to reduce surface distortion by vibration. The U-tubes had a bore of 5 cm. Differential pres- sures in the range 3 X 10~^ to 3 X 10~- torr were

measurable. At pressures above the latter value, the

interference fringes disappeared. This was ascribed

by Barus to the glass disks on the mercury not re- maining horizontal, but was more probably due to the fact that he used white instead of monochromatic

light. Barus states that measurements of vacuum would

be feasible, a conclusion not to be doubted.

Thomas, Johnson, and Little [62103] have developed an oil manometer specifically for measuring vacuum,

in which the interference fringes measure the changes

in the liquid level. The design is shown schematically

in figure 6. Light from a point source F passes through

green filter G to reflector E and through lenses D.

Part of the ray passes through window C and optical

flat B to the oil surface where it is reflected. Another

part of the ray is diverged by prisms / before passing

through C and B in order to be reflected from the oil

E \

0 f=^

' —Pi

J

11

P2

Figure 6. Interferometric micromanometer.

A. concentric cisterns; B, optical flat; C, window; D, lens; E, mirror;

F, light source; G, green filter; H, telescope; J, prism; K, brass block; P1—P2, differential pressure.

surface of the other leg of the U-tube. The two reflected rays in retraversing their paths give rise to interference

fringes which are viewed in telescope H and counted.

Tubes lead to the space above each liquid surface so

that desired pressures PI and P2 can be applied. Temperature inequalities are minimized by the massive

brass block K, and by having the overall height of the

liquid columns small. The liquid, dioctyl sebacate, has

a low vapor pressure but, like other liquids except

metals, absorbs gases significantly. The instrument

included equipment for distilling the oil into the manometer under vacuum conditions and always maintaining PI and P2 at vacuum values, and the technique

of operation adopted minimized this source of error. Since the manometer was constructed primarily to determine if the interferometer would work, the fringes were counted by direct observation while the pressure was changing. Obviously, an automatic method of counting fringes is needed. Based on the use of two

photocells, such a counter has been developed for application in metrology by Cook and Marzetta

[61238]. They found that a pressure change of 10~^

torr caused a shift of 55 fringes, which gives a sensitivity of 2 X 10~^ torr for a motion of 1/10 of a

fringe.

Feube [63184] has constructed a differential mercury manometer in which changes in the height of the mercury column are measured by counting interference

fringes. The mercury surface is covered by a glass

plate and in turn by an oil film. The claimed accuracy

is 0.1 of a fringe, equal to 0.01 N/m^ or 7.5 X 10"^

torr.Aubry and Delbart [65103] developed the Peube

design still further, using an interferometer essentially as shown in figure 6 but without brass blocks. Both

mercury and a silicone oil were used. The main dif- ference from the design shown in figure 6 was that interferometric measurements were made only on one

leg of the U-tube. Aubrey and Choumolf [65330] used

the instrument as a stanJard in calibrating ionization gages at pressures around 10~* torr. Stevenson and McFadden [6592] describe an inter- ferometric micromanometer using a laser beam. Inter- ference fringes were secured from both legs of the

U-tube. The liquid was galvanometer damping oil. Reflections were secured from mirrors in the oil. The

probable error was stated as 10 ~^ mm in measuring

liquid column height. White light was compounded

with the laser beam so' as to facilitate counting the interference fringes.

2.5.2. Interferometric Mercury

Surface Detectors

Here the interferometer is kept in a fixed position

relative to the mercury surface by moving the optical

flat, and measuring its displacement. The central fringe

obtained with white light is used as the detector of the

null. The displacement of the optical flat is usually

measured by a micrometer.

Manley [2701] set up an interferometer for each

leg of a manometer. The interferometer for one leg

8
of the manometer was used for reference purposes; the pressure above its mercury surface was maintained

significantly below that to be measured. A micrometer was used to measure the displacement required to se- cure the null position of the optical flat, which is a measure of the pressure. The micrometer was cali- brated by counting interference fringes. Pressures were

measurable in the range 10~* to 20 torr. Ripples on

the mercury surfaces were bothersome; like Barus

six year earlier, Manley proposed placing thin glass or stainless disks on the mercury surface. Terrien [59192] reviews three ways in which inter- ference fringes from two mercury surfaces can be used

to detect the relative vertical distance between the mercury surfaces of a barometer. One of the methods

originates in Japan, another in Russia, and the third

is due to Terrien. In all cases, the length of the signif- icant light paths must be equal. This is secured by a displacement of a reflector or reflectors, the amount

being a measure of the column height. In Terrien's design, a beam of white light is reflected from both of the mercury surfaces of the U-tube by means of a Michaelson interferometer. Upon reflection, the beams reverse their paths and are reunited as they

issue from the interferometer. If the optical path lengths

are exactly equal, and if the mercury surface has in- finitesimal ripples (difficult to prevent), the observed

fringes are white, not colored. The fringes are detected by a photocell. To obtain exact equality in the light

paths, two horizontal prism reflectors are adjusted

horizontally as a unit, to increase the light path to one mercury surface and decrease it to the other. The

amount of their horizontal motion is a measure of the change in height of the mercury column. The instru- ment is planned to have a range of 1 atm with an

accuracy of 10 ~^ torr, limited by the accuracy of meas- urements of displacement by a line standard. This

design has no significant advantage in accuracy over

simpler designs of micromanometers.

The Japanese and Russian interferometer applications require two light sources and two interferometers.

obtain the liquid column height. For one design in- volving the use of a force balance, see section 2.11.2. The photocell, also an electrical transducer, has been

considered in sections 2.2.1 and 2.4.3.

2.6.1. Capacitance Transducers

Of more historical than technical interest is the de- sign by Simon and Feher [2905]. A U-tube consisting

of a cistern and a slant tube, short in length, had tinfoil wound around the slant tube. A glass cylinder was

mounted in the slant tube so that the mercury was

constricted to an annulus 0.5 mm thick. Changes in the

capacitance, tinfoil-mercury-gas, were measured by

two radio circuits nearly in resonance. The frequency

of one radio circuit was maintained constant, that of the other monitored by the changing capacitance. The

differential output was measured by a milliammeter.

The sensitivity was stated as 0.05 torr, the accuracy

0.2 torr. The design of the pickup proposed by Sasimenko,

Kulin, and Shushkevich [6633] is similar to that of Simon and Feher. The tube of a cistern and tube

manometer was surrounded by a short metal cylinder

in the vicinity of the liquid surface. An electrical ca- pacitor was formed by the cylinder and liquid which

varies with the height of the liquid column. The output

of the capacitance bridge was a voltage which could

be recorded. The design by Los and Morrison [5104] is indicated

in figure 7. Here A and B are the U-tube cisterns; CI

and C2, invar disks forming an electrical capacitance

with the mercury surface; D and E, oscillators; F, a mixer; G, an oscilloscope; and H, an audio signal

generator. The cisterns were 8.8 cm in diameter.

Changes in beat frequency, produced by changes in the mercury level up to 2.5 torr, were measurable.

The reproducibility was 1 to 2 X lO"* torr in the pressure range up to 0.2 torr and 0.1 percent at higher

pressures. The sensitivity was nonlinear, but constant within 5 percent in the pressure range below 0.02 torr. The theory of operation was given.

2.6. Electrical Transducers

Changes in liquid column height can be measured

directly by changes in electrical capacitance, liquid surface to a metal disk (sect. 2.6.1), or in changes in the electrical resistance secured by a wire immersed in the liquid (sect. 2.6.3). Since the pressure range measurable by using changes in electrical capacitance is small, this parameter is usually used to indicate a null value, necessitating the measurement of a displacement of some sort to obtain the column height. Thus

far, measurement of the change in electrical resistance of an immersed wire does not have adequate sensitivity for micromanometers.

Other electrical transducers, such as inductances

(sect. 2.6.2), linear transformers, etc., require an inter- mediate element such as a float. Obviously, these trans- ducers are used to the best advantage as null indicators,

requiring measurement of some other parameter to

F >— G H

A — —' B

Figure 7. Capacitance micromanometer. A and B, cisterns; Cl and C2, metal disks; D and E, electronic oscil- lators; F, mixer: G, oscilloscope; H. audio signal generator; PZ—Pl,

differential pressure.

9
Constant sensitivity over the entire pressure range

is achieved if the capacitance, mercury surface to metal

disks, is used to indicate a null. Hutton and Gilheany

[58164] designed a micromanometer in which one of

the cisterns {B in fig. 7) was movable vertically with

the displacement measured by a micrometer when

capacitance CI = C2. The positioning of the movable

cistern to balance the capacitance is carried out auto- matically by a supporting piston. The operation is initiated by the voltage generated by unbalance in the bridge circuit containing the capacitances. Upon amplification, the signal is fed to a servomotor which drives

a pump, which controls the flow of oil to and from the

piston. Two micrometers, connected by a precision

bubble level, are positioned over the centers of the two covers of the cisterns. As the movable cistern is raised or lowered, its micrometer is adjusted to keep

the bubble level horizontal. The differential pressure range of the instrument is two inches of mercury. The

uncertainty in reading is 1.6 X 10~* in (4 X 10~^

mm) , about the same as that of the simple U-tube using

micrometers with index points to measure the column

height.

Long [5304] also designed an instrument relying on the detection of a null position of the liquid level, here the interface of two liquids. Two cisterns, one containing water and the other a mixture of chlorobenzene

and mineral spirits, are connected by tubing from the bottom of one cistern into the liquid through the top

of the other. A section of the tubing is vertical, so that the liquid interface position is a function of the pressure. A "proximity-switch" is installed outside of the tubing at the liquid interface position at zero differ- ential pressure. To detect changes in the liquid interface

level, a substantial difference in the dielectric constant

of the two liquids is essential. By means of a relay, the switch operates a servomotor and thereby a precision screw to which one of the cisterns is attached. The

vertical motion of the screw is indicated and is proporFiGURE 8. Stimson-Guildner manometer.

A, B, C, and D, cisterns; BR, capacitance bridges; CA, capacitor

disks; CI, cast iron base; G, gage blocks; P and Po, system and refer- ence pressure; Kl and K2, knife edges; T, tubing; TM, tilt meter.

tional to the differential pressure. The use of these two

liquids gave a sensitivity 17 times that of a U-tube water manometer. An accuracy of 5 X 10"^ in of water (1.2 X 10~^ mm) is claimed. Seven readings per minute can be obtained. The application is for measuring low airspeeds with a pitot-static pressure

head.

Stimson [5579], and later Guildner [62238], de- signed and continuously developed a mercury manometer for precise measurements of pressure for use in basic gas thermometry. A schematic diagram is shown

in figure 8. Two cisterns A and B, 76 mm in diameter,

are connected by metal tubing T which has flexible joints so that cistern A can be raised or lowered. Gage

blocks G serve to measure the difference in elevation

of cisterns A and B and hence of the mercury columns.

A capacitor CA is formed in each cistern by the mercury surface and a metal disk, the latter supported by

a glass optical flat. Each capacitor is connected to a capacitance bridge BR. The tilt meter TM consists of two cisterns C and D connected by tubing and sup- ported on knife edges A^^l and K2 which are part of the

pedestals for A and B. Cistern C can be adjusted vertically by screw /. Mercury to metal disk capacitors

connected to capacitance bridges BR detect changes in the mercury level produced by tilt in the plane of

cisterns A and B. The manometer is mounted on a massive cast iron base CI, and is installed in an underground temperature-controlled room. In operating the manometer, a reference position is established for the gage blocks when pressure in A and B is equal by

lowering cistern A until the bridges BR connected to cisterns A and B are in balance. Any small residual un- balance is eliminated bv adjusting a trimmer capacitor

in one of the bridges. To measure absolute pressure P,

cistern A is kept evacuated, and is adiusted vertically

with gage blocks until the bridges BR connected to cisterns A and B are again in balance. The added gage

blocks give the difference in height of the cisterns and

thus of the mercury column. Readings on the tilt meter

are taken concurrently and are used to apply a cor- rection for the small changes in tilt of the base CI

which have been found to occur. The overall results are accurate within 3 parts in a million in the pressure

for pressures below 760 torr. The uncertainty increases

at pressures below about 100 torr.

2.6.2. Inductance Transducers

Hart [6119] uses the null position of a float, in- dicated by an inductance transducer and produced by

a piston controlling the liquid level, to measure small

pressures. The piston motion, proportional to the pressure, is measured by a micrometer. In the design,

figure 9, the U-tube manometer consists of concentric

legs C and A -\- B, or A -\- C and B, selected by op- erating the valves indicated in the tubing connecting

to pressures PI and P2. This selection is needed be- cause of limitations in the transducer motion. The

float F is connected to the movable iron core element

of the linear differential transformer E. Deviations

10
P2 PI P2

Figure 9. Float micromanometer, null type. A, B, and C, concentric cisterns; D, piston controlled by micrometer M; E, electrical inductance; F, float; G, inductance bridge; H, potentiometer; Pi, P2, applied pressures.

from its position at zero differential pressure are in- dicated by inductance bridge G and potentiometer H.

Piston D is operated by micrometer M to bring the in- ductance back to the null value. The sensitivity is controlled by the cross-sectional area of the piston and

also by the combination of cisterns selected. Toluene was the liquid preferred over water, water with an

aerosol added, or kerosene. The range of differential pressures measurable varied from 10~* to 1 in of water (2.5 X 10~^ to 25 mm). The stated accuracy is 10^® in of water (2.5 X 10~^ mm). The instrument was designed to measure low airspeeds in a wind

tunnel with a pitot-static head. Possibly vacuum could

be measured also if a low vapor pressure oil were used

as the liquid.

Elgeti and Eckert [65349] employed a simpler de- sign than Hart for the same purpose. In figure 10, a

float F in one leg of the U-tube is attached to armature AR. A commercial inductance transducer C detects the

float-armature position, the signal is amplified by A,

and the output voltage indicated by voltmeter /. The

pressure range was 2.5 mm of water (0.18 torr) with

a sensitivity of 3 X 10~^ mm of water. The differential pressure was measurable to 0.001 mm of water with an estimated accuracy of ±3 percent. A plunger PL

operated by micrometer M was used to calibrate the micromanometer.

Golek, Klimek, and Matysik [6819] surrounded each

leg of a U-tube manometer with a primary and second- ary coil. In effect the arrangement is a linear differ- ential transformer with the change in the mercury

level controlling the output of the secondary coil. The input voltage was 220 V ac. The output of each

secondary coil was fed to a bridge. The difference in the rectified voltage of the two bridges was measured.

The accuracy was stated as 1 percent. The theory gov- erning the operation of the gage was given in detail. Reamer and Sage [6008] developed an instrument

to measure differential pressures at ambient pressures

as high as 15,000 psi (1000 atm) , at temperatures from

400 to 1500 °F. The precision was 0.05 torr with an

estimated accuracy of 0.25 torr. Schematically in figure

11, C and T form a U-tube mercury manometer en- closed in heavy walled chambers. A flexible metal

Figure 10. Float micromanometer-inductance transducer. A, amplifier; AR, armature; C. inductance transducer; F, float; /, voltage indicator; M, micrometer; P—Po, differential pressure; PL,

plunger.

Figure 11. High-pressure micromanometer.

A, piston; B, high-pressure housing; C, high-pressure cistern; D, dia- phragm; LT, linear differential transformer; M, micrometer; Po, ref- erence pressure; P—Po, differential pressure; T, manometer tube.

Figure 12. High-pressure micromanometer.

A, amplifier; AR, armature; C, coils of inductance transducer; L,

flexible tubing; P—Po, differential pressure; R, restriction; S, sprocket; SM, servomotor; U, manometer tube.

diaphragm D divides chamber C, with mercury below

and an oil above the diaphragm. A linear differential transformer LT indicates the deflection of the dia- phragm, but is used only as null indicator. To measure

the differential pressure P — Pq, the volume of mercury

removed or added to restore diaphragm D to its null position is measured. To make the measurement, piston

A enclosed in housing B is moved up or down by a

precision screw M and gearing (not shown) to obtain

sensitivity. The motion of the piston was calibrated in terms of P — Po, which had a range up to 1 atm.

11
Bell [65348] also designed a manometer to measure

differential pressures at high pressures, in this case

in the range 0.02 to 100 in (0.5 to 2500 mm) of liquid

column height at absolute pressures up to 2500 psi

(170 atm). An inductance device detects the null posi- tion of the liquid surface, water or mercury, and by

a feedback circuit raises or lowers one leg of the U-tube

to maintain the null. The details are indicated in figure

12. An armature AR floats in U-tube leg U. Its position

is detected by fixed-inductance coils C, the output of which, amplified by A, is fed to servomotor SM. The

latter rotates a sprocket wheel S, which lowers tube U

when a positive differential pressure P — Po is applied,

until the null position is restored. The measured angular deflection of SM equals one half of the liquid col- umn height P — Po- The tubing L is flexible. A restric- tion R in the connection to Pq was found necessary. The time lag was 2 min.

2.6.3. Resistance Transducers

The variation of an electrical resistance immersed

in a mercury column has the virtue of simplicity, but

the sensitivity of designs thus far developed is inadequate. Simon and Feher [2905] describe one design.

A closely wound coil of wire is located in the slant tube of a U-tube manometer. The electrical resistance of the wire above the mercury surface is the pertinent

value, since the mercury column practically short cir- cuits the part of the wire still in the mercury. To measure the change in resistance with change in pressure, Simon and Feher placed the wire in the filament heat- ing circuit of a vacuum tube and measured the output

of the vacuum tube with a milliammeter. An accuracy

of 0.1 torr was obtained, inadequate for most applications. Capillary irregularities and heat conductivity

effects contribute to uncertainties in accuracy. Stock and Fill [4926] used platinum wires in each

leg of the U-tube mercury manometer, and made meas- urements with an unbalanced bridge.

Zalma, Guerin, and Fraissard [6811] looped a platinum wire in one leg of a U-tube filled with mercury. The electrical resistance of the wire was recorded

with a sensitivity of 1/10 f2. No details on the pressure

sensitivity were given.

Klumb and Haase [3207] investigated the use of a tungsten wire submerged in a mercury column and came to the conclusion that it was of no value in measuring absolute pressures below 1 torr. However, Sidenius [6814] installed a loop of tungsten wire in an oil- filled manometer tube. The wire was heated to 350 °C

in air. The heat loss with change in liquid column

height was measured as a change in voltage while the

electric current in the circuit was maintained constant. The pressure range was 1 to 1000 mm of oil; the resolu- tion was 0.03 mm of oil; and the accuracy ±1 percent.

2.7. Ultrasonic Transducer

Wallace and Tiernan have announced (October 1968)

the development of a sonar mercury manometer, the novelty of which merits including a brief description.

A large-bore U-tube, temperature controlled, has a means for generating ultrasonic sound pulses at the bottom of each leg. These pulses traverse the mercury

columns and are reflected back at the mercury surface. The electronics is designed so that the time between

the return of the two echoes, proportional to the dif- ference in mercury column height, is determined by

counting pulses from a clock oscillator. The resolution

and sensitivity claimed are 0.001 in of mercury (0.025

torr)

.

2.8. Linear Amplifiers of Column Height

The designs to be described here include only those

in which the primary column height has been linearly

amplified by producing a displacement in an auxiliary

liquid surface. Where a fixed point index or the inter- face of two liquids are involved, the discussion is more

conveniently given under those headings. This leaves two fundamental designs to be discussed: first, those

having gas bubble indication, and second, one in which the volume of the liquid column is transferred

to a capillary tube to obtain a long liquid filament.

2.8.1. Gas Bubble Designs

A gas bubble has been used as a detector by a number of experimenters, often unaware of previous de- velopments. A small-bore tube is essential to contain

the bubble, this usually being the tubing connecting the two cisterns of the U-tube. Thus, the bubble movement

is always much greater than the change in column

height. The greatest sensitivity is obtained when the bubble tube is horizontal. The magnification then ob- tained is proportional to 0.5 D^/d^, where D is the bore of the manometer tubes at the liquid surfaces, and

d the bore of the bubble tube. Instruments have been

built with magnifications up to about 1000. Designs

have been proposed in which the bubble motion is an

indicator of the pressure change; others in which the bubble is used to indicate a null position secured by

tilting, the amount of which is the desired indication.

If the gas bubble is used when the manometer fluid

is water or liquid other than mercury, the gas bubble

may be partially or completely absorbed. This, of course, can be countered by having the liquid in the saturated condition, which may involve temperature

control, since the amount of gas absorbed is a function

of temperature. In any .event, the rates of absorption

and desorption are small enough to permit unaffected readings to be made on a short-time basis. The trans- ference of liquid across the bubble is another source

of error. It is avoided in part by enclosing the gas bubble in small-bore tubing and by selecting the liquid,

about which more will be said. Inevitably, some liquid transference will occur whenever the bubble moves at least its own length, but this transfer will normally be

insignificant.

When mercury is the manometer liquid, it becomes

important to have the bubble tube bore as large as possible to prevent sticking of the mercury column and not

so large as to permit liquid transfer. The sticking mani12
JL

P2

//V /

Figure 13. Gas bubble micromanometer. A and B, cisterns; C, gas bubble; PZ—Pl, differential pressure; M,

micrometer.

fests itself by a variable meniscus height and is a source of error to the degree that a pressure difference

exists across the mercury surface. Tapping the tube

reduces the sticking, but does not necessarily eliminate

it. The use of gas bubble tubing much below about 2 mm in bore introduces a source of intolerable random

error in this respect. There is one advantage with

mercury; no gas from the bubble is absorbed by the mercury, and distillation of the mercury across the bubble is slow. The earliest use of the gas bubble indicator appears

to be Threlfall [0401], Roberts [0603], and Henry

[1201]. The design is shown in figure 13 and consisted

simply of cisterns A and B and bubble C; the other

parts shown are not here pertinent. Roberts preferred

alcohol over water; Henry used either water or carbon

tetrachloride. The above-described simple design using

mercury was constructed by Hanley [6452] and, using

a low-density liquid (unspecified), by Burka [6458].

In both designs a motion of the bubble was about 16

times the change in column height of the liquid. Hanley

secured a sensitivity of 0.01 torr in the pressure range

0.01 to 5 torr. The design shown in figure 13 was developed by

Ower [3010, B496]. The entire instrument has a ful- crum at cistern A and a micrometer M for tilting the

entire instrument. It is filled with xylol. Any difference

in pressures PI and P2 produces a movement of the gas

bubble; operation of micrometer M restores the gas bubble to the initial zero position. The amount of the

tilt is measured and, from a knowledge of instrument

geometry, the differential pressure can be calculated. The sensitivity obtained was 5 X 10~® in of water

(1.3 X 10~* mm). The design is an improvement on

the Chattock manometer, described in section 2.9. Duffy and Norbury [6710] reverted back to the Chattock design with some simplifying changes. Refer- ring to figure 13, the tube connecting the two cisterns was brought into cistern A from below and protruded

into it. The denser liquid, a mineral oil, was in cistern A, the less derise, an alcohol, was in cistern B. A gas bubble separated the two liquids in the small diameter

protruding tube. When a pressure was applied at P2,

the position of the bubble was maintained constant by

tilting the manometer by micrometer M, as in the Chattock gage. From the tilt the differential pressure P2 —

PI was computable. The sensitivity claimed was 15 X

10-6 in of alcohol (about 2.2 X 10"^ torr).

Young and Taylor [4716] developed a design specifically developed for measuring vacua. The design is

Figure 14. Two-liquid, gas bubble micromanometer. A and B, cisterns; C and D, auxiliai-y cisterns; F, pentane; Hg, mercury; G, gas bubble; P—Po, differential pressure.

shown in figure 14. Pressure is applied to cistern A

while cistern B is maintained at a high vacuum. The

mercury columns extend from A and B down to cisterns C and D. The upper parts of C and D and the connecting tubing, except for gas bubble G in the horizontal

part, are filled with pentane. The application of the pressure causes gas bubble G to move; the geometry

is such that the pressure equals %/1056, where x is the displacement of the bubble. The pressure range measurable is 8 to 83 X 10~'^ torr; the estimated accuracy,

1 percent. The theory was presented. The bore of the gas bubble tube was 1.26 mm; reduction to 0.92 mm

increased the time for equilibrium from 0.5 to 2 min.

2.8.2. Puddington Manometer

The monameter proposed by Puddington [4829],

figure 15, is ingenious. As in Pearson's micromanometer, section 2.2.2.2, a volume change is measured. It was found to have little practical value because erratic

capillarity significantly affected the accuracy. Los and

Morrison of Puddington's group subsequently devel- oped a preferred design of micromanometer [5104]

which is discussed in section 2.6.1. In figure 15, A and

B are cisterns which are subjected to pressures PI and

P2. Capillary tubing D, and an auxiliary reservoir C,

form part of the instrument as shown in the figure. To

obtain a reference reading, valve V\ is opened, pres- sures PI and P2 are equalized; the volume of mercury

PI JL Jk

Figure 15. Puddington micromanometer. A and B, cisterns; C, reservoir; D, capillary tube; PJ—P2, differential pressure; Vl and V2, valves; a and b, liquid level change from Pl=P2 to P1—P2; c and d, fixed marks.

13
in the system is adjusted (means not shown in fig. 15)

to bring the mercury level to mark J on a capillary tube

above reservoir C; valve VI is closed and the mercury

in C forced to flow until cistern B is filled to mark c

in the capillary tube. The mercury surface falls to mark a in capillary tube D; its location on a scale is the zero reading. The mercury is then returned to reservoir C, valve VI is opened, and if needed, the mercury volume adjusted to mark d. A small pressure

applied to cistern A results in a rise in the mercury in cistern B. Valve VI is closed, and again the mercury

forced to mark c, resulting in a reading b of the mercury surface in tube D. The volume of mercury in the

capillary tube between points a and b equals the change

in volume of mercury in cistern B, produced by the pressure difference PI — P2, from which PI — P2

can be calculated. In one design, a magnification of 1760 was obtained, that is 1760 {P1 —P2) = b —a. This involved using capillary tubing D of 0.78 mm in bore; erratically variable capillarity prevented reliable readings of a and b.

2.9. Two-Liquid Designs

Two liquids are used in micromanometers in various

designs. A design reviewed at length by Ower [B496],

and used for measuring small differential pressures at atmospheric pressure, will be briefly discussed. In its simplest form the manometer is a U-tube with a reser- voir at the top of each tube. Two immiscible liquids of different densities are poured into the U-tube so that an interface forms in the vertical section of a tube

and the free surface of each is in its reservoir. A differ- ential pressure Pi — P„ applied to the reservoirs re- sults in a displacement of the interface. It can be shown

that

Pi - P„ = [(P2 - pi + (pi + p2) IgH

where Pi is applied to the reservoir containing the

less dense liquid; p2 and pi are the densities of the

liquids; r and R are the internal diameters of the tub- ing and the reservoirs ; g is the acceleration of gravity

;

and H is the displacement of the interface. The recip- rocal of the bracketed quantity is the amplification,

which Ower states will not exceed 10 or 12 in practice.

Ower also describes a design in which the U-tubes

are concentric, again with reservoirs at the top. There

is no difference in principle except that the concentric

tube design eliminates one of the two tilt errors. Long's design [5304], described in section 2.6.1, is essentially the same as the above described design, ex- cept for the means of indication. The design by Young

and Taylor [4716] was described in section 2.8.1. The Chattock micromanometer [B496] is of the

tilting type where an oil separates the water used in the U-tubes and the liquid interface is used to indicate the null to be obtained by the tilt. Ower [3010] substituted with advantage a gas bubble as the indicator

of the null; it is described in section 2.8.1. The earliest micromanometer, usually ascribed to Huygens, circa 1650, may be visualized if tube D in

r

Hg

Figure 16. Modified Huygens manometer. A and B, cisterns; C. oil; D, horizontal tube; P1—P2, differential pressure.

figure 16 is vertical instead of horizontal. An oil was

placed on top of the mercury in one cistern. Practically, the rise of oil in the tube is about the same as

that in a U-tube manometer with water as the liquid,

Huygens constructed a barometer, in which cistern A

was elevated to secure a head of mercury of barometric

height, and evacuated.

Drucker, Jimeno, and Kangro [1504] modified

Huygens' design (possibly not the first to do so) by

making tube D horizontal as shown in figure 16. They

used sunflower seed oil on top of the mercury ; oils with

lower vapor pressure, but not lower gas adsorption, are now available. In their design, the amplification in

oil surface displacement over that of the mercury col- umn was of the order of 150, a tenfold gain over Huygens' design.

Burka [6458] proposed, but did not construct or

analyze a design in which tube D, figure 16, was elimi- nated and one of the two immiscible liquids was placed

in cistern A and the other in cistern B. The interface was formed in tube E. An analysis indicated the best amplification occurred when A and B have equal and

large cross-sectional areas and the cross-sectional area

of E is as small as practicable. A magnification, as high

as 50, of the indications of a U-tube manometer could

be secured. The proposed design differs from the Threlfall design using a gas bubble (described in section

2.8.1) only in the substitution of the interface of two

immiscible liquids as an indicator. The design proposed by Brow and Schwertz [4720]

is shown in figure 17. It is a variation of Pearson's

design, shown in figure 2. The two liquids are water,

LI, and colored kerosene, L2. Pressure PI is applied

to cistern A and pressure P2 to cistern D. A change in the differential pressure produces a vertical displacement h in the liquid interface in tube C, which is observed. The relation PI —P2 = Kh gives the pressure where K is a constant depending on the geometry; = 35 for the constructed instrument. A sensitivity

JL JC

B - L2

C P2 JL

LI n'=—

—H 1

1

Figure 17. Two-liquid micromanometer. A and D, primary cisterns; B, auxiliary cistern; C, capUlary tube; Ll, water; L2, colored kerosene; P1—P2, differential pressure.

14
of 10~^ in of water was claimed. If mercury is used as

the primary liquid LI, and an oil for transfer liquid

L2, small absolute pressures would be measured with

about the same amplification factor K, where PI —P2

would now be in terms of the height of a mercury

column.

2.10. Inverted Bell and Cartesian Diver

In an instrument often imprecisely but conveniently

called a cartesian diver, an inverted bell B floats on

mercury, forming a concentric U-tube as shown in fig- ure 18. Neglecting capillary forces, the weight of the

bell, plus controlling weight C, and the force due to the gas pressure acting on the upper surface of the

bell, are balanced by the buoyant force of the mercury

plus the force due to the gas pressure under the bell. For measuring low absolute pressures, the gas under

the bell is evacuated, for which purpose valve V is provided. The system pressure PI is admitted to container A. Displacement of bell B is measured by a

scale on rod or metal strip E, using disk D as a refer- ence. An increase in pressure PI results in a downward

force on bell B, equal to the product of the pressure in- crease and the cross-sectional area of bell B. This force

is balanced by the increase in buoyancy of bell B

as the liquid level rises inside B. In practical designs, the displacement of E is about 10 times that of the corresponding height of the mercury column. The

theory of operation is given by Germann and Gagos

[4311] ; the instrument is described by Reilly and Rae

[B533], who describe an alternative and probably more sensitive method of indication. Blase [60227]

proposes, without details, the use of a differential trans- former for measuring the displacement of rod E; a complication not worthwhile for a simple, rugged, lowsensitivity instrument such as this. While not entirely germane here, the application of the cartesian diver to pressure control should be mentioned. The upper end of rod E, figure 18, could be

equipped with a disk or a needle to seat at disk D. PI

is now connected to a vacuum source, and tube F to the system the pressure of which is to be maintained

constant. If the pressure rises above the set value, the valve at D opens, and gas is pumped out through PI

until the falling pressure in A causes valve closure. If pressures below the set pressure can develop in the system, it is seen that another controller is needed

which would be a second manostat of the same design,

except that the valve at D is set to open if the pressure

falls below the set pressure, and the manostat is con- nected to an appropriate source of pressure. Gilmont

[4633] develops the underlying theory of the manostat and [5169] describes a number of designs for various

applications. Oxley and Stockton [6623] describe a pressure regulator in which a photocell senses the posi- tion of the diver, and in turn controls the valves. The instrument developed by Hindley [4702] may

be called either an inverted bell or a gasometer-type

micromanometer. It is useful only for measuring differ- ential pressures differing slightly from ambient atmospheric pressure. Commercial versions differing essentially from Hindley's design in the means of indication

have been available in past years, but seem not to have been described in technical publications. The

application of a commercial version as a standard is briefly described by Perls, Kaechle, and Goalwin

[5305]. Referring to figure 19, identical inverted cups B dip into reservoirs of kerosene or other low-density

liquid. The spaces above the liquid in cups B are con- nected to pressures PI and P2, the difference between

which is to be measured. Cups B form two arms of a

balance, pivoted at C; any change in the balance, nor- mally due to a change in PI —P2, is indicated by

pointer E moving over scale S, observed with the aid

of optical magnification. The fulcrum is a beryliumcopper strip normal to the plane of figure 19, its center fastened to balance arm D and its ends fastened se- curely, so that the forces acting on cups B are balanced

by the elastic twist of the fulcrum strip. The torques

to be measured are very small; the necessity of elimi- nating friction is obvious. The changes in buoyancy

of the cups with pressure changes are small, so that the major forces are produced by the vertical pressure

difference across the cups. The pressure range for the instrument as constructed was 10"^ to 0.05 torr. An inverted bell instrument utilizing photocells, de- scribed by Ower, is briefly discussed in section 2.4.3.

c "3"

P2

S Figure 18. Cartesian diver. A, tube subjected to pressure Pi; B, diver subjected to pressure Pl—PZ; C. weight; D, reference disk; E, rod connected to B and C;

F, tube; V, valve.

Figure 19. Inverted bell micromanometer.

A, cups; B, inverted cup or cell; C, fulcrum; E, pointer; Pi —Pi?, dif- ferential pressure; S, scale.

15
2.11. Force Balance Designs

The use of weights to return a significant part of the instrument to a null position is attractive in view

of the inherently high accuracy of weights. However,

in micromanometers, the force to be applied is small, so that frictional and other extraneous forces must be

minimized in practical designs.

2.11.1. Hickman Gage

Hickman [2903] describes a design used in manufacturing vacuum tubes to measure pressures in the range 0.01 to 5 torr. The entire instrument is free to turn about fulcrum Z), figure 20, and is balanced by the buoyant force of float F in reservoir C containing mercury. The equilibrium position when pressures PI and

P2 are equal is indicated by arm E when opposite to a mark at H. A pressure increase in P2 causes the mercury level to fall in cistern B and arm E to rise to H'

.

Weights applied at G return E to position H. The differ- ential pressure, P2 —PI = KW, where W is the weight

added to G, and ^ is a constant depending upon the geometry. A rough calculation indicates that K equals

1/150 when P2 —PI is in torr units and W is in grams. Note that the buoyant force on F remains constant when arm E is in null position H. Hickman expected

and encountered difficulty with errors caused by erratic

capillarity. This he reduced by using a wetting agent on the surfaces of the mercury, either butyl phthalate or tetra-ethylene-glycol methyl ether; these in turn introduced errors due to their absorption of the ambient gases.

1 P2

E A

F

/ ^^^iirr C

D //////

Figure 20. Buoyant force balance micromanometer.

A and B, cisterns; C, reservoir; E, pointer; F, float; G, weight pan; H and H'. null (P2—Pl = 0) and position when P2 exceeds Pi.

2.11.2. Kemp Gage

Kemp [5945] utilized weights to balance an elastic stress caused by the shift in liquid in the U-tube due

to a pressure change. The cistern A, figure 21, is firmly

held, while cistern B is held by elastically identical tubes Tl and T2 fastened to A. The reference pressure

is Pq. Any increase in pressure P causes the liquid in cistern B to fall, and in cistern A to rise. The loss of

liquid in B is balanced by a change in the stress in tubes Tl and T2, while maintaining a difference in column height proportional to P — P^,. To determine

the null position of the liquid surface in A, an induct- ance transducer E is used, one element of which is mounted on float F. Weights are added at C to bring

the transducer and the float back to null. The pressure

difference P—Po = KW, where W is the weight ap- plied at C, and is a constant depending upon the

Po

Figure 21. Elastic force balance micromanometer.

A and B, cisterns; C, weight pan; E, inductance transducer; F, float; Po, reference pressure; P—Po differential pressure; Tl and T2, tubes,

elastically alike.

elastic characteristics of the tubing and the U-tube

geometry. Water was the manometer liquid used. At

first sight, it appears that a vacuum could be measured

with the same numerical accuracy but in millimeters of mercury instead of millimeters of water, but only exper- imentation can verify this conclusion. The differential pressure range of the instrument extended to 5 mm of water; at the upper part of the range the estimated er- ror was 0.01 mm of water; at 0.01 mm of water, the estimated error was 5 X 10 ~* mm of water.

2.11.3. Ring Gage

One of the advantages of the ring gage is the possibility of measuring small differential pressures at high

absolute pressures, since a metal ring can have the

strength to withstand high pressures. This application

has received some attention, but needs no further consideration here except to mention Schmidt's discussion

[3601].

Hickman [2903] describes a ring gage found to be

useful only for rough measurements of vacuum. The

gage consists of a tube in the form of a ring. An air- tight disk at the top secures two pressure compartments.

Mercury is in the lower third of the ring. The ring, in Hickman's design, is pivoted at its center and restrained

from deflecting angularly by a spiral spring of small

stiffness. A difference in pressure across the airtight

disk causes the ring to deflect angularly until the re- storing torque of the spring equals the torque produced

by the unbalance in the mercury columns caused by

differential pressure. The measured angular deflection

is a function of the pressure difference. Blase [60227] outlines briefly a design of a pivoted

ring gage in which the null position is restored by

weights, or automatically by a force produced electrically. He states that the latter type is available commercially in Germany. •

2.11.4. Weighing Barometers

Weighting barometers or manometers should be mentioned, in view of their great sensitivity. These are de- scribed by Middleton [B641] as barographs. The

classical design has the barometer tube suspended from

one arm of a precision balance and otherwise free, except for the lower end dipping into a cistern of mercury. As the mercury level in the tube changes, so does

the tube weight.

Brown [6704] describes a variation from the abovedescribed design. One leg of a U-tube is suspended from

16
a precision balance and is connected by flexible tubing

to the other leg and to a source of vacuum. Deviations

from the weight of the tube at zero differential pressure

give the absolute pressure P in absolute units by the simple relation

where mg is the change in weight of mercury column

from zero differential pressure and A is the cross-sec- tional area of the U-tubes. Overall accuracy claimed is ± 0.001 in of mercury (0.025 torr). While the re- quired flexible joints to the weighted barometer tube

received considerable attention, there lingers some

doubt that all possible sources of joint error have been

eliminated.

3. Gas Column Manometers

Gas columns in relatively long U-tubes can be used

to obtain small computable pressure differences if the temperature or gas composition of one leg differs from

that of the other. Fry [1308] had an inverted U-tube filled with air. The temperature of each leg was controlled. The pres- sure difference at the bottom of the legs of the U-tube

is proportional to the difference in the reciprocal of the temperatures multiplied by the height of the U-tube. This pressure could be varied by tilting the U-tube,

in effect reducing its height. The difference in pressure

thus obtained was used to calibrate micromanometers.

Pressures below 0.1 torr are obtainable.

Simmons [5488] designed an instrument for measuring small differential pressures at approximately

atmospheric pressures produced by a pitot-static tube

installed in a wind tunnel. The upper ends of two

long vertical tubes were connected respectively to the

pitot tube and the static tube. The temperature of the

air-filled tubes was controlled; that connected to the

static tube was the hotter. The airspeed in the wind

tunnel was adjusted so that the pressures in the two

vertical tubes were equal. To determine equality in the pressures the two tubes were connected at the bot- tom, with two smoke-filled reservoirs in the connecting

tubing. A short tube between the reservoirs was viewed

by a microscope to detect the passage of smoke, in one

direction or the other. The absence of smoke motion

indicated pressure equality. From the geometry and

the temperature of the vertical tubes, the difference in the applied pressures was computed. The pressure range

of the instrument as constructed and operated was 0.5

to 14 dynes/cm^ (3.8 to 105 X lO"* torr), with a

sensitivity of 0.0005 dynes/cm^ (3.8 X lO^'^ torr).

Both Threlfall [0605] and Lynn, Corcoran, and Sage

[5614] used the gas-column manometer to measure

the density of a gas. The gas of unknown density was

admitted at the top of one leg of a long U-tube (over

100 in high), and a gas of known density to the other

leg. Two cisterns were installed, one at the bottom of each leg and connected by a tube with a horizontal section. The cisterns contained a liquid, methyl alcohol in the case of the Lynn design, with a gas bubble in the horizontal tube section. The displacement of the bubble

is a measure of the pressure difference at the bottom

of the two legs. The temperature of the U-tube legs was maintained constant at selected values. From a knowledge of the column height, the differential pressure, gravity, and the density of the reference gas, the density of the test gas can be computed. Lynn obtained

a sensitivity as good as 2 X 10~® in of methyl alcohol

(roughly, 3 X lO-^torr).

Herskovitz [6629] applied a Michelson interferometer to measure the change in light path of a gas column

in order to measure the gas pressure. Briefly the number of fringes counted is a function of the index of

refraction of the gas and the length of gas column

traversed by the light beam. The index of refraction is a function of the gas density, from which the gas pres- sure can be calculated, if the gas temperature is known.

It also varies with the gas composition, which must

therefore also be known. The gas sample was sealed

in a cylindrical container. The light beam was reflected from an optical flat at the bottom of the container. A

monochromatic light source was used. A change of 0.1 fringe was measurable which was equivalent to a pressure change of about 1 torr for atmospheric gases. Further development could increase the sensitivity, per- haps into the micromanometer range, but the chief drawback is that the gas composition must be known.

4. Elastic Element IVIicromanometers

4.1. Primary Elastic Elements

In general, in a micromanometer of this type, an

elastic element is interposed between the system in which the pressure is to be measured and a reference system. If the reference system is at zero or constant

pressure, absolute pressure is measured; if the refer- ence pressure is not zero and variable, differential pressure is measured. If the reference pressure is

atmospheric pressure, gage pressure is measured. If atmospheric pressure is measured, the instrument is an aneroid barometer.

The pressure sensor may be either a flat or corru- gated diaphragm or capsule, or a Bourdon tube, or a bellows. Its deflection under presure is generally amplified either by mechanical, electrical, or optical means.

Before considering these transducers, the fundamentals

of the various sensors will be reviewed.

17
Van der Pyl has compiled a bibliography on dia- phragms and aneroids [60231] containing 171 abstracts, and also one on Bourdon tubes and Bourdon

tube gages [5384]. Wahl [5796] has prepared a sur- vey on flat diaphragms listing 41 references. The first two listed were issued as ASME preprints and there- fore unfortunately are probably available only in the Engineering Societies Library in New York. Attention

is called to the book on elastic elements of instruments

by Andreeva [B622].

On many of the designs to be described, data are given on the accuracy or sensitivity of the indication

as obtained by the designer. These values may not be

the ultimate obtainable; subsequent improvements in the construction of the pressure sensor, diaphragm.

Bourdon tube, or bellows, and the development of

better materials may have by now made greater sensitivity possible.

4.1.1. Diaphragms

Metal diaphragms may be either flat or have one

or more corrugations. Flat diaphragms are initially more sensitive than corrugated ones of the same diameter and thickness. By controlling the number and shape

of the corrugations, a wide range of pressure-deflection

relations is obtainable with corrugated diaphragms, in- cluding deflections linear with pressure. In the case of

flat diaphragms, buckling (oil-canning) is avoided by

placing them under radial tension, created thermally

during installation. The manufacture of corrugated

diaphragms to have identical sensitivity seems practically impossible, so a selection process must be used. Way [3411], and others, have developed theories

governing the relation of pressure to strain for both

the edge-free and the edge-clamped flat diaphragm

without radial tension. Only the edge-clamped, thin dia- phragm, with initial radial stress, is of interest here. Wahl [5796] indicates that a theoretical analysis of

the latter case has not been made.

Theodorsen [3108] has discussed practical problems

involved in flat diaphragm gages used in aeronautical

research. His theory indicates that the diaphragm deflection is directly proportional to the differential pressure. On the other hand, his data, and that of many

other experimenters, show that the deflections may be

either linear or nonlinear with pressure. Probably the method of clamping (Carter, et al. [4927]), and to a greater degree, the amount of initial radial tension, account for the variations from linearity. Theodorsen

emphasized the necessity of having the diaphragm

under initial radial tension to avoid an unstable zero. His significant contribution was to determine that the abnormally large temperature effects were caused by

differential expansion of the various materials composing the pressure cell. The differential expansion

changed the initial radial tension, aggravating the temperature effect. Incidentally, he compensated for temperature changes by soldering a central disk of a

different metal to the diaphragm; this was necessary where instrument temperature was not controlled. Carter [4927] machined the diaphragn and support

out of a solid block of metal; the minimum diaphragm

thickness was 0.004 in, too thick for a micromanometer.

Usually flat diaphragms now used are of metal. However, some experimenters have made use of plastics or a rubber in order to obtain greater sensitivity. One

possible objection to the use of plastics or rubber is the tremendously greater effect of temperature changes on the stiffness. The theory covering the elastic deflection of corru- gated diaphragm capsules has been developed by Griffith [2807] and Grover and Bell [4832] and for clamped diaphragms by Haringx [5795]. These the- ories have been summarized by Wildhack, Dressier,

and Lloyd [5772], together with a theory by Dressier

[59194], for both the free (capsule) and clamped cor- rugated diaphragm. Computations using Dressler's the- ory practically require the use of an electronic computer. A theory, checked by experiment, was also developed by Akasaka [5583] in Japan.

For a given deflection of a corrugated diaphragm,

the central force equals about 0.4 of the product of the pressure and the area of the diaphragm. For a thin

flat diaphragm this value is about 0.25 [5772].

Corrugated diaphragms are generally formed, when

small quantities are required for experimentation, by

hydraulically pressing a flat blank into a die; instru- ment manufacturers find this procedure too slow and

expensive and use two dies in a press with the blank

between the dies. By suitable heat treatment and pres- sure cycling, equivalent performance can be secured

from diaphragms made by either process. Some data on the effect on the pressure-deflection curves of various corrugation shapes, depths, and numbers are summarized in [5772]. However, more data

are needed to complete the picture.

The corrugations are generally concentric. Diaphragms thinner than 0.002 in (0.025 mm) are hard

to handle. Cordero, Matheson, and Johnson [5771]

describe a diaphragm having radial corrugations

formed from brass 0.001 in thick. The required pres- sure-deflection relation was that P = kd^" over the pressure range —30 to -|-30 dynes/cm^ (2.2 X

10""^

torr)

.

Capsules constructed of several corrugated dia- phragms are commonly used in instruments where the

deflection is multiplied by levers and gears. Where

electrical or optical means are used to obtain an in- diction, a single diaphragm, flat or corrugated, is us- ually used. In micromanometers measuring low absolute pressures, the reference pressure should be low to avoid

stressing the diaphragm unnecessarily, and is generally maintained by a pump at a value significantly

below the system pressure.

4.1.2. Bourdon Tubes

Bourdon tubes are flattened or elliptical tubes bent

into various shapes, commonly to form either a circular arc or a helical coil, and rarely, a spiral. One end is fixed where the gas (or liquid) is admitted and the other end free to deflect. The deflection is angular.

18
An outstanding characteristic of Bourdon tubes is the small ratio of torque developed by the tube to the pressure causing it. The Bourdon tube gage is widely

used for measuring differential pressures above about

5 psi (250 torr) . In the micromanometer range, helical

coil Bourdon tubes of glass or quartz have had some

application, as will be described later.

It should be mentioned that extensive work has been

done on the theory of Bourdon tubes, culminating in that proposed by Dressier [65341]. See also Vasil'ev

[65340].

4.1.3. Bellows

Metal bellows are particularly useful as pressure

sensors when a large deflection and force are required.

They have, however, not been manufactured to have the

sensitivity required for micromanometers. Accordingly,

they have been used in micro .nanometers in special

situation^ only.

Manufacturers' catalogs are generally relied upon

for performance characteristics. The force developed by

a bellows is the pressure change times the average of the cross-sectional area fixed by the outer and inner

radial diameter of the convolutions.

4.1.4. Performance Criteria

All of the elastic sensors—diaphragms. Bourdon

tubes, and bellows—have elastic defects and are temperature sensitive. Elastic defects are of two kinds, one independent of time and the other time dependent.

Both occur simultaneously and are hard to separate in practice. Hysteresis is due to the fact that the strain, or

deflection, depends upon the direction which the stress, or pressure, is applied. Drift is the continued change

in strain with time after a stress is applied. Obviously,

a measured hysteresis will include some drift as well

as the hysteresis independent of time. Drift is quite

rapid initially and tapers off with time, but actually

may continue indefinitely if the stress is great. Experi- ments indicate that no matter how fast a pressure cycle

may be imposed (drift therefore small) or how slowly

(drift cancelled out) some hysteresis will be evident,

indicating a component independent of time. The effect of temperature is due to both the thermal

expansion (especially in constructions using dissimilar materials) and the thermal change in the modulus of

elasticity. The coefficient of the latter is of the order of 10 times greater than the former for most metals. Notable exceptions are certain nickel alloys. Generally,

thermal expansion causes a zero shift, while a thermal

change in the modulus of elasticity causes a change in the sensitivity to pressure. Usually the situation is not

that simple, since side effects may occur, such as thermal expansion changing the radial tension in a flat diaphragm and, thus, the sensitivity to pressure. In

practice, micromanometers are commonly used in air-conditioned rooms, which minimizes temperature

errors. The main improvement in performance of diaphragm

elements has come from the development of materials

which can be hardened by heat treatment after forming the diaphragm. The old standbys, phosphor bronze

and nickel silver, hardened only by cold working, still find application when the utmost in performance is not needed. Beryllium copper [4417], with about 2 percent

beryllium, is now generally used when instrument

temperature changes are not a factor. Ni-Span-C, an

iron-nickel-chromium-titanium alloy, has a temperature

coefficient of elasticity of nearly zero over a limited,

but useful, temperature range, and otherwise a per- formance about equal to that of beryllium copper. The

improvement can be measured by the fact that phosphor

bronze corrugated diaphragms had a useful deflection of about 2 percent of the diameter 30 years ago, and

now, with either beryllium copper or Ni-Span-C, this figure is up as high as 7 percent, without significant

increase in the elastic hysteresis or drift. For diaphragms unstressed except when a small dif- ferential pressure is applied, as is normally the case

for micromanometers, the elastic defects, hysteresis,

and drift, can be below about 0.01 percent of the total pressure change. This assumes the use of selected materials such as beryllium copper, or steel in the case

of flat diaphragms, all properly processed. Extraneous

effects such as those caused by poor clamping, or the use of soft solder, must be found and eliminated.

Also, the closer the procedure of calibration simulates the conditions of use, particularly in the time

rate of application of pressure, the smaller will be

the uncertainty in the measurement. Normally, the

elastic defects are not a limiting factor in the accuracy

of micromanometers.

If the diaphragm is normally in the stressed condition, as is the case in aneroid barometers where the diaphragm capsule is evacuated and its exterior subject to atmospheric pressure, the elastic defects are much larger. It is difficult to give a valid single number for the effect which will cover the many possible

designs and conditions of use: approximately, in the diaphragm capsules in aneroid barometers, hysteresis can be held to 0.1 percent of the pressure change and

the drift to about 0.2 percent. This percentage is for a large pressure change; for small pressure changes

the percentage will be somewhat greater.

What has been said about diaphragms applies equally

well to metal bellows. ITiese are available commercially

in beryllium copper and Ni-Span-C, so that about equal

performance can be obtained.

Only Bourdon tubes of quartz (fused silica) or glass are of interest here. Quartz has a very low drift and

elastic hysteresis compared to that of metals and thus

finds application in micromanometers of high repeatability, in making pressure measurements. However,

sensitive quartz Bourdon tubes respond sensitively to any imposed vibration. The temperature coefficient of

elasticity, while less than most metals, is still appreciable. Sosman [B271] gives +12 X 10~^ per

degree C for the temperature coefficient of rigidity: that for Young's modulus will not differ substantially.

Note that fused silica stiffens with increase in temperature in contrast to the behavior of most metals.

19
4.2. Secondary Elastic Elements

Torsion wires or filaments, usually of tungsten or fused quartz, are often used to restrain the angular

deflection of vanes (see sect. 6) or spoon-shaped Bour- don tubes (see figs. 27 and 43). Their elastic quality

is thus as important as that of the Bourdon tube. The

performance characteristics of fused quartz have al- ready been discussed. It remains to be said that the apparent modulus of rigidity of both tungsten and

fused quartz filaments increases as the diameter of

the filament decreases from about 1 mm [B271].

In micromanometers in which the pressure element

deflection is multiplied mechanically, hairsprings are

installed on the pointer shaft to obviate backlash. Although the spring torque on the pointer shaft is small, the elastic properties of the hairspring require some attention. The hairspring deflects with pressure changes and its stiffness (amplified by the amplifying

mechanism) is an addition to the stiffness of the pressure element. Elinvar hairsprings are available

commercially made of alloys of characteristics similar

to that of Ni-Span-C.

Helical springs are used in some designs of mechanical instruments to maintain the pressure element, us- ually a diaphragm capsule, in the null position. Its deflection is a measure of the pressure change. Obviously here the elastic properties of the spring materials are important. If temperature effects are not

important, the springs can be made of available good

quality alloy steels. Otherwise, isoelastic alloys can

be used [5691].

4.3. Sensor Deflection Measured

Mechanically

4.3.1. Deflection Amplified Mechanically

The differential pressure gage with amplification

of the deflection of a diaphragm, diaphragm capsule, or Bourdon tube by levers, sector, and pinion driving a pointer over a scale, is an old development. Improvements in performance have followed from those found

necessary in aneroid barometers, aircraft speed indi- cators, and particularly in aircraft altimeters. In micromanometers, when a corrugated diaphragm capsule is the sensor, the uncertainty in measurement is at best about 0.1 torr, with a practical limit to the range of about 20 torr. Friction and backlash in the multiplying

mechanism are the chief diSiculty in securing greater accuracy. To obtain greater sensitivity, a leather diaphragm

backed by a plate or D-spring to give stiffness, or a

synthetic rubber diaphragm, have been used as the

sensitive element. Such instruments were used initially to measure draft in power plants and are called draft gages. Their pressure range is as low as 1 in of water

(roughly 2 torr) ; the sensitivity is about 0.05 torr. The uncertainty is at best about 0.1 torr. Aneroid barometers and altimeters as commonly de- signed will not be discussed in detail, since they hardly

can be called micromanometers ; however, some designs

having high sensitivity will be covered later. Data on

the accuracy of precision aneroid barometers in survey- ing has been given by Kissam [4418]. On the performance of aviation altimeters, Johnson [4833] covers

their behavior in dives and climbs and Gracey [65343]

outlines recent developments.

Bourdon tubes mechanically connected to an indicat- ing pointer have little application as micromanometers.

Modern efforts to increase their sensitivity are dis- cussed by Van Kuyk and Huston [65344].

4.3.2. Deflection Not Amplified

Two designs in which the diaphragm deflection is measured directly are of some interest. The first is the Goldschmidt aneroid barometer dating back to about

1877. In figure 22, D is an evacuated diaphragm capsule which deflects freely except to control the position of lever LI. A similar lever L2 is positioned by micrometer A. To make a measurement, the markers E\ and E2

are brought into coincidence by the micrometer as viewed by microscope M. The change in reading of the micrometer, about twice the deflection of the capsule, is a measure of the change in the atmospheric

pressure. Practically, as an aneroid barometer the sensitivity limit is about 0.1 torr; assuming the use of sev- eral diaphragm capsules, the sensitivity could be pushed

to perhaps 5 X 10~" torr at the risk of increasing the

elastic defects significantly.

The second design proposed by Spence [4021] is shown in figure 23. To measure the pressure of corrosive gases, a glass bellows B is connected to a vertical capillary tube C. The bellows is filled with mercury

with a free surface in the capillary tube. An increase

E2\

— L2 M

1 --^-^—

— LI

D —

II

Figure 22. Goldschmidt aneroid baromter.

A, micrometer; D, evacuated diaphragm capsule; El and E2, markers;

F, fulcrum; Ll and L2, levers; M, microscope.

Figure 23. Corrosive gas manometer.

B, glass bellovfs; C, capillary tube; d, deflection of mercury column; Po and P, reference and applied pressure.

20
in P compresses the bellows and forces the mercury

to rise in the capillary tube. In the design described by

Spence the deflection in the tube is about one-fifth of

that of a U-tube manometer; obviously this is not a micromanometer. However, it would be possible to increase the sensitivity of the elastic element and to have the capillary tube horizontal in order to approach

the sensitivity of a U-tube manometer.

A Bourdon tube of glass to withstand high pressure

applied externally was designed by Foord [3405]. A

long glass pointer was attached to the free end of the Bourdon tube. Its angular deflection, observed on a

scale, measured the pressure. The sensitivity was a

pointer deflection of 0.54 mm per torr. The vibration

sensitivity was not mentioned.

4.3.3. Force Balance Systems

The discussion here will be limited to the instrumentation where the balanced condition is obtained manually. Two types are described, one in which the re- storing force is a spring and the other, a solenoid.

Electrical null detectors, which lead to the use of feedback to maintain the balance, will be considered

later. A classical example of the first type is the Paulin

aneroid barometer. A schematic diagram, lacking some

of the detail of the null detector, is shown in figure 24. A description and some performance data were given

by Werkmeister [3114]. The evacuated diaphragm

capsule D is kept in the null position, or at least centrally, by helical spring F. The latter is adjusted manually by a precision screw M, with provision in the design to avoid applying a torque to the spring. A

pointer P rotated with the screw indicates the pressure on scale S, which may cover as much as two revolutions. To detect the null position, a rigid frame H moves

vertically with the central area of the diaphragm.

Metal strips /I and /2 are attached to H and the case

of the instrument. Strips K\ and K2 are attached to /I and /2 and to opposite sides of a disk on the shaft

of tendency pointer TP. Thus, any deviation of the dia- phragm from the null causes H to move and, through

strips / and K, to rotate pointer TP, the position of which is indicated on a second scale. Actually, the mechanism of transferring the motion of strips / to pointer TP is somewhat more complicated than shown.

As constructed, the tendency pointer is normally about

five times as sensitive as the pressure-indicating pointer

P. Under normal conditions of use, the accuracy ob- tained in precision types is about 0.1 torr, with a sensitivity of about 0.05 torr. One drawback of this type

of instrument is the necessity of making a manual

adjustment to obtain a reading. This is obviated by

a feedback to maintain the null, of which a number

of types are described herein; one applicable here is described in section 4.5.3.5.3. It remains to say that the Paulin barometer could be used to measure gage

pressure in the micromanometer range merely by opening the diaphragm capsule to the system pressure to be measured. The obtainable accuracy would be improved, but not enough to make such application

worthwhile.

Figure 24. Paulin aneroid barometer.

D, evacuated diaphragm capsule; F, helical spring; H, rigid frame;

Jl and J2, metal strips; Kl and K2, offset metal strips; M, micrometer; P, pressure indicating pointer attached to M; TP, tendency

pointer indicating null.

S D r<!>

0

C

Figure 25. Electromagnetic force balance.

B, balance detector; C. balancing coil; D, diaphragm; /, microammeter; M, permanent magnet; P—Po, differential pressure; S, helical spring.

The instrument described by Blase [60227] restores the null position of the diaphragm by a solenoid. Referring to figure 25, D is a diaphragm, S a helical spring, and M and C form a solenoid. When the dia- phragm deflects due to increase in pressure P, the current in coil C is increased to restore the diaphragm

null as indicated by the position of lever B. The current through microammeter / is a function of the pressure. Blase states that a commercial instrument is available

for measurements in the range 0.05 to 0.15 in of water

(0.093 to 0.28 torr).

4.4. Optical Transducer

The most common design uses a light beam reflected from a mirror which is turned by the deflecting pres- sure sensor. Less common are those depending on opti- cal interference such as Newton rings.

4.4.1. Light Beam Transducer

The deflection of a diaphragm, less often of a Bour- don tube, has been amplified by an optical lever by

many experimenters. The essentials of the design are

21
\ / \ / — \ / /

= \ / '

- s

\l/ L_J1=

1

Figure 26. Optical lever micromanometer.

D, diaphragm; G, glass window; L, light; M, mirror; OL, optical

lever; P—Po, differential pressure; R, rod actuating OL; S, scale.

shown in figure 26. The diaphragm D, as it deflects, rotates the optical level OL by means of push rod R. A support F for the fulcrum of OL must be provided.

A mirror M is attached to OL which reflects a light

beam from L to scale S. The light beam is obtained

from a single linear filament bulb and may be focused on the scale by a simple lens system.

Kenty [4008] lists various designs of micromanometers up to 1940, including optical types, required for particular applications. Some of these require a small volume of the measuring chamber and, in Kenty's

case, ruggedness. A few modifications of the optical

type are described below.

Kornfeld and Klingler [2904], in measuring the absolute pressure of NO2, constructed the corrugated

diaphragm and other parts in contact with NOo of a noble metal in order to avoid chemical reaction. The

lowest range of their several instruments was 0.40 torr, and the sensitivity, 0.01 torr. The diaphragm deflec- tion was nearly linear with pressure. Stewardson [3007] used a flat diaphragm, either of

glass or mica, to measure absolute pressure. The sensitivity obtained was 5 X 10~* torr per millimeter

deflection of the light beam.

Hurst [4114], to obtain high sensitivity, used a rub- ber diaphragm with a centrally attached aluminum disk. Otherwise, the design is as indicated in figure 26. The

sensitivity obtained was 3 X 10""* torr per millimeter

scale division. Grigorovici [3904] mounted a mirror on a rod at- tached firmly to a glass diaphragm near its outer edge.

The deflecting diaphragm in effect rotated the mirror

and thus the light beam. The pressure range was 0.1

to 5 torr; sensitivity 0.002 torr; and accuracy 2 to 3

percent.

Crompton and Elford [5722] used an optical lever

to measure the deflection of an evacuated diaphragm

capsule. A concave mirror was used. They were in- terested in the pressure range from 0 to 20 torr. The

sensitivity obtained was 0.1 torr per millimeter light

beam deflection on the scale. The accuracy at 1 torr was 1 percent.

Buckmaster and Mears [58173] initiated the de- velopment of a sensitive aneroid barometer for altitude surveying. Briefly, two corrugated diaphragm capsules

control the angular position of a mirror pivoted by

flexure strips. A light beam passes through a glass

scale, 20 lines per millimeter and is reflected by the

AC R B

P

Figure 27. Spoon Bourdon tube-bifilar micromanometer.

A, adjustable support; B, spoon Bourdon tube; C, end of rod R; E, aluminum sheet; H, damping magnet; Af, mirror; P—Po, differential pressure: T, silk thread.

mirror to pass through an index reticle. The reading

system was a microscope with a magnification of 50 XThe expected altitude sensitivity was 5 ft, equivalent

to about 0.1 torr at sea level. At this point the discussion turns to Bourdon tube

micromanometers with optical magnification. The

Bourdon tubes were earlier made of glass; in modern

designs, of fused quartz. Eight references are listed here; perhaps a dozen more could be found, dated

before 1930.

In an early development by Landenburg and Leh- mann [0606], a thread connected the free end of a

glass Bourdon tube to a mirror, free to deflect angularly as the Bourdon tube deflected. A light beam was

deflected from the mirror to a scale. The sensitivity

obtained was 0.03 to 0.05 torr. The necessity of avoiding chemical reactions present with other forms of micromanometers led to this design.

Both Lewis and Style [3718] and Amphlett, Mullinger, and Thomas [4831], used a mirror on a bifilar suspension. The latter used a quartz Bourdon tube

wound in the shape of a truncated cone, (see fig. 28)

while Lewis and Style used a glass "spoon-shaped"

Bourdon tube. The latter, viewed edgewise, is a seg- ment of a circle, and has a rod attached to the free end. The older instrument [3718] was far more sensitive, and is therefore described here. In figure 27, B

is a plan view of the spoon-shaped Bourdon tube with

a long light rod R attached, to magnify the deflection perpendicular to the page. A silk thread, attached to R

at C, and to an adjustable support A, supports the mirror M in a bifilar suspension. An aluminum sheet E

in the thread loop supplies damping in the field of magnet H. Note that the sensitivity increases the closer A and C are together. When the separation of A and C

was^.l3 mm, the light beam reflected from the mirror

had a deflection on the scale 2 meters away of 1 mm

for 4 X 10~^ torr. The spoon Bourdon itself deflected 8 mm for a pressure change of 10 torr.

22
p

Figure 28. Optical beam-Bourdon tube micromanometer.

B, helical glass Bourdon tube; E, electric light: G. glass windows; L,

lens; M, mirror; P—Po, differential pressure PO, pointer; S, scale.

Yorke [4513] designed a somewhat similar micromanometer which was vertical with the following

components, starting at the top: support, filament,

mirror, filament, helical Bourdon tube, inlet tube, and

support. The sensitivity reported was not great, 4 to 5 mm light beam deflection per torr. Ewing [5580] substantially modified Yorke's design, mainly to ease the glassblowing. A truncated cone Bourdon tube, figure 28, has a 5-cm pointer PO

attached to its free end and an inlet tube and support

T at its fixed end. A small bead at the end of PO is in the optical path of light from filament E, through

windows G. lens L, and mirror M, to scale S. The

greatest sensitivity is obtained when PO is attached

to B so that the bead has the most vertical motion. The

optics are such that an image of the bead is super- imposed on the filament image on the scale. The sensitivity was an image deflection of 16 mm per torr. Barnartt and Ferguson [4312] had a filament con- necting the free end of a horizontal pyrex spoon Bour- don tube to a short length of capillary tube, the axis

of which was horizontal. The latter was angularly deflected as the Bourdon tube deflected. A mirror attached

to the capillary tube reflected a light beam to measure

the deflection. The sensitivity obtained was 0.02 torr and in one design was 5 X 10~^ torr: the device

withstood an overpressure of 50 torr. Aylett [60228] described a robust design somewhat

similar to that described above. Here the free end of the glass spoon Bourdon tube was connected to a balance wheel by a platinum wire. The deflection of the Bourdon tube turned the balance wheel against the

slight torque of a hairspring installed to prevent backlash. A mirror was attached to the balance wheel which,

with the usual light source and scale, completes the

description. For a scale 1 m from the mirror the light

beam deflection was 5 cm per torr. For a pressure range of it 2 torr, the hysteresis did not exceed 0.01

torr.Heiland [5172] describes an aneroid barometer for surveying, designed by Graf and intended for sale by

Askania-Werke (Berlin), which is essentially the same

in design as the experimental aneroid barometer of Buckmaster and Mears [58173] which has already been

described. Either the Graf design was overlooked by

Buckmaster and Mears, or Askania did not go through

with its manufacture. In detail, Graf used an evac- uated Bourdon helix instead of diaphragm capsules

for the pressure sensor, and an autocollimator instead

of a microscope for amplifying and measuring the

deflection of the Bourdon tube. The light beam passes through a transparent scale, is reflected from a mirror

attached to the free end of the Bourdon tube, and then

through an index to an eyepiece. Each scale division

is equivalent to a pressure change of 0.1 torr. The

sensitivity is about 0.01 torr. The scale is visible for a pressure range of 10 torr. To cover the range 300

to 900 torr, the Bourdon tube as a whole is angularly

deflectable by means of a micrometer screw, with provision for equating the pressure to the angular motion.

4.4.2. Interferometric

Scheel and Heuse [0902] describe in considerable

detail the design and calibration of a micromanometer

used in measuring the vapor pressure of water at pressures below 0.001 torr. Simply, a small glass optical flat was fastened centrally to a very thin, flat copper

diaphragm which was under radial tension. Another

glass optical flat was installed just above the one on

the diaphragm. To secure interference fringes, a monochromatic light beam fhelium 5876-angstrom line) impinged on the optical flats. One fringe passed for a pressure difference across the diaphragm of 3 X 10~*

torr. Calibration was obtained by using a U-tube mercury manometer using two index points controlled by

micrometers, and also by volumetric division. Kenty [4008] describes an instrument based on Newton's rings, using a diaphragm and an optical flat both of quartz. His measurements extended to 54 atm

and to temperatures up to 820 'C. At the lower pres- sures the sensitivity obtained was 0.5 torr. Perhaps of interest is a method of recording the

interference fringes developed by Buck [5282]. A highspeed motion-picture camera was used, together with

a tailored optical system, for recording dynamic pres- sures using a quartz diaphragm as a sensor. Bogatvrev. Kosov. and Kurlapov [6728] used a Ravleigh t\"pe interferometer to measure gas pressures

in the range 0 to 800 N 'm- ('6 torr). Two parallel

tubes, 1 m long, were filled with a gas of high molecular weight to increase the number of the interference

fringes. One tube was connected to the system with a

liquid bubble intervening and. similarly, the other tube

to the reference pressure. Thus the pressure measure- ment was made independent of the composition of the

gas. Collimated light passed through both tubes and a

lens to the eye of the observer. The light paths were

equalized by angularly deflecting an optical flat in the reference pressure path. The amount of this angular motion was a measure of the pressure difference

in the two tubes.

23
4.4.3. Photoelectric

Heiland [5172] incompletely describes a barograph,

in which photocells detect the deflection of the Bourdon

tube, their output being recorded by a microampere

recorder. Boschi and Garcia [6726] detect the deflection of a

glass bellows by a photocell. A shutter which is immersed in a liquid is attached to the free end of the

bellows. The amount of a light beam passing through

the liquid was controlled by the shutter and was re- ceived by a photocell. The output of the latter is fed

to a Wheatstone bridge and indicated on a potentiometer. The pressure range of the constructed instrument was 1 to 700 torr with an estimated sensitivity of 0.1

torr.

4.5. Capacitance Transducer

The relatively great sensitivity of the capacitance

transducer coupled to a diaphragm has resulted in the development of many forms of instrumentation and in a wide variety of applications. The large number of technical papers on the capacitance gage in recent

years, far greater than for any other type relying on

an elastic element, testifies to its importance. A some- what extended treatment is therefore justified.

The principle is simple. An elastic element, usually a flat diaphragm, sometimes a corrugated diaphragm,

and, rarely, a metal bellows, separates two chambers,

the difference in pressure in which is to be measured.

An insulated metal disk and the grounded diaphragm,

mounted parallel and close to each other, form an

electrical capacitance (see fig. 29). Or, two capacit- ances may be formed by using two disks with the dia- phragm between them (see fig. 30). The change in the capacitance (s) as the diaphragm deflects is a function of the pressure. The diaphragm capacitance us- ually forms part of a capacitance bridge, the output

of which may be measured in various ways, or it may

be used to indicate the null position of the diaphragm

while the restoring force is measured, all as discussed

later.

4.5.1. Theory

The theoretical analysis published to date covers only

the diaphragm sensing element. Bellows-capacitance

instruments have been little used; Bourdon tubes ap- parently not at all, although attempted by Yasumori

[6712]. The theory presented here for single-electrode

elements can be applied with minor modifications to the bellows-capacitance gage. The change in the electrical capacitance, as a differ- ential pressure causes the diaphragm to deflect, can merely be measured; this is the open-loop case. In a closed-loop situation, the electrostatic force required

to maintain the diaphragm in the null position can be

applied by feedback from the primary capacitor. This

electrostatic force is proportional to the applied dif- ferential pressure. Theory covering both the open- and closed-loop in- struments has been developed by Drawin [58110],

Po JL

p

L2

C2 0

Figure 29. Single capacitance micromanometer.

A, amplifier; Cl and C2, capacitances; D, diaphragm; E, metal disk; Ll and L2, inductances; M, microammeter; P—Po, differential pressure; R, recorder; S, radio frequency power supply.

Cope [6217]^ and Rony [64265]; for the open-loop

instrument only by Lilly, Legallais, and Cherry

[4701]; and for the closed loop only by Drawin

[6081].

The theory developed by Drawin [6081] for the

closed loop will be presented first. For one electrode and a flat (or corrugated) diaphragm, figure 29, with

all quantities in consistent SI or cgs units:

APtt/?

where

5o =

C/2, or (2)

(3)

(4)

Here AP = P — Po = pressure differential across

the diaphragm (P exceeds Po)

R, r = diaphragm and electrode radius, respectively

do = gap between electrode and diaphragm

e = dielectric constant of gas (with refer- ence to vacuum)

U = electric potential applied to electrode and

diaphragm to maintain diaphragm in null position

It is assumed (a) that the electrode and diaphragm

surfaces are parallel, (b) that stray capacitances are

negligible, and (c) that the null position of the dia- phragm does not significantly vary with the differential pressure P — Po. The effect of the expected variations

in the dielectric constant with pressure and with possible arcing of the gas will be discussed in section 4.5.4. As shown by eq (3), the square of the measured potential is proportional to the differential pressure.

If AP is in torr and U is in volts, eq (3) becomes

AP = 3.333 X 10-1" e (-^)^ U\ (3a)

In practical designs U will be less than 100 V for AP

at 0.01 torr, and still smaller as AP decreases.

24
In making calculations with eq (3a), c?o is not easily

determined; substituting ~ ire ^j- 1 {C^ — Ci), and

adjusting the constant to use C„ — C\ in picofarads, eq (3a) becomes

aP = 4.30 X 10-« e m. (3b)

Here Co and Ci are respectively the diaphragm-to-electrode capacitance and the stray capacitance.

Drawin [6081] further presents a calculation for

the case when the diaphragm surface is slightly curved,

resulting in a slight increase in the capacitance Co in eq (3b). This calculation appears of little practical use

in a closed-loop instrument, since information on the curvature of the diaphragm is difficult to obtain, and

is not really needed in a closed-loop force-balanced

instrument.

The above theory holds for one electrode. The varying cases for two electrodes can be considered by applying eq (3). If, as shown in figure 36, one electrode is grounded, the other at a constant voltage JJ, and the diaphragm subjected to an adjustable voltage f/1, eq

(3) becomes

AP = So [([/ - viv - ui^]

(5)

aP = 5o {U -2U' Ul).

Thus AP is proportional to the voltage change Ul;

when Ul = 1/2 U, AP = 0.

If the circuit now has the diaphragm grounded and

the two electrodes initially at voltage U, and the volt- age on one electrode adjusted to null the diaphragm

position,

AP = 5o (t^2 - f/P). (5a)

Here AP is proportional to the square of the adjust- able voltage Ul.

Again let the diaphragm be grounded with both

electrodes initially at voltage U (see fig. 36). To null the diaphragm, the voltage on one electrode is in- creased and on the other decreased equally by a volt- age Ul. Then

AP = Bo [{U -\- Ul)^ - {U - Ul)^] (5b) = 5o (4 C/ Ul).

Here AP is proportional to the voltage change Ul.

Cope [6217] and Rony [64265] present the theory

in more detail. In the open-loop case, where the diaphragm is al- lowed to deflect freely, the theory is complicated by

the various relations which exist between pressure change and diaphragm deflection for various dia- phragm designs. For a radially stretched flat diaphragm

three regimes exist: (a) the deflection large compared

with the diaphragm thickness, (b) both of the same

order, and (c) the deflection comparatively small. Probably case (a) is most applicable to micromanometers. If a corrugated diaphragm is used, it is probably

advantageous to have a single corrugation at the rim

and have a stiff circular central plate which is elec- trically coupled to a parallel circular electrode. In the

latter design, the capacitor gap varies very little radially, and the diaphragm deflection can be made to be linear with the pressure change, an advantage for micromanometers.

In open-loop designs, theoretical diaphragm deflec- tion-pressure relations are not sufficiently exact to permit reliable calculation of the micromanometer per- formance, and the micromanometer must be calibrated

against a standard. The chief value of the various the- oretical relations between diaphragm deflection and

pressure is in selecting and designing the diaphragm.

Theory which includes diaphragm performance is given

by Lilly. Legallais, and Cherry [4701], Drawin

[58110], Cope [6217], and Rony [64265].

The simplest case is where the deflection of the dia- phragm is linear with pressure and the electrical ca- pacity varies linearly with the reciprocal of the gap

between the electrode and diaphragm. Then for a

single electrode, figure 29:

P-Po = AP = Kd (6)

and assuming the diaphragm deflection d is constant

radially,

^

(7) do — d do C - Co = AC =

anc AP

KdoAC

AC + K^/do

eA

(8)

477 Here do is the diaphragm-electrode gap at zero differ- ential pressure, d is the diaphragm deflection at differential pres- sure AP,

AC is the change in electrical capacitance at AP,

e is the dielectric constant of the fluid in the gap, and

A is the area of the capacitor.

Ki/do is large compared to AC, so that in the practical case AP is directly proportional to AC.

If two electrodes are used, figure 30, assuming the diaphragm-electrode gaps initially identical (= do)

CD-<2)

Figure 30. Double capacitance micromanometer.

A, amplifier; B, capacitance bridge; D, diaphragm; E, metal disks: G, galvanometer; P—Po, differential pressure; S, power supply.

25
and the two capacitors forming two arms of a bridge

circuit

:

do — d dn C -Co = ACi (9)

Co — C = AC2 = -y- (10)

do do -\- d

Then in a two-capacitor bridge circuit, where E2 is the

electrical output,

Co + ACi

Co — AC2

^3£'2-

For the single-capacity bridge circuit, where Ei

electrical output, Co + ACi

Co

The relation of their outputs is

E-2. Co £1

KsEi.

(11)

is the

(12)

(13) Co — AC2

The relative gain in bridge output by using two

electrodes is given by eq (13) ; since d cannot exceed

do, the gain varies between the limits of 1 and 2. Drawin [6081] considers theoretically several sources of error for the closed-loop case. However, his conclusions are largely applicable to the open-loop

case; for the range of pressures measured by micromanometers they are:

(a) the effect of pressure on the dielectric constant e (present as a factor in Ki, eqs (7) and (9) ) at pressures below 10 torr is insignificant;

(b) the effect of moderate temperature changes on the value of e is likewise insignificant, even for gas molecules with a dipole moment;

(c) the influence of adsorbed gases in altering the contact potential, and thus of the nulling voltage,

is not significant;

(d) the effect of temperature changes on the dia- phragm dimensions and stiffness, and hence on the gap, is significant, and will be discussed in section

4.5.4. See Pressey [5307].

4.5.2. Electrodes and Pressure-Sensitive

Elements

Usually the pressure-sensitive element is a flat metal

diaphragm. Some experimenters have used metal dia- phragms with a single corrugation, notably Cook and

Danby [5302], and Perls, Kaechle, and Goalwin

[5305]. To obtain additional sensitivity Beynon and

Cairns [6446] used a plastic diaphragm (Terylene),

aluminized on one side to obtain an electrical conducting surface. Either one or two metal disks have usually been

used as electrodes to form a capacitor with a dia- phragm. If one electrode is used, and electrostatic null- ing is used, the differential pressure is of necessity

always applied so that the capacitance decreases. Two variations in design are of interest. In one, shown in figure 31, due to Lovejoy [6108] and Mitsui

[64180], a beryllium copper diaphragm D is clamped

Figure 31. Lovejoy capacitance element. A and B, glass blocks; D, metal diaphragm; L, evaporated metal film; P—Po, differential pressure.

Figure 32. Bellows-capacitance micromanometer.

B, metal bellows; Dl and D2, metal disks; FM, mixer; I, insulator; M. McLeod gage; N, frequency indicator; P, system pressure; Po, ref- erence or balancing pressure; PS, power supply; RB, resonant fre- quency bridge; S, glass stops.

between pyrex glass blocks A and B. A metal film is deposited on the pyrex surfaces L to secure the two

capacitances. Holes in the pyrex admit the gas and

permit leads to be brought out from the metal surfaces. In another, figure 33, developed by Suetin and Volobuev [6485], two nesting, corrugated diaphragms are

used. See section 4.5.3.3.3 for a description.

Figure 32 illustrates the electrode design with a metal

bellows as the sensitive element. All designs [60104,

6344, 6594] have means for initial setting of the gap

between the electrode and bellows, by moving either the electrode or bellows.

4.5.3. Measurement Circuits

The major methods of measurement will be outlined. These are in general equally applicable devices using

either one or two electrodes. A number of instrument

companies manufacture some form of capacitance pres- sure gages; these have been discussed as of 1965 by

Rony [64265]. Probably their circuits will not be

novel except in details. The fundamental development

work to achieve a precise and accurate instrument has

been done by five groups: Lilly, Legallais, and Cherry

[4701], Opstelten and Warmoltz [5562, 5616, 58117],

Becker and Stehl [5212], Drawin [58106, 58110,

6081], and Lamers and Rony [64265]. The performance of precise commercial instruments has been given

26
by Mueller [60112] and by Utterback and Griffith [6601].

Undoubtedly, circuit variations from those to be

described are possible, and have merit. Only those described in the literature as applied to the capacitance

pressure gage are presented.

4.5.3.1. Capacity Bridge Balanced, Change in Capacitance Measured

Heylen [60104, 6344] designed a pressure sensing

element which could be baked out at 430 °C. Only the pressure element design, not the measuring circuit, is indicated in figure 32. This design consisted of stainless steel bellows B, to which a metal disk Dl was

fastened at one end with an intervening insulator /. A

disk D2 parallel to the first, formed the capacitance

which varied with change in deflection of the bellows. The inside of the bellows was connected to the pressure

to be measured, while the outside was maintained at a high vacuum (not as indicated in fig. 32). A commercial proximity meter (British term for a form of capacitance bridge) was used to measure the change

of capacitance with pressure. In figure 29, capacitance

C2 (and CI) would be adjusted to secure a null read- ing on milliammeter M; the change in capacitance is a function of the change in pressure. In Heylen's design

the initial clearance between disks jDI and D2 is adjustable by raising or lowering disk D2, figure 32,

permitting adjustment to any pressure range up to 25

torr. The best sensitivity obtained by Heylen was 0.02

torr.Beynon and Cairns [6446] also measured the change

in capacitance as a function of pressure, using a commercial capacity bridge, as did Heylen. Their contribution is in the design of the pressure sensitive element. Instead of a metal diaphragm (fig. 29), one

of plastic (Terylene) was used to increase the sensitivity. One side was aluminized. The calibration curve

for the range 0 to 50 X 10""^ torr is nonlinear; the change in capacitance for this range was 12 pF. The

sensitivity obtained was 4 X 10~^ torr.

4.5.3.2. Capacity Bridge Unbalanced

Two means of measurement are used, (a) most com- mon, the current due to the unbalance is measured, and

(b) the unbalanced voltage is measured by a potentiometer. The discussion will be in broad outline; consult

the references for details. A nonlinear twin T network for capacitive trans- ducers was described by Lion [64271].

4.5.3.2.1. Current Measured. Becker and Stehl, and

Drawin appear to have made the major contributions

to the design of accurate and stable instruments of

this type. Their circuits will be described first. The Becker and Stehl [5212] design is shown sche- matically in figure 30. An aluminum flat diaphragm is installed between two metal disks E, forming two ca- pacitances. The latter are connected to high-frequency

capacitance bridge B; the unbalanced bridge current

is fed to amplifier A ; and the rectified current indicated on galvanometer G. Their main contribution was metic- ulous attention to details. The construction was sturdy.

The stability in performance was checked and was believed good enough to warrant the use of the instrument

as a secondary standard. The only drawback according

to Rony [64265] is the difficulty in constructing the pressure transducer. The galvanometer used had a sensitivity of 1 X 10~^ A per scale division; this cor- responded to a pressure of 2 X 10~® torr. A typical capacitance bridge circuit for the single- electrode instrument due to Drawin [58106, 58110] is shown in figure 29. Here electrode E and diaphragm D

form one capacitance in the bridge formed by capaci- tances CI and C2 and inductances LI and L2. The

radiofrequency power supply S supplies a-c at a constant frequency. Deflection of the diaphragm unbal- ances the bridge; the voltage due to the unbalance is fed to amplifier A. The resulting direct current can be

read on microammeter M or fed to recorder R. Drawin

developed this design for use in the range 2 X 10~^

to 30 torr, and also a null type for measurements down

to 10~^ torr. An output linear with pressure was obtained. A diagram of a similar circuit is given by

Opstelten and Warmohz [58117] for measurements

above 1 torr. Extensive experimental and theoretical work was

carried out by Lilly, Legallais, and R. Cherry [4701] on the capacitance transducer-diaphragm gage for dynamic measurement, particularly that of explosive de- compression occurring in pressurized airplanes. Circuit details were not given but figure 29 applies es- sentially, except that the output was displayed on an

oscilloscope.

Mueller [60112] describes a commercially available

instrument which had a double-capacitance formed by

a stainless steel diaphragm between two disks. The cir- cuit is essentially as shown in figure 30. However, two

additions were made. First, an ac output can also be

obtained, useful when dynamic measurements need to be made. Second, the output of the bridge is balanced

by an ac bucking voltage from the power supply

(2500 Hz) which is measured by a series of resistances calibrated directly in pressure units. For the dc output,

eight pressure ranges from 0.01 to 30 torr are obtainable, with an accuracy of ± 3 percent, and a maximum

sensitivity of 10~* torr. For the ac output, the pressure range is from 1 to 30 torr with a maximum sensitivity of 0.01 torr. The accuracy when the bridge output is manually balanced is ± 1 percent of the balancing

resistance dial reading.

The electrical circuits used by Lovejoy [6108] and

Mitsui [64180], figure 31, do not essentially differ from that shown in figure 30. The sensitivity obtained was 10"^ torr, which practically fixes the lower end

of the range at 10~^ torr. Three applications of the single-capacitance pressure

sensor should be mentioned. Baird and Banwell [4019],

Johnson and Chiles [5784], and Jones and Forbes

[6230] each developed a microbarograph to record

atmospheric pressure oscillations. These are described

in section 8.2.1. 4.5.3.2.2. Voltage Measured. Two commercially

available instruments, one described by Mueller

[60112] and one described by Rony [64265], provide

27
a voltage output. As mentioned in section 4.5.3.2.1,

voltage from the ac supply nulls the ac output of the capacitance bridge. The variable resistors controlling

this voltage are calibrated in pressure units. Utterback and Griffith [6601] state that a commercial instrument of similar design had a sensitivity of

4.5.3.3. Resonant Capacity Circuit, Resonance Maintained

4.5.3.3.1. Capacitance Measured. The capacitance

gage was first developed by Olsen and Hirst [2902].

Their measurement circuit is now of historical interest only. A glass diaphragm was used, to which a single

metal electrode was attached. A circuit was formed by

the sensitive element capacitance, a variable capacitance, and an inductance. A quartz crystal oscillator was inductively coupled to the sensitive element circuit. As the diaphragm deflected, the variable capacitor was adjusted to maintain resonance with the quartz

oscillator. Resonance was indicated by a milliammeter

in the quartz oscillator circuit. The change in capaci- tance to maintain resonance was indicative of the pres- sure change. The sensitivity reported was 3 X

10""*

torr.4.5.3.3.2. Frequency Change Measured. Cook and

Danby [5302] set up a capacitance-inductance bridge

circuit of which the single capacitance pressure sensor formed one arm. This was maintained in resonant vi- bration with the aid of a pentode electron tube. The

change in the natural frequency of this bridge as the diaphragm deflected under pressure changes was measured by a wave meter. Resonance was indicated by

auxiliary circuits incorporating two milliammeters, one

for coarse and the other for fine indications. For a pressure range from 5 X 10"^ to 120 X 10~^ torr the resonant frequency shifted from about 5.8 to 6.6 MHz. The resonant frequency-pressure curve was very

nearly linear. The instrument was used to measure

rough vacuum in connection with the operation of a mass spectrometer.

Chester, Choudhery, Jones, and Williams [6815] de- signed a single electrode capacitance-diaphragm gage

to measure liquid helium pressure. The novelty here was the low temperature of the liquid helium in which

the gage was immersed. A stainless steel diaphragm, 3 cm in diameter, was used. The electrical circuit was

arranged to measure changes in resonant frequency.

The frequency was measured by an electronic counter and displayed as a voltage by means of a digital-analog converter. The sensitivity was 87 Hz per millimeter

change in the liquid helium level. 4.5.3.3.3. Beat Frequency Measured. The design of the instrument developed by Suetin and Volobuev

[6485] is shown in figure 33. The nesting diaphragms,

Dl and D2, form a capacitor and were connected into an oscillating circuit RB. The interior of the capsule

is connected to the reference pressure Po and the posi- tion of D2 is adjustable by screw S. The power supply

PS is a 1000-kHz crystal-stabilized oscillator. As the diaphragm deflects, the resonant frequency of oscilla- tion in RB changes. The outputs from RB and PS are

fed into a mixer M and then into a frequency meter FM, where the beat frequency is measured. In the range 1 to 30 X 10~^ torr, the output, 20 to 450 Hz, was linear. It follows that the sensitivity was 6.75 X

10-2 torr/Hz.

4.5.3.4. Resonant Capacity Circuit; Unbalanced Current Measured

Perls, Kaechle, and Goalwin [5305] used the circuit devised by Cook [5383] in their micromanometer. The

circuit is shown schematically in figure 34. Capacitances CI, C2, and C3 plus the diaphragm D and elec- trode disk form the resonant bridge, excited by the

crystal oscillator CO. The output of the bridge changes

with a change in pressure, P — Po, is amplified by Al,

and passes to discriminator DI of the direction of un- balance of the bridge. From amplifier A2, the output

passes to an oscilloscope 0 or other means of indication. The null output, when the pressure P — P^ = 0

and the bridge is balanced, is indicated by the detector

A^. The frequency of oscillation of CO was 500 kHz.

Leads as long as 20 ft connected the bridge to amplifier Al. The authors point out the need for good shield- ing and firm construction of the bridge parts. The dia- phragm had a single corrugation near its rim so that the electrode disk was faced by a flat portion. The sensitivity was 10~^ torr and the range 10"^ to 10"^ torr.

1C 1 p D

II C2 =

C3

I

Figure 33. Nesting diaphragms—capacitance micromanometer.

Dl and D2, nesting diaphragms; FM. frequency meter; M, mixer; P and Po. pressure and reference pressure; PS, power supply; RB,

oscillator; S, adjusting screw.

Figure 34. Cook resonant capacitance circuit. Al and A2, amplifiers; Cl, C2. and Cs, capacitances; CO, crystal controlled oscillator; D, diaphragm; DI, discriminator; N, detector; O,

oscilloscope; P and Po, pressure and reference pressure.

28
Rideal and Robertson [5570] also used a resonant

bridge circuit that was operated at 0.8 Hz off resonance. The power supply was a crystal-controlled oscillator of radio frequency 3.505 MHz. The bridge output was

fed to a detector, through an amplifier, and then to an

oscilloscope, since the application was to investigate

gas-phase reactions. The sensitivity was 10~* torr, the range 0 to 2.20 torr, and the deviation from linearity was 2 percent at the highest pressure. The frequency

response extended to 10* Hz.

4.5.3.5. Elastic Element Null Restored

While subjected to a differential pressure, the elastic element has been restored to its null position by an

electrostatic voltage, by applying a balancing pressure, or by a helical spring. These procedures are discussed

below. Of these, only the first two merit serious attention. Complete restoration of the null position is achieved only by a balancing pressure. The restoring

electrostatic force acts on a central portion of the diaphragm with its outer periphery left under some

stress as the capacitance is brought to its initial value. Any effect of this residual distortion can, of course, be

eliminated in the calibration of the instrument. This

distortion of the diaphragm may become serious if a central force is applied to null the diaphragm, in that the resultant elastic hysteresis and drift can limit the accuracy.

4.5.3.5.1. Electrostatic Voltage Restores Null. Based on a single capacitance formed by diaphragm D and

a metal disk, Drawin [58110] developed the circuit shown in figure 35. The bridge is formed essentially

by capacitances CI, C2, C3, and C4. The temperature

of the pressure-sensor unit is controlled at 40 °C above

ambient temperature. The output amplified by A is fed to a phase discriminator DI and null indicator N.

-250V

The power supply PS had a frequency of 20 kHz. To

restore the null when the diaphragm deflects, potenti- ometer E is adjusted to apply a voltage to the sensor

electrode of CI. The square of the measured voltage is directly proportional to the differential pressure P —

Po- Note that any voltage difference between the dia- phragm and the electrode results in their mutual at- traction, so that it is necessary for the diaphragm to

deflect away from the electrode with increasing differ- ential pressure. The pressure range [6081] was 10"'^ to

1 torr, with a 1 to Yo percent uncertainty in the measurements. While manual adjustment of the potentiometer is here indicated, feedback circuits have been

developed [58117, 6217, 64265] for making the ad- justment automatically.

Improvements in Drawin's single-capacitance design were made by Ryzhov [63345], and used by him as a standard in the pressure range from 0.001 to 0.1 torr. Drawin [6081] developed theory (eqs (2) to (4),

sect. 4.5.1) to compute the sensitivity of his micromanometer. This was reviewed by Ryzhov [63345].

For a variety of gases, including some hydrocarbons,

all at 52°C, Drawin obtains differences well within 2 percent on the average (maximum 3 percent) for the computed value of (eq 4) and the experimental

value, using a McLeod gage as a standard. He considers sources of error also, details of which are pre- sented later, and concludes with good reason that the micromanometer has application as a secondary

standard. Two designs of electrostatic nulling have been de- veloped using a diaphragm between two disks to form

two capacitors. The first to be discussed is that de- veloped by Opstelten and Warmoltz [5562, 5616,

58117], in which one electrode is manually maintained

at a constant voltage U -\- Ul and the other at U — Ul,

and the diaphragm is grounded. The circuit diagram

is shown in figure 36. The two capacitors formed by

the diaphragm D and two disks are part of bridge B, which is activated by an ac powder supply PS having a frequency of about ^/o MHz. Any deflection of the dia- phragm unbalances the bridge, the output of which is amplified by A and fed to null detector A'. The dc volt- age restoring the diaphragm to the null position as indicated by null detector N is obtained from potenti- ometer circuit R. The measured restoring voltage Ul

u + ui

u-ui n

KZ)

PS

Figure 35. Drawin electrostatic null micromanometer.

A, amplifier; Cl, C2, CS, and Ci, capacitances; D, diaphragm; DI, phase discriminator; N, null indicator; E, potentiometer; P and Pa, pressure and reference pressure; PS, power supply.

Figure 36. Opstelten-JFarmoltz electrostatic null micromanometer.

A, amplifier; B, bridge; D, diaphragm; A', null detector; P and Po. pressure and reference pressure; PS, power supply; R, potentiometer; U and Ul, electrostatic voltages.

29
PS

B

A N

Figure 37. Automatic electrostatic null micromanometer.

A, amplifier; B, bridge; D, diaphragm; G, crystal oscillator; N, null detector and feedback; P and Po, pressure and reference pressure; PS, power supply; R, to recorder; V and Ul, electrostatic voltages.

is directly proportional to the pressure change (eq

(5.2)). At absolute pressures above 1 torr, the dc

voltage causes a glow discharge so that the pressure range is limited to below about one torr. However, for

differential pressures at absolute pressures of 1 atm,

the design might be usable. The range of the instru- ment is from 10~^ to 1 torr. The accuracy [5562]

above 10~" torr is 0.1 percent, at 10~^ torr, 10 percent. This indicates a sensitivity of 10~^ torr. The other design, for which a circuit was given by

Opstelten and Warmoltz [58117], described in detail by Rony [64265] and by Cope [6217], adds a feed- back to the circuit of figure 36 to apply the restoring

voltage automatically. The circuit is shown schematically in figure 37. The diaphragm capacitances form

part of bridge B. When the diaphragm deflects, the

resulting unbalance of the bridge is fed through amplifier A to null detector A^. The latter contains a phase

discriminator and the feedback, whereby the initial voltage U on the two electrodes is reduced in one case

to U — f/1, and increased in the other to U -\- Ul,

to restore the diaphragm to a position where the two

capacitances are equal. The diaphragm is grounded.

The voltage Ul is indicated at R, or may be recorded.

The power supply PS operates a crystal oscillator G,

the output of which is fed to bridge B and to null de- tector A^. The voltage Ul is directly proportional to the differential pressure. Rony gives the range of his instrument as 10~* torr. Its use was abandoned for his particular application in favor of a deflecting instru- ment (see sect. 4.5.3.2.1, fig. 30) because of inferior

stability and inferior pressure ranges. Undoubtedly,

further development work would rectify these short- comings measurably.

A variation from the circuit diagram given in figure

36 was used by Sharpless, Clark, and Young [61235].

Here the nulling voltage was applied only to one elec- trode. The diaphragm was grounded. Two capacitances,

formed by the diaphragm, and two electrodes were con- nected to the bridge. The nulling voltage was applied

automatically by means of a servomotor which controlled the applied dc voltage. The differential pressure P for their sensor was given by P = 2.30 X 10""'' t/^, where U is the applied voltage. The sensitivity was 3 X

10~^ torr, equivalent to the effect of a change in sensor temperature of 0.002 °C.

4.5.3.5.2. Pressure Restores Null. The reason given

for the development of this class of instrument was

to isolate the system from contamination, but the construction is also essential in gas thermometry to maintain a constant amount of gas in the system. While

perhaps more expensive, the purpose could be achieved

by evacuating an enclosed space surrounding the pressure-sensitive element and using a capacitor to measure

the deflection of the sensitive element, and thus the pressure directly. However, in current designs, the pressure external to the sensitive element is controlled

to restore the pressure sensor to the null position as indicated by restoration of the initial capacitance value,

and this balancing pressure measured.

Figure 32 is a diagram of the instrument developed

by Hackam, Austin, and Thomas [6594]. The bellows

B is connected to the system pressure. A metal disk Dl

is rigidly connected to the free end of the bellows but

insulated from the bellows by a glass ring /. A fixed disk D2 and disk Dl form the capacitance. The system

pressure is balanced by pressure applied at Pq. The

capacitor Dl — D2 forms part of a bridge RB in res- onance with a 1 MHz oscillator PS. Any difference in the frequency of PS and RB is fed to the mixed FM

and to an indicator A^, which is used to determine the equivalence of the two pressures. The balancing pres- sure is measured by McLeod gage M or other absolute

type, depending on the range. The circuit is similar to that shown in figure 33 except for the null feature. The pressure, in the desired range, 0.1 to 760 torr, could be nulled to an accuracy of ±: 5 X 10~^ torr. Full scale on the frequency meter N in pressure units was 20 X lO-'"* torr. The null-reading gage developed by Alpert, Matland,

and McCoubrey [5101] is now of more historical than

technical interest. A corrugated diaphragm and disk

formed a capacitance in a bridge powered by a lO-kHz

generator. The output of the bridge was fed to a volt- meter which indicates the null position of the dia- phragm, as the system pressure on one side of the dia- phragm was balanced by a pressure applied on its other

side. An oil U-tube manometer measured the applied

pressure. The accuracy of the nulling system was ±

10~~ torr, equivalent to ± 0.1 V. A diaphragm motion

of 5 X 10~^ mm was detectable. The gage was de- signed primarily to make rather coarse vacuum measurements, as simply as possible.

4.5.3.5.3. Spring Force Restores Null Flauraud,

Mears, et al. [5490], investigated microbarometric

oscillations using an automated version of the Paulin

barometer (fig. 24). In this recorder, shown in figure

38, capacitance disk CI is attached to the corrugated,

evacuated diaphragm capsules D. Disks C2, attached

to the case through insulators, form two capacitances

with CI. When the diaphragm capsules deflect from

the null position, capacitance bridge B becomes un- balanced, the output, amplified by A, activates servo- motor SM, turning micrometer screw MS to adjust the force on spring 5, to return disk CI to the null position.

The angular motion of MS is recorded on recorder R. A setting mechanism is provided to adjust the recorder

30
SM R MS

Figure 38. Barograph, spring force restores nail. A, amplifier; B, bridge; Cl and C2, capacitance disks; D, diaphragm

capsules; MS, micrometer screp; P, pressure; R, recorder; S, spring; SM, servomotor.

to any desired 35 mbar (26 torr) range of pressure. The pressure range was 990 to 1045 mbar (742 to 784

torr). The sensitivity was of the order of 0.035 mbar

(0.026 torr) per scale division (about 0.6 cm) on

the recorder chart. The speed of response was 0.5 mbar

(0.37 torr) per minute. The instrument was designed

for field use; therefore, the pressure-sensitive unit was

thermostated and the electronics, battery-powered.

4.5.4. Performance Factors

Rony [64265] lists about a dozen performance fac- tors for capacitance gages. Of these a number will be

considered here as being fundamental. Only the best obtained performance will be presented, which will

limit the number designs discussed. Dynamic response

will be considered in section 8.1. See also section 4.14.

4.5.4.1. Sensitivity, Linearity, and Stability

It is desirable in a precision instrument that the

sensitivity or resolution at the worst be 1 percent of

the measured pressure. Instruments have been devel- oped which have a sensitivity of 10~^ torr at pressures

in the range from 10~^ to 10""* torr; bettering this

sensitivity may be possible, but will not be easy. Instru- ments in the 10~^ torr range of sensitivity are reported

in [5212, 5305, 5562, 6081, 61235, 6601]; this sensitivity was achieved with either a deflecting diaphragm

or a diaphragm returned to the null position.

As regards pressure range which can be covered, the

null type of instrument has a substantial advantage

over the deflecting type. When the diaphragm is maintained near its initial position, the range is limited only

by the range of the nulling voltage, and if the system

pressure is proportional to the square of this voltage, a further advantage ensues. Drawin [6081] indicates a possible range from 10~'' to 1 torr. In most designs where the diaphragm deflects freely, the range is limited to about two or three decades of

pressure, owing to the inherently small value of the capacitance and the limited range of the measurable

capacitance. Although the maximum deflection of the diaphragm is fixed with narrow limits, the pressure range can be selected by using a diaphragm of appropriate stiffness. In the designs where the output of the

bridge is nulled by a voltage [60112, 6601], the pres- sure range can extend over four decades. The sensitivity of the type using a null detector voltmeter is controlled by modifying the input signal in eight steps. Linearity within 1 percent has been achieved without

difficulty in deflection-type instruments, as is predicted

by eq (8). In nulling instruments, the differential pressure may either vary linearly within close limits with the square, eq (3), or with the first power of the

nulling voltage, eqs (5), (5.2), depending upon the manner of its application.

As regards stability, Rony [64265] has obtained data on both short-term (30 seconds) and long-term effects. For a commercial instrument his values are respectively

10~^ torr and 2 X 10~^ torr per hour; for his own

best design, 10~^ torr and 3 X 10"^ torr per hour.

These values are essentially equalled by the designs

of Becker and Stehl [5212] and by OpsteUen and Warmoltz [5562, 5616]. The instrument of the latter was

the nulling type; that of the others, the deflecting type.

Incidentally, Rony states that the superior short- and

long-term stability of the Becker and Stehl instrument

is due to the superb design of the diaphragm capaci- tance element.

4.5.4.2. Temperature Effect The effects of temperature changes on a capacitance

gage are threefold: (a) change in capacitance of the pressure sensor due to dimensional changes; (b)

change in stiffness of the diaphragm, and, (c) change

in the dielectric constant of the gas.

First, the change in dielectric constant with temperature was considered theoretically by Drawin [6081].

The effect is greatest for gases of molecules with the

greatest electrical dipole moment, notably water vapor

and hydrocarbons. He concluded that for modest temperature changes, and for low pressures, the effect was

negligible.

By choice of a material for the diaphragm which has

a very low temperature coefficient of elasticity, the change in stiffness with temperature can be held to a low value. There remains also the variation in stiffness as the radial tension is changed by differential expansion of various parts of the assembly, or the slight

buckling of a corrugated diaphragm from the same

cause. Obviously, as the parts of a pressure sensor expand

as the temperature rises, the diameter of the electrodes increases and the gap, electrode to diaphragm, changes,

thus changing the capacitance.

Temperature effects have been considered theoretically by Pressey [5307] and notably by Drawin

[6081]. From the practical standpoint, a gage can be

calibrated at the same temperature at which it is to be used. In this case, only the degree to which the temperature can be held constant need be considered.

Calibration can be made also at various temperatures

so that correction can be applied for intermediate temperatures of the instrument. Fluctuating instrument

temperatures will give rise to significant uncertainty.

Following Drawin [6081], with voltage U resulting

from pressure change AP on a null-type instrument

31
aP = BJJ^ (3)

where 5 = B„ (1 + a^T) (14) — J_ M

and Ar is the change in temperature.

He obtains two values for the temperature coefficient a, one where the diaphragm remains flat, and the other where the diaphragm is slightly curved. He computes a. for the flat diaphragm case to be between 10~* and

10~^ per degree Celsius. The value of a for his instrument was measured at 50 °C intervals from 50 to 200 °C and was —1.15 X

10-3 at 50 °C, and —1.40 X IQ-^ per degree Celsius

at 200 °C. The theoretical calculations were within 10

percent.

For a deflecting instrument, Pressey [5307] obtained

a value of a of — 100 parts per million per degree

Celsius for a pressure sensor especially designed to reduce the temperature error. His theory gave a =

144 ppm. Thus, Drawin obtains a temperature effect of about 0.11 percent per degree Celsius and Pressey re- duces it to about 0.01 percent per degree Celsius, for equilibrium conditions.

Dean and Flynn [6606], in connection with a cryo- genic application, presented data on the temperature

effect in the range 77 to 530 °K for their instrument for pressures up to 500 psig, well above pressures of

interest here.

4.5.4.3. Gas Composition

Drawin [6081] considers the effect on the instru- ment indication of the variation of the dielectric constant of various gases. For a very wide variation in the dielectric constant, he computes that the effect on

the instrument indication is 0.0017 percent per torr. For pressures in the micromanometer range, this effect

is insignificant. As stated in the preceding Section, the temperature variation of the dielectric constant also has no significant effect on the instrument indication. Experimental data on the sensitivity of a nulling

instrument for a group of gases, including a number

of hydrocarbons, given by Drawin [6081], indicate no significant effect of gas composition. Utterback and

Griffith [6601] present data for a deflecting instrument

which likewise shows no effect ; in fact, their data check

substantially the change in ionization gage sensitivity

with gas composition.

4.5.4.4. Gas Adsorption

Drawin [6081] discusses two effects of gas adsorption. First, a contact potential may exist between a clean metal surface and an adsorbed gas. He estimates

that this contact potential will not exceed 0.25 V, and

concludes that in measuring a nulling voltage the error

will be about 1 percent at 10"^ torr. At higher pres- sures the error is negligible.

Second, an adsorbed gas may slightly alter the gap

distance between an electrode and diaphragm. The er- ror introduced in a measurement of pressure was computed to be insignificant, although this differs from

the conclusion reached by Milazzo [5677].

K the micromanometer is used to measure absolute

pressure, the chamber on one side of the diaphragm

must be evacuated to a pressure at least 1/100 of the lowest pressure to be measured. Below about 10"^

torr, continuous evacuation is recommended by most

experimenters. Bakeout may be desirable in some applications, in which case the pressure sensor design,

and particularly the possible annealing effect of the high temperature on the diaphragm, require attention.

4.5.4.5. Ionization of Gases

Opstelten and Warmoltz [58117] state that at absolute pressures above 1 torr, an electrical discharge occurs between the electrode and diaphragm of micromanometers, if an electrostatic voltage is used to re- store the diaphragm to the null position. Both Opstelten

and Warmoltz. and Drawin [58110], propose for measuring pressures above about 0.1 torr the use of designs

in which the capacity bridge is unbalanced by the pres- sure change and the resulting current is measured.

4.5.4.6. Variation of Null With Pressure

Invariably, when the null position of the diaphragm

or bellows is restored by an electrostatic force, the null position is indicated by a constancy of the capacitance

of the pressure sensor. Always, some portion of the outer area of the diaphragm remains under stress and,

to this extent, the null position for zero differential pressure is not restored. See also Drawin. section 4.5.1. The effect increases with increase in the differential pressure. No quantitative data appear to be available,

but the effect in good diaphragm-electrode designs is believed to be small. H a bellows is used, the effect may

become significant. In both cases, the effect is wiped

out by calibration of the instrument. This failure be- comes much more significant if the center of the dia- phragm is restored to null by a central force. Here

most of the advantage of nulling, in minimizing elastic defects such as drift and hysteresis, is lost. While of limited application, perfect nulling is ob- tained by using a balancing pressure; unfortunately,

measuring the balancing pressure still remains a problem.

4.5.4.7. Stray Capacitances

Stray capacitances within the bridge circuit of the instrument, if constant in value, lower the sensitivity of response and, if variable with pressure, introduce an error. Since the capacitance of the sensor is small,

in the range 20 to 400 pF (lO^^^ F), designers have

made efforts to reduce the extraneous capacitance to a minimum. Good insulation between the electrodes and pressure element (diaphragm or bellows), and

shielded, short lines for the bridge circuit, are pro- vided. A high-frequency power supply is used. Suitable

guard rings or shields would improve many designs.

4.5.4.8. Overpressure

Since the gap between a single electrode and a dia- phragm in deflecting instruments is largest (within

the maximum permissible deflection of the diaphragm)

at zero differential pressure, syslem overpressure brings

32
the two into contact, thus supporting the diaphragm.

Permissible system overpressures of at least one at- mosphere have been obtained. In nulling instruments, overpressure deflects the diaphragm away from the

electrode if the nulling electrostatic voltage is not

applied.

If two electrodes are used, protection against overpressure, either side, is obtained. The use of nesting

diaphragms, one being the electrode (Suetin and Volobuev [6485], fig. 33), should be mentioned as another

method of protection against overpressure, but constructional difficulties are a bar to its general use.

4.6. Inductance Transducers

Three variations of inductance transducers exist: the differential transformer, the variable reluctance (two coils magnetically linked by a metal armature),

and the mutual inductance (two concentric coils on a ceramic form) . All are highly sensitive to small dis- placements.

4.6.1. Differential Transformer Transducer

The instrument developed by Sancier and Richeson

[5617] is shown in figure 39. As bellows Bl moves, it deflects an iron core C in the field of two transformer

coils Tl and T2. Power is supplied to coil Tl by PS;

the change in induced voltage in T2 is measured by a

sensitive voltmeter VM. An additional bellows B2 is rigidly connected to 51 and is vented to the reference

pressure Po- This bellows compensates for thermal

expansion of fil. but not for the change in the elastic modulus with temperature. The stiffness (pressure

change per unit deflection) is the sum of the stiffnesses

of the two bellows. This application was for measuring

the pressure of corrosive fluids, so monel bellows were

used. The frequency of the 3-A power supply was variable in the range 1000 to 10,000 Hz. On the voltmeter

0.005 mV was detectable; on this basis the sensitivity was 0.05 torr at 1000 Hz, 0.02 torr at 2000 Hz, and

0.005 torr at 10,000 Hz. The gage designed by Tsujimura, Takahashi, and

Fujisawa [6821] for measuring the differential pressure

of fluorine is essentially the same as that of Sancier

1 rp

Figure 39. Bellows-differential transformer micromanometer.

I Bl and B2, metal bellows; C, iron core; P and Po, pressure and refer-

^ ence pressure; PS, ac power supply; S, a stop; Tl and T2, primary

and secondary transformer coils; VM, sensitive voltmeter.

and Richeson shown in figure 39. Their gage had a

linear range of ± 150 torr and sensitivity of 1.7 mV

per torr. Hooley [5797] hung the iron core of the linear dif- ferential transformer from the free end of a glass

spoon-shaped Bourdon tube. The output of the trans- former was amplified, converted to direct current and

recorded on a millivolt recorder. The accuracy was

estimated to be 0.1 to 0.2 torr. The pressure range of the constructed instrument, — 100 to 650 torr, is out- side the range of interest here, but could be made so by using a more sensitive Bourdon tube. However, at- tention would have to be given to reducing the zero

drift caused by the weight of the iron core, as pointed

out by Hooley.

Sheft [6602] measured the deflection of a flat dia- phragm with a linear differential transformer. The

electrical circuit was as shown in figure 39. A vacuum

tube voltmeter was used to measure the output. The

linear range of the transducer was ± 1.52 mm and the output 1.02 mV per 0.1 torr. It was used to secure

distant indication of the pressure of corrosive gases. While the pressure range of Sheft's instrument was

about 1 atm, the same design with a more sensitive diaphragm would bring the instrument sensitivity into the micromanometer range.

4.6.2. Mutual Inductance Transducer

Dibeler and Cordero [5102] depended on the varia- tion in mutual induction with the proximity of a metal

diaphragm. Eddy currents generated in the diaphragm

increases the coupling between the coils as the dia- phragm recedes from the coils. The design is shown

schematically in figure 40. The corrugated diaphragm

D is part of a capsule which is connected to the pres- sure P. The instrument case is kept evacuated at a pressure Po, preferably much below P. The two induction coils CI and C2, wound on a ceramic form, are mounted above the center of the diaphragm. One coil, C2, is activated by the radiofrequency power supply

PS; the voltage induced in coil CI is amplified by A,

rectified by R, and the resultant current is indicated on dc microammeter /. For a pressure range from

100 X 10~^ to 1 torr, the sensitivity was 10~* torr. The gain was adjustable to give an output of 50/xA for a pressure of 25 X lO"* torr. It is of interest to note

p

FiGDTtE 40. Mutual inductance vacuum gage.

A, amplifier; Cl and C2, inductance coils; D, diaphragm; /, micro- ammeter; P and Po, pressure and reference pressure; PS, power supply; B, rectifier.

33
that the diaphragm was made of brass 0.001 in thick

and had 26 corrugations. It had a central deflection of about 2 X 10 in (5 X 10"* mm) per 10"^ torr. The micromanometer application was for measuring

the pressure of gas samples being admitted to mass

spectrometers.

4.6.3. Variable Reluctance Transducer

Halliday [4801] designed a micromanometer with

electrical transmission in order to eliminate the lag

introduced by pressure transmission through tubing. In figure 41, two bellows, 51 and 52, have interior pres- sures of PI and P2 respectively. These are rigidly con- nected to lever arm A with a fulcrum of crossed strips

at F. Soft iron strips, 51 and S2, one attached to one end of the arm A, control the inductance of two coils, CI and C2. The output from coil CI and from the similar coil C2 goes to bridge circuit B. The unbalance,

caused by a bellows deflection, is fed to servomotor M,

which, through gear box G, moves the second soft iron

strip S2 until the bridge is balanced. The gear rotation

is indicated by a counter CO and is a measure of the pressure P2 — PI. A power supply PS actuates the

B M

CO G

S2

B2

- PS

C2

Figure 41. Variable reluctance micromanometer.

A, lever arm; B, inductance bridge; Bl-BS, metal bellows; Cl, C2, inductance coils; CO, counter; CW, counterweight; F. fulcrum; G, gear box; M, servomotor; Pi, P2, pressures; PS, power supply; Si,

S2, soft iron strips; V, check valve.

inductance coils. The lever arm has a counterweight

CW. For damping, two oil-filled bellows 53 and 54 are connected as shown. Oil flows from one bellows to the other as 51 or 52 deflects. An additional bellows 55

is connected to 53 and 54 through a check valve in order to compensate for volume changes in 53 and 54.

The range was 3 in of water (5.6 torr) with a sensitivity as good as that of a 26-in Chattock gage (sect. 2.9) (0.001 torr).

Cox, Atanasoff, et al. [4902] describe a microbarograph used to detect infrasonic waves in the atmosphere

caused by severe explosions. Schematically in figure

42, the flat diaphragm D encloses a chamber in which,

by means of a selected restriction LI, low-frequency

pressure waves are not transmitted into the chamber

and a reference pressure Po is obtained. Restriction L2

connects the main chamber with the atmosphere to suppress high-frequency oscillations. Pressure oscilla- tions having a frequency above 10 Hz were eliminated

from the chamber; at 4 Hz their amplitude was re- duced 50 percent. A variable reluctance transducer

VRI consists of a soft iron pole piece fastened to the diaphragm, and of two induction coils. A similar sec- ond transducer VR2 is fixed in position and is the

reference. The primary coil of both VRI and VR2 is fed by an ac (10 kHz) power supply PS. The output

of the secondary coils, one with constant induced cur- rent and the other with induced current controlled by

the diaphragm deflection, is fed to a bridge circuit 5

and amplified by several amplifiers A. The amplified

output is rectified by C and recorded on milliampere

recorder R. The best sensitivity obtained was a recorder

deflection of 0.1 mm per microbar (7 X 10~* torr).

Means for compressing the deflection at high pressures were incorporated so that any expected pressure range

could be recorded. Very approximately, the recorder

deflection was proportional to the logarithm of the

pressure. Yasumori, Ohno, and Miyazaki [6712] attached an inductance transducer to a Bourdon tube, in contrast to the many variations of mechanical and optical

transducers devised by experimenters in the past for

this type of sensor. In figure 43, T is the spoon-shaped

Bourdon tube to which is attached an aluminum disk

Figure 42. Variable reluctance microbarograph.

A, amplifier; B, inductance bridge; C, rectifier; D, diaphragm: Ll, L2,

restrictions; PS, power supply; P, atmospheric pressure; Po, refer- ence pressure; R, recorder; VRl, VR2, variable reluctances.

Figure 43. Variable reluctance Bourdon gage.

A, amplifier; B, ac bridge; D, aluminum disk; E, detecting coils; F,

ferrite cores; P, Pa, pressure and reference pressure; PS, power supply; R, recorder; T, Bourdon tube.

34
D. Detecting coils E are imbedded in ferrite cores F. The output of E is fed to an ac bridge B, amplified by

A, and recorded by voltage recorder R. The pressure P in slow gaseous reactions was measured; Pq was the

reference pressure. The pressure range was 20 torr, with 7 X 10~^ torr detectable. The response time was

0.6 s at atmospheric pressure Po and 4 s at Po = 10"^

torr, the difference probably due entirely to tubing lag.

4.7. Strain Gage Transducers

Until quite recently only resistance wire strain gages have been used as strain transducers. These have been

either bonded to the elastic element or unbonded.

Recently, strips cut from single-crystal semiconductors,

either of silicon or germanium, have come into use as strain-measuring elements. Their electrical resistance

also varies with imposed strain. Sion [65345] states that the semiconductor strain gage, also called piezoresistive, is 70 to 80 times more sensitive than the

resistance wire types. Incidentally, he includes a theory

of typical measurement circuits in his review on the semiconductor type. A transistor is installed in the cir- cuit for temperature compensation; otherwise the temperature effect would be 0.4 percent per degree Celsius for a silicon transducer. See also Tufte and Long

[63344].

The principal advantage of the strain gage transducer

is its inherently greater speed of response, compared

to that of the inductive or capacitance types where the

electrical circuitry is a limiting factor. The strain gage

instrumentation described in the literature for measuring dynamic pressures usually is not designed to measure pressures in the micromanometer range and, therefore, is not discussed here.

4.7.1. Unbonded Strain Gage

Micromanometers

Matheson and Eden [4803], in an instrument now

largely of historical interest, used unbonded resistance wires to measure the deflection of a diaphragm capsule. As shown in figure 44, nesting diaphragm capsule

D is connected to a commercial wire strain gage S so

that as the capsule deflects, the stress in two wires

increases and in two, decreases. These four resistances form Wheatstone bridge B, the output of which is in- dicated by galvanometer G. The diaphragms were of beryllium copper 0.0022 in (0.055 mm) thick. Excess

pressure of 1 atm external to the capsule, and 0.2 atm internal, was safely withstood. Differential pres- sures were measurable to 0.001 torr in the range ± 0.5

torr. The diaphragm capsule was stiffer by about 12

percent when the lower pressure was inside the capsule.

Keenan and Mcintosh [4830] also used an unbonded

wire strain gage. Eighteen strands of "Advance" wire were connected to a brass metal bellows and a support.

The change in resistance was measured by balancing a Wheatstone bridge. In the range from 0 to 12 torr the

sensitivity was 0.003 torr, but the poor elastic properties of the resistance wires used increased the meas- urement uncertainty to 0.04 torr.

E. -<7)<

' ir OP Po

Figure 44. Unbonded strain gage micromanometer.

B, bridge; D, diaphraerm capsule; G, galvanometer; L, leads; P, Po,

pressures; S, strain gage unit.

CA

T

Figure 45. Semiconductor strain gage micromanometer.

A, amplifier; B, bridge; CA, long cable; CH, chopper; D, diaphragm;

/, milliammeter; P, Po, pressure and reference pressure; R, rectifier; S, T, single silicon crystal strips.

Hayashi and Tsukakoshi [64119, 64276] designed

a gage using an unbonded semiconductor strain gage.

In the diagram, figure 45, a thin invar diaphragm D

compresses three silicon strips 5, cut from a single

crystal, as pressure P rises. Two auxiliary silicon strips

T are added to obtain temperature compensation. The

strips S and T form part of Wheatstone bridge B, the output of which was converted to alternating current by chopper CH and fed to amplifier A. The amplifier

output is rectified by R and indicated by milliammeter

/. Distant indication of the pressure was desired; it was

found that a cable CA from 2 to 300 m long carrying

the dc output from the bridge had no effect on the

indication. The pressure range was 1 to 760 torr; the

sensitivity, 0.1 torr per 0.01 mA indication on /. The

pressure range could be reduced and the sensitivity

improved by using a less stiff diaphragm of a better material than invar, such as Ni-Span-C or berylliimi copper. A recent development, described in an insert in a paper by Moore [6801], is the application of a piezoelectric transistor to pressure measurement. A silicon npn junction planar crystal changes its output voltage

upon application of small forces. By mechanically

coupling the crystal to a diaphragm, pressures can be

measured. Data presented for one design show that a

linear response was obtained for a pressure change

from —4 to -|-4 in of water ( —7.5 to +7.5 torr),

35
for which the output change was 2 V; this is a sensitivity of 0.13 V per torr.

4.7.2. Bonded Strain Gage Micromanometers

The strain gages may consist of either a loop of wire or a foil patterned to be equivalent to a wire loop.

The literature on the wire loop is extensive and avail- able; and the strain elements are commercially available. The foil strain gages are considered in some detail by Mukhin [65353] and Sinev and Etingof [6632].

The latter discuss their application as pressure trans- ducers. A transitorized circuit for strain gage pressure trans- ducers is described in detail by Ayling [6812]. He

states that the resolution obtained was as small as 0.02 percent of the pressure range of the transducer. Thureau and Lemiere [62123] were interested in measuring feeble oscillatory pressures developed in a micro Pitot tube. A rectangular mylar diaphragm, 9 X

34 mm, had four strips of bismuth evaporated on its surface. These formed four resistances of a Wheatstone bridge. Deflection of the diaphragm altered the

electrical resistance and the output of the bridge, which was measured by an oscilloscope. The natural fre- quency of the diaphragm was 16,500 Hz. Incidentally,

Koike and Kurokawa [6624] have investigated the

elastoresistance performance of evaporated bismuth

films. The deflections of the diaphragm were linear with

pressure up to ± 2 mbar (1.5 torr), at which the bridge output was about 200 fxY. Although not useful as designed for measuring low

pressures, the design developed by Carter, Ghosh, et

al. [4927] could be adapted to do so. They bonded a

resistance wire strain gage to a flat metal diaphragm,

thus differing from the Thureau design. The change in curvature of the diaphragm with pressure changed the

strain and, therefore, the resistance of the strain gage.

Similarly, Wenk [5173] bonded two resistance wire

strain gages to an aluminum alloy diaphragm % in in diameter and 0.01 in thick. One, in tension as the dia- phragm deflected, was placed in the center of the dia- phragm; the other, in compression, was placed at the periphery. At 1 psi (50 torr) the best resolution was

0.025 psi (1.25 torr). Obviously, if desired, indication

in the micromanometer range is possible if the dia- phragm diameter is increased and its thickness

decreased. Three recent designs merit mention. Styburski

[6820], who bonded a strain gage on a flat diaphragm,

had the more sensitive instrument; differential pres- sures as low as 1 mm of water (0.07 torr) were measured. Parameswaraiah and Sankaranarayanan [6823]

described a similar design. The pressure range was ± 5 psi (260 torr) ; the natural frequency was 3000

Hz.Kimura, Sakurai, and Kondo [6822] combined a diaphragm and cantilever spring with the strain gage on the spring. They present both theory and perform- ance data on their instrument. Its natural frequency was 130 Hz.

4.8. Electrical Conductance IVIanometer

Pappenheimer [5456] developed an instrument for physiological research, based on a design proposed over 40 years earlier and then neglected. It is based on the

variation in conductance of an electrolyte, a sodium

chloride solution, controlled by pressure change. In

figure 46, Z) is a quartz diaphragm clamped between

quartz blocks Q. Two chambers in Q on each side of D are connected by a conduit G, with the gap between

D and Q about 20 to 25 fim. Any deflection of the diaphragm causes the gap G to increase on one side of D and decrease on the other side, changing the cross- sectional area of the electrolyte which fills the instru- ment and, thus, the electrical current in the two arms

of G. Silver electrodes Al and A2 are connected to form one arm of an ac bridge B, and A3 and A4< to form another. An oscilloscope / measures the bridge

output. Al and A2 are tubes so that pressures Po and P

can be transmitted to the diaphragm. A3 and A4' also are tubes connected to electrolyte reservoirs. The greatest sensitivity obtained was 0.41 mV per torr. When

the system was critically damped, 95 percent of the

final output was obtained in 12 ms when the instrument

had the above given sensitivity.

Massey and Kavrak [6604] describe an instrument

of the electrical conductance type, which is discussed

in section 8.8.

A2 •

/

/ / / //

////

/ /

A3

G

A4

Figure 46. Electrical conductance manometer.

Al, A2, A3, Ai, silver electrodes; B, ac bridge; D, diaphragm; G, conduit: Li- electrolyte;/, oscilloscope; P, Po, pressure and reference

pressure; Q, quartz blocks.

4.9. IVIicrowave Null Detector

Kramer and Platzman [5841] desired to isolate a system from the liquid type manometer used to measure the system pressure. The solution adopted is unique but probably of limited interest. Essentially, a

steel diaphragm 0.004 in thick isolates the primary

system from the measuring system. Microwaves (8650

MHz) are produced and transmitted to the resonant

cavity bounded by the diaphragm. The reference res- onant frequency was measured with no differential pressure across the diaphragm. When a differential pressure deflected the diaphragm, its null position was restored as indicated by the reference frequency

by controlling the pressure in the measuring system.

36
This pressure was measured by the U-tube manometer.

The pressure range of the instrument was about 1 atm

with a sensitivity of 2.4 MHz per torr. A change in the null pressure of 0.1 torr was easily detectable. The

authors state that with added electronic apparatus the microwave sensitivity could be improved.

4.10. Vacuum Tube Transducer

Essentially, the design consists of a diaphragm which

is rigidly connected to the anode or grid of a vacuum

tube. The output of the latter is dependent on the deflection of the diaphragm and hence, on the pressure. The vacuum tube and one side of the diaphragm must

normally withstand atmospheric pressure. This limita- tion on the sensitivity of the diaphragm makes this transducer normally too insensitive for use as a micromanometer.

The design and performance of the various types of diode and triode vacuum tube transducers are given

by Olson [4729]. Day [4928] described a diode type

for use as an aviation altimeter, where the position

of an anode pair (one on either side of the cathode)

mechanically connected by an insulator was controlled by a diaphragm. For recording blood pressure, Pet- tersson and Clemedson [5059] had the diaphragm control the position of the anode in a triode tube, the whole small in size (8 mm in diameter and 20 mm

long).

Sinclair [65351] designed an instrument for dustdevil measurement, in which a diaphragm capsule was

connected to the anode of a vacuum tube through a

flexible joint. The inside of the capsule was connected

to the atmosphere and the enclosing chamber also, but

through a restriction. Thus, the rate-of-change of pres- sure was measured as in a microbarograph. See section

8.2. The output of the vacuum tube was fed to a

bridge, the unbalanced current of which was measured.

The sensitivity was 0.1 mbar (0.07 torr).

4.11. ]VIicrophone IVIicromanometers

The three instruments to be described are, for want

of a better term, called microphone micromanometers,

since the heart of the instruments is a diaphragm maintained in vibration. Dimeff, Lane, and Coon [6215] developed their in- strument for making dynamic measurements in wind

tunnels. The need for long connecting tubing was elim- inated; also the transducer element could be small;

for example, one 0.28 in in diameter was constructed. A schematic diagram is shown in figure 47, where D is a flat diaphragm of high natural frequency (about

1000 Hz) ; DE, the driving electrode; PE, the pick-up

electrode; DO, a variable-frequency oscillator tuned to the natural frequency of the diaphragm. If the pressure P changes, the amplitude of vibration of the diaphragm,

driven by DO, also changes due to viscous drag. The

capacitance formed by PE and D changes, is picked up

by the displacement indicator DI. The energy input by

DO is adjusted to return the capacitance D — PE to

its original value. This change in energy is measured

DE PE

I

Figure 47. Vibrating diaphragm manometer.

D. diaphragm: DE, driving electrode; DI, displacement indicator; DO,

oscillator; F, frequency indicator; /, indicator of energy input; P, pressure; PE, pickup electrode.

by / and is a function of the pressure P. A frequency

indicator F is useful for checking performance. The

instrument actually constructed was automatic in operation. Feedback, controlled by a servomotor, maintained constant the amplitude of diaphragm vibration. The angular deflection of the servomotor was proportional to the cube root of the absolute pressure. The

range was approximately 10~* to lO'' torr. Applicable

theory is given, together with data on the effect of changing such parameters as electrode-diaphragm

clearance, natural frequency, electrode curvature to match vibrating diaphragm, and gas composition.

Schwarz [5663] did some preliminary work on

measuring pressure with a resonant diaphragm. He kept

the diaphragm vibrating at resonance frequency, and

found the ac current driving force to vary with pressure

in about the same pressure range obtained by Dimeff.

Noiseux and Maidanik [6711] had a driver DO to keep the diaphragm vibrating at a constant amplitude,

as indicated in figure 47. However, their transducer was a microphone which was used to pick up the energy of the sound in the air chamber between the diaphragm and microphone. The microphone output was amplified by an electronic circuit. This output in decibels was directly proportional to the logarithm of the pressure over the pressure range from 10~* to 760 torr, except for a transition region 0.03 to 0.3

torr, unfortunately in the micromanometer range. Above and below the transition region the slopes of the curves were the same. A theory was presented.

Antal and Koenig [5773] had a design which es- sentially anticipated Noiseux and Maidanik. A loud- speaker was at one end of a chamber, closed except

for a pressure connection, and a receiver microphone

at the other end. The measured output of the microphone was a measure of the chamber pressure in the range from 1 atm to 0.05 torr.

4.12. Vibrating Wire Gage

The vibrating wire gage* has distant indication as

its principal utility. Prast, Calhoun, et al. [5585] de- scribe a vibrotron for use in measuring atmospheric

pressure on guided missiles. In figure 48, W is a vibrat- ing wire connected to diaphragm D. Deflections of the

* Known as the Vibrotron.

37
FA

AG

Figure 48. Vibrotron micromanometer.

AG, autogain amplifier; D, diaphragm: FA, feedback amplifier; M,

electromagnet; P, pressure inlet; R, recorder; Rl, R2, resistances; W, vibrating wire; WS, static wire.

SF

SS

PS IN Figure 49. Vibrotron microbarograph.

A, amplifier; B, Wheatstone bridge; F, frequency multiplier; IN, in- tegrator; M, mixer; P, pressure inlet; PS, pulse shaper; R, recorder; SF, 100 kHz reference frequency; SS, scale selector.

diaphragm due to changes in pressure P cause the tension on the wire to change, which changes its nat- ural frequency. An alnico magnet M causes a voltage

to develop in the vibrating wire. This voltage is fed

to a Wheatstone bridge composed of resistances Rl and R2, and to a duplicate, but not vibrating, wire,

WS, which is for temperature compensation. The

bridge output is fed to feedback amplifier FA and to an audio gain amplifier AG. The output is telemetered

in this application, and in other applications, trans- mitted long distances over telephone lines to a recorder. Part of the output is fed back to wire W to keep it vibrating. Wire W is under stress and may have a frequency of vibration within the limits of 400 and

70,000 Hz. The square of the vibration frequency is proportional to the differential pressure (Morris

[6706] ) . The design is such that the wire frequency

decreases with increase in differential pressure. The

frequency which is finally recorded is precisely the natural frequency, or a multiple thereof, of vibration

of the wire. The dynamic response of this pressuresensitive unit is very fast; Poindexter [5281], for one

design, quotes perfect response at 5000 Hz. However,

other elements of the system slow down the overall response. The telemetering system described by Prast

et al. at best had a pressure sampling rate of 14 per

second. Prast gives no sensitivity data; Ohman [5584]

for a microbarograph design gives a sensitivity of 3 X

10~^ atm (2.3 X 10~^ torr). Performance data and

possible applications are discussed by both Ohman

and Poindexter.

Recently, Morris [6706] has described the circuit of a microbarograph measuring absolute pressure in which the vibrotron unit is the pressure-sensing ele- ment. A block diagram is shown in figure 49. Here B

is a bridge containing the vibrating wire unit, shown in more detail in figure 48, but not described by Morris.

The output frequency from B is increased ten times

by multiplier F; M is a mixer of the output from F, and from a stable 100-kHz reference frequency SF.

Successively, the output from M is amplified by A,

passes through pulse shaper PS, integrator IN, scale

selector SS, and finally to electrical recorder R. Means

for eliminating temperature errors are described. The

response time of the instrument is adjustable in the range from 0.3 to 10 s. The scale selector S5 permits

variation in full-scale output of the recorder for dif- ferential pressures from 0.5 to 40 /.ibar (0.4 to 30

torr). The best sensitivity is 0.01 )U,bar (0.0075 torr).

For the pressure range from 0 to 1050 //.bar, the fre- quency of the vibrating wire varied from 11,000 to 9900 Hz. The technology and application of the vibrotron have

been reviewed by Lefcourt [6817]. The electronics with

special application to underwater pressure measure- ment are discussed by Rolfe [6818].

5. Piston Gages

Piston gages have long been used to measure high

pressures but only recently to measure pressures in the micromanometer range.

5.1. Tilted, Air-Lubricated Piston Gages

The tilting air-lubricated piston gage for measuring

differential pressures up to about 12 torr was developed

by Hutton [5910]. In figure 50, C is the cylinder of

1^/4-in precision-bore glass tubing, and PI is the piston.

To avoid friction between the piston and cylinder, the cylinder is mounted in bearings and provision is made to rotate it by means of a fan motor. To prevent

oscillation and rotation of the piston, it is eccentrically

loaded with small shot, indicated by Wl. To obtain

various pressure ranges, weights W2 are addeo. The

reference pressure Po could be controlled by placing

the entire instrument in a chamber in which the pres- sure is controlled. The variable pressure P was applied

to the bottom of the cylinder as indicated. To compensate for gas leakage past the piston, a small flow of

air is maintained through nipple F. For any one loading

of the piston and pressure P within the measurable

range, the piston assembly was tilted until the piston

weight balanced the differential pressure. The height h was measured principally by gage blocks G, and within

38
Figure 50. Tilted, air-lubricated piston gage.

C, cylinder; F, nipple; G, gage blocks; M, micrometer; P, Po, pressure and reference pressure; PI, piston; PA, parallelogram structure; Wl,

W2, shot weights.

1 in by micrometer M. The micrometer was supported

by a horizontal bar forming part of parallelogram PA,

which maintained M in a vertical position. A level on

the base plate and adjusting screws were used to keep

the base plate horizontal. The pressure P is given by

mgh P =

ad = Kh (15)

where m is the mass of the piston ; d is the length of the hypotenuse; a, the effective area of the piston; h, the

altitude (fig. 50), and g the acceleration of gravity.

When the constants m, a, d, and g are determined,

measurement of pressures P — Po require only meas- urements of h. Various performance factors were considered and

test results given by Hutton. At an inclination based on a height A of 5 in, corresponding to a differential pressure of about 10 torr, the maximum predicted er- ror in an absolute measurement was 2 X 10""^ torr, and for a relative measurement, 1 X 10 ~^ torr. Operation at low absolute pressures was considered

only on an experimental basis. Electrical charges on

the piston, and inadequate lubrication if dependent on

air, were outstanding limitations. Operation down to a few torr was achieved, with extension to below 0.1 torr believed ultimately possible.

Douslin and Osborn [6596] modified Hutton's de- sign in order to measure vapor pressures in the range

0.01 to 30 torr. The top of the piston was subjected to a vacuum maintained by a pump and the bottom to the vapor pressure. As in Hutton's design, the cylinder was rotated while making a measurement, but the ec- centric weight on the piston permitted the piston to

oscillate, thus minimizing piston-cylinder adherence.

The cylinder was tilted to obtain a balance; the tilt angle was measured on circular scale using a micro- scope to a precision of 1" of arc. As expected, outgas

sing on the vacuum side of the piston gave trouble at low pressures. The piston was lubricated with the vapor, the pressure of which was being measured. At

0.01 torr, the accuracy was ± 0.001 torr; at 40 torr, ± 0.012 torr.

5.2. Vertical Piston Gages

Gramentskii and Khansuvorov [64277] (32 refer- ences) cover briefly the various designs of packless

piston gages, chiefly Russian developments. Apparently none of the designs discussed are capable of measuring

absolute pressures extending down to the micromanometer pressure range. Several of the designs are substitutes for a mercury barometer.

One feature of interest [64277] is the use of buoyant

force to balance the weight of the piston, thus making

possible the measurement to lower differential or absolute pressures with vertical piston gages. Here a

pivot at the end of the piston rests on the central part

of a member having the shape of a hollow donut which

is immersed in a liquid. There are other alternatives for measuring low absolute pressures. One is the tilting air-lubricated piston gage described above. Another is to use two piston gages as described below, or finally a

controlled pressure and one piston gage, where a high

absolute pressure is the reference pressure fed to the primary piston gage. See Lloyd [6703].

The design illustrated in figure 51, described by

Desgranges and Huot [61237], and Gramentskii

[64277], provides a means for making absolute pres- sure measurements conveniently. The compensating

piston gage A contains piston F/1, and the primary

gage B, piston PI2. These differential pistons must be

geometrically the same. The lower end of P/1 is maintained at a pressure Po, significantly below pressure P

which is to be measured. Gages A and B each have an

auxiliary chamber connected to each other, filled with

a liquid L and sealed off. The liquid pressure PI, with

weight Wl constant, will vary with atmospheric pres- sure by the same amount in both A and B. Thus, the change in Pi compensates for the change in atmospheric pressure acting upon the outside of piston P/2,

but correction must be made for any difference in liquid head acting on the two pistons. The absolute pressure is measured by the applied weights W2.

Means R are provided for adjusting pressure PI and, not shown, means for adding liquid to the system. One

design had a range from 6 to 780 torr, with an accuracy

of 0.03 percent.

Dadson and Greig [65347] used a piston design in which the area in contact with the cylinder was reduced

PI 2

Figure 51. Absolute pressure piston gage.

A, compensating piston gage; B, primary piston gage; L, liquid; Po, reference vacuum; P, pressure; Pi, pressure on liquid; PIl, PIS, pis- tons identical in dimensions; R, adjustment for Pi; Wl, WS, weights.

39
by reductions in its diameter at intervals along its length. This reduced friction during piston rotation.

5.3. Piston-Type Pressure Amplifier

Ludwieg [5174] describes a piston-gage pressure

amplifier for use in measuring pitot-static pressures be- low about 1.25 mm of water (0.09 torr). The primary

piston PIl, figure 52, is attached to rod R, at the ends

of which are secondary pistons PI2 and F/3. The piston

axis is maintained horizontal by an adjustment and

bubble level. The differential pressure P2 — Fl to be

measured is amplified, to secure P4 — P3 in the ratio of the cross-sectional area of PIl to PI2. In Ludwieg's

design the amplification is about 105. Pressure P4 —

P3 is measured by a U-tube manometer or other instru- ment. To balance the piston gage automatically, a constant air pressure is applied at A, with leaks at B

and C controlled by the horizontal motion of the piston.

For example, if P2 increases, the piston assembly moves horizontally to the right, increasing the leak through B, decreasing the leak through C, and permitting PS to decrease and P4 to increase until the piston

is in balance.

C PIl PI2 PI 3

R W

Figure 52. Piston gage pressure amplifier. A-C and A-B, air pressure to maintain pistions PI2 and PIS bal- anced; PIl, amplifying piston; P2—Pi, primary pressure; PS—Pi,

amplified pressure; R, piston rod; W, air-driven turbine.

Auxiliary details include means to minimize piston

friction by providing airflow through piston-bearing

clearance, and by rotating the piston assembly by an

air jet operating on the vanes of wheels W. A sensitivity of 0.001 mm of water (7.3 X 10~^ torr) was

obtained; this required close control of the pressure

supplied at A, and the piston axis to be horizontal.

6. Vane Gages

Vane gages are commonly of two types, one where

the vane is pendulously suspended and the differential pressure across the vane is balanced by a component

of its weight; the other, where the vane is free to ro- tate about a vertical axis and the differential pressure

is balanced by the torque of the wire or filament from

which it is suspended. Both types have been widely

used in measuring low vapor pressures. Recently, in- terest has built up in developing the torque type for making absolute pressure measurements in the micromanometer range. Deflection types have been developed

also; their description follows.

6.1. Deflection of Vane Measured

Green [6385] has described a simple vane instru- ment of the gravitational balance type, shown sche- matically in figure 53. A rectangular steel vane D, 1 by

2 in and 0.028 in thick, fits into a housing with a clear- ance of 0.01 in. A magnet M holds the vane in a socket

so that it can deflect angularly about a horizontal axis, as observed on scale 5 engraved on glass. Neglecting

W the effect of the magnet, PI — P2 = — sin a, where

a W is the weight of the vane, a its angular deflection from the vertical, and a its area. For a differential pres- sure PI - P2 (or P2 - PI ) of 0.1 in of water (0.186

torr), the vane deflection was 30°. This indicates a

sensitivity of at least 0.006 torr per degree.

Weber and Plantenberg [4634] measured the impact pressure of the vapor from liquid metals which

condensed on the vane. In figure 54, L is a liquid

metal in a temperature-controlled enclosure, with an

orifice above which is vane V. This vane is suspended

from quartz spring S. A vacuum is maintained at Pq

by a pump. The spring deflection due to the impact

force of the condensing vapor on V is measured by a micrometer microscope with a sensitivity of 4.20 X

10 ~" g/micrometer scale division. Theoretically,

FiCUBE 53. Gravity-balanced vane gage.

D, diaphragm; M, magnet; Pi, P2, pressures; S .scale. J

Figure 54. Impact vane gage.

L, vaporizing metal; Pa, vacuum; S, quartz helical spring; V, vane; P, vapor pressure being measured.

40
p =

2ttF

dsdiv

(16)

where P = the vapor pressure; F, the impact pressure;

ds, the orifice area ; and dw, the solid angle of gas efflux from the orifice. If the impinging gas sticks to the vane,

correcting F for the additional weight may be necessary. Only one vapor pressure measurement was re- ported, 0.0166 ± 0.0017 torr, for bismuth at 970 °K.

Further application of this design does not appear to have been published.

6.2. Force on Vane Balanced

Hickman, Hecker, and Embree [3701], constructed

a gage for measuring low vapor pressures as shown in figure 55. As the liquid L, maintained at a constant temperature, evaporated, a light, pendulously mounted

vane V opened. The entire assembly was then oriented

about axis A until the vane just closed. The angular deflection was measured on scale S, or a more sensitive equivalent. This process could be repeated for various

controlled temperatures of the space above the liquid

to secure a vapor pressure-temperature relation. A

pump maintained a reference pressure Po well below

the vapor pressure P. The pressure P = K sin 6, where

6 is the measured angular deflection, and X is a constant determined by calibration. The pressure range was from 0.001 to 0.1 torr with a sensitivity at low

pressures of ±: 3 X 10"* torr. Verhoek and Marshall [3906] modified the Hickman

design by adding a liquid air-condensing tube to trap

the effusing vapor in the space at pressure Pq, figure

55, and a heater for the vane to eliminate condensation.

Measurements were made in the range from 7.4 X

10-3 to 0.8 torr. A number of experimenters have described electrical force balances for measuring low vapor pressures. Balson's design [4727] will be described in detail. In

figure 56, a vane V in the shape of a dome separates

the chamber at the reference vacuum Pq from that at the pressure P, which is maintained by the boiling

liquid L in container C. The vane or lid is suspended

from a spring S. An iron core A in the suspension

forms part of an electromagnet, the coils of which are

indicated by E. The electrical current, sufficient to cause the lid just to seat, is measured by milliammeter

MA, and is proportional to the vapor pressure. Three

vapor pressures were providing by three weights of the lid. The vapor pressures measured were from

0.001 to 5 torr. The instrument was calibrated against

a McLeod gage. An earlier design of the force balance by Rodebush

and Coons [2706] was for measuring the vapor pres- sure of corrosive gases. A graphite disk replaced V

in figure 56; the iron core A was enclosed in glass; and

a quartz fiber cantilever spring replaced the helical spring S. The balancing electrical current was proportional to the pressure in the range from 0.01 to 0.07

torr.Deitz [3611] used a quartz disk in place of V, figure

56, so placed that the balancing magnetic force measured by milliammeter MA had to be applied downward to break the seal. The furnace containing the sample was below the disk. A pointer, attached to the spring from which the disk was suspended, was viewed

through a lens to determine the point at which the seal was broken. This instrument was used to measure the vapor pressure of salt crystals in the range from 30 X

Figure 56. Electromagnetic force-balanced vane gage.

A, iron core; C. temperature-controlled chamber; E, electromagnet;

L, vaporizing liquid; MA, milliammeter; P. vapor pressure; Po, vacuum; S, helical spring; V, vane.

0 — Po

td

Figure 55. Gravity-balanced vane gage.

A, axis for entire apparatus; L, vaporizing liquid; P, vapor pressure;

Po, vacuum; S, scale; V, vane.

Figure 57. Spring-balanced piston gage.

L. vaporizing liquid; P, vapor pressure; Po. vacuum: PI, mica disks, forming a piston; S, helical spring; W, windlass to keep PI in position.

41
10 ^ to 1 torr. It was calibrated by loading the disk

with deadweights.

Ernsberger and Pitman [5518] designed what was

essentially a spring-balanced piston gage for measuring

low vapor pressures. The piston PI, figure 57, was

formed by multiple mica disks in order to reduce leak- age. It was connected to the lower end of a quartz

helical spring 5 and the latter at the top of a windlass

arrangement W by which the piston was kept in the balanced position. The spring deflection d was measured with a cathetometer to 0.05 mm. The liquid L is shown in a temperature-controlled chamber. The refer- ence vacuum is Pq and the vapor pressure, P. The mica

disks were heated to prevent condensation; the piston

clearance was 0.006 in. The pressure range was 20 X

10~^ to 0.5 torr. To check its performance, the vapor

pressure of mercury was measured in the range 4.8 X

10~^ to 0.6 torr. The deviation from the accepted

values was less than 1 percent, on the average about

0.2 percent.

6.3. Torsion Vane Gages

Reichardt [3510, 3511], for use in gas turbulence

measurements, designed what was in effect a sensitive piston gage in which the pressure was balanced by

the torsion of a wire. In the plane view of figure 58,

PI is the arcuate or "curved" piston which juts through

a hole in a wall dividing two chambers, and swings in the plane of the figure. The reference pressure Po is maintained in one chamber, and the pressure P to be

measured in the other. The piston PI is suspended

from a torsion wire T at right angles to the plane of the

figure. A mirror on the anchor end of the torsion wire

reflects a light beam on a scale, by which means the balancing torque can be measured. (For simplicity,

pointer PT and scale S are shown in figure 58 as a

substitute for the torsion wire measuring system.) Oscillations are damped by hanging a vane immersed in a liquid from the piston. Two hollow, lightweight pis- tons were constructed, one of light metal, the other

of glass. The range with the one of light metal was 0.1 mm of water (0.007 torr), sensitivity 10~* mm of water (7 X 10~^ torr), with a vibration period of 8 s. The instrument with the other had one-tenth of the range and sensitivity, and a vibration period of 25 s. Lloyd [6703] sketches a vane manometer which is estimated to measure absolute pressures down to 10~^

torr where the uncertainty is 100 percent, decreasing

at higher pressures. In figure 59a, the rigid unit comprising vanes VI and V2 and mirror M was suspended

from wire filament F. When pressures Po and P are equal the vanes close the openings to the tubing. When

pressure P exceeds Po, the opening of the vanes is counteracted by applying a torque at C to filament F. This torque to close the vanes is proportional to the pressure difference. The closure position of the vanes

is indicated by a light beam L reflected from mirror M

to photocell PH, the output of which could be used to maintain automatically the closed position of the vanes. Performance details are not available.

Figure 58. Torsion-piston micromanometer.

P, Po, pressure and reference pressure; PI, pistion; PT, pointer; S,

scale; T, torsion filament from which PI is suspended.

Figure 59A. Torsion-vane micromanometer.

C, balancing torque; F, wire filament; L, light source; M, mirror;

P, Po, pressure and reference pressure; PH, photocell; S, scale; Vl,

V2, vanes.

Figure 59B. Vane flowmeter.

F, torsion filament; S, chamber; SC, scale; V, vane assembly.

Measurements of low gas flow have been made by

Gerlach and Mayer [2914], and for other purposes by

a number of other experimenters. One arrangement

proposed by Gerlach and Mayer is indicated in figure 59b. Here the measured pressure difference is a function of the flow rate and the system constants. Flow

through tubing, into and out of reservoir S in the di- rection indicated, causes vane V to deflect clockwise.

The torsion of a wire filament F from which the vane is suspended balances the force on the vane. Since gas

flow is the desired measurement, calibration by means

of known flows seems indicated. In view of the avail- ability of other means of measuring gas flow at micromanometer pressures, the device has very limited

application. The interest here is the fact that the orifice- vane combination, when the vane is positioned by an

elastic pressure element, has had considerable applica- tion in controlling pressure in industrial processes.

42
7. Centrifugal Micromanometers

The centrifugal micromanometer may have partic- ular application as a calibration standard and has been

so applied by Kemp [5955] to measure pitot-static tube

pressures in the micromanometer range. The first of two instruments to be discussed is that developed by

Gross [5401]. In figure 60, Tl and T2 are two tubes

of different diameters, closed except for outlets from

the center controlled by valves V\ and V2. These tubes

are rotatable about their individual vertical axes by

electric motors at speeds up to 1000 rpm. A diaphragm

D with a null detector can be connected to either T\ or T2. The theory shows that the differential pres- sure P — Po is a function of the rotational speed of

the tube, the change in volume of the system caused

by the deflection of diaphragm before it is brought

to the null (Au in fig. 60), and other factors which

are constant for each rotating system. In operation, the system and /, the instrimient to be calibrated, are subjected to a small pressure above atmospheric, causing

a deflection of D. Valves F4 and V2 are closed, T\ is rotated to bring D back to the null position. Valve V\

is now closed and V2 opened, and the null again ob- tained by rotating T2, the speed of which will differ from that of Tl. From these data Af can be calculated and then P — P^y. Gross emphasizes the need for temperature control, and for stability in the atmospheric

pressure Po; if this is unstable, valve F3 can be closed

at the same time as F4. The sensitivity obtained was

10-6 psi (5 X 10-^ torr).

To measure low pitot-static pressures, Kemp [5955]

improved a design developed by Nickel in 1951. In

T2

V4 7

schematic figure 61, S is a thick disk with 8 radial

holes, two of which are shown. It is rotated by motor

MO about a vertical axis. The reference pressure Po

is maintained at the axis of rotation; the output pres- sure developed at the periphery of rotating 5 is led to glass tube G, and opposed by the pressure P which is to be measured. The rotational speed is adjusted so that P

and the output centrifugal pressure are equal, as deter- mined by the absence of flow in viewing tube G. Atomized oil sprayed into G is illuminated by electric light L, and viewed by microscope M to observe when

flow equilibrium exists. Two mercury seals C are provided. To calibrate an instrument, /, shown at A in the figure, it is merely necessary to connect it to the output side of the centrifuge and compare its indication

with the centrifugal pressure. Theory is given by Kemp.

The output pressure is proportional to the square of the speed of rotation. The design has a pressure range

from 5 X 10-=* to 20 mm of water (3.5 X 10"* to

1.5 torr) with an accuracy of 1 percent.

Lofquist [6221] adapted Kemp's design in order to measure water pressure. The pressure range measurable was from 5 X 10"^ to 0.1 mbar (3.7 X 10"^ to 0.075 torr).

H S

31 n//////\r////A

I ^

' -n-L/—n_ -u—r-iT

j M

-TP- P -LLT °

I

Figure 60. Centrifugal micromanometer.

D, diaphragm; /. instrument under test; N, null indicator; P, Po, pressure and reference pressure; Tl, T2, rotatable tubes; Vl, V2, VS, Vi, valves; Af. a volume.

Figure 61. Centrifugal microcanometer.

A, modification when calibrating instrument /; C. mercury seal; G,

glass viewing tube; H, housing; L, light source; M, microscope; MO,

motor; P, Po, pressure and reference pressure; S; rotatable disk.

8. Special-Purpose Gages

Micromanometers may be designed to be useful only

for a particular application and may be of little use for other applications. Thus, some designs are uniquely

useful for measuring low vapor pressures, or atmospheric pressure oscillations, or oxygen pressures, or low differential pressures at high ambient pressures. Another class of micromanometers exists for which

there are additional requirements which do not impair

its general use. These requirements may be the need

for dynamic measurements, for measuring the pressure

of corrosive gases, for distant indication, or for a smallsized gage. Designs to meet each of these particular require- ments will be considered below, noting that for some

applications more than one of these requirements must

be met in a particular instrument. Some of the designs

have already been described; for convenience these will be mentioned again here.

43
8.1. Dynamic Pressure Measurement

Dynamic pressure measurement may be defined as the measurement of rapidly changing pressure such as

exists in an explosion or in an internal combustion

engine. The need for dynamic pressure measurement

is rarely met within the pressure range of micromanometers, since rapid pressure changes are usually

associated with much higher pressures. Dynamic pres- sures must be recorded or displayed on an oscillograph

of high natural frequency. Generally, no instrument

responds accurately to a pressure change having a fre- quency greater than the natural frequency of the in- strument; in fact much less, particularly when damping is added to prevent overshoot. U-tube liquid manometers are of little use in making

dynamic measurements and will not be discussed. It should be noted that it is necessary to allow sufficient time for equilibrium to occur before making readings on a U-tube manometer. In the case of micromanometers, this time is governed by other considerations

than the lag-in-response of the liquid column.

In general, neither piston nor vane gages are suit- able for dynamic measurements; this fact restricts consideration to elastic element, electrical conductivity,

and piezoelectric gages in the micromanometer range. The measurement of atmospheric pressure oscilla- tions is unique in the regime of dynamic measurement

and, therefore, is discussed separately in section 8.2.

8.1.1. Theory

The lag in dynamic response of an instrument sys- tem is due to two major components: that of the in- strument element, and that of the tubing connecting

the instrument to the point at which the pressure meas- urement is desired. Considering the lag due to the con- necting tubing, three principal regimes exist, one in which the flow in the tubing is viscous, one in which

the flow is free molecular, and last, a transition region

between viscous and free molecular flow. The transition region occurs when the mean free path of the molecules

is about the same as the diameter of the tubing. Ordinarily viscous flow exists at pressures above 1 torr;

free molecular flow exists at pressures below about

10""^ torr; transition regime flow will usually exist

in the pressure range from 10"^ to 1 torr, exactly in the micromanometer absolute pressure range. When

differential pressures are of interest at absolute ambient

pressures above 1 torr, the gas flow is in the viscous

regime. Generally, if pressure pulses are of a frequency

such that the line lag is excessive, recourse is to elec- trical transmission from the pressure element. The theory governing the line lag when the gas flow

is viscous, assuming that the pressure pulse is small compared to the initial pressure, was given by Wildhack [3719], and by a number of others. A more complete theory was developed by Iberall [5058]. Theory

and experimental data covering multiple tubes and gage

volumes, mainly for aeronautic application, were given

by Bergh and Tijdeman [65346].

The theory for line lag under free molecular flow conditions (pressures in the vacuum range) has been

developed by Schaaf and Cyr [4925], Harris [5577],

and Matricon [6284]. Ainsworth and LaGow [5623]

considered the line lag in making ambient pressure measurements in rocket flights. See also Lyubitov

[B671] on "Molecular Flow in Vessels," who presents

theory for both the free molecular and transition flow regimes, and for the Knudsen effusion cell. Davis

[5846] presented the theory for molecular flow, and

presented data on line lag at pressures down to 0.2

torr, which included some data covering the transi- tional flow regime.

Hord [6725] reviewed the theory of line lag for

step inputs for free molecule, transition, and continuum

flow regions.

For the viscous flow region, the line lag is conveniently represented by a time constant \, which is e — 1 the time for , or 63 percent, of the imposed

e pressure step to be indicated, where e is the base of

natural logarithms. The indicated pressure approaches

asymptotically the final value with elapsed time. For

molecular free flow and the transitional flow regions, the line lag time is often defined as that when 95 per- cent of the imposed pressure change is indicated. The

ratio of the indicated imposed pressure change to the

actual imposed pressure change varies linearly with

the time elapsed after imposition of the change in pres- sure; see [4925].

An extensive literature exists on the theory governing the dynamic response of pressure-measuring in- strumentation, most of which is not pertinent in this survey. Theory covering the time lag of elastic element

instruments is broadly covered by Huebner [5487].

Such theory is of limited usefulness, since other sources

of lag may be significant. Huebner mainly considered

instruments with electrical transducers, where most

of the lag was in the elastic element. He was interested mainly in the lag for imposed pressure pulses having a

definite frequency, as in measuring acoustic pressures.

8.1.2. Piezoelectric Gages

A voltage is induced in piezoelectric crystals, such

as quartz, barium titanate, and others, while a force

is being applied. To measure pressure, means must be

used to apply the pressure directionally. Their speed

of response is high, of the order of 10"® s, so that they

have been widely used to measure dynamic pressures;

however, but rarely at the pressures as low as here of

interest. One instrument development, that by Willmarth

[58151] used to measure air dynamic turbulence,

will be described. Two barium titanate disks, 0.162 in

in diameter and 0.04 in thick, cemented together, were mounted flush with the inner wall of a 4-in pipe. The

output of the barium titanate crystals was fed to a cathode follower, an amplifier, and an oscilloscope. The

sensitivity was 0.88 X 10~® V per dyne/cm^ (7.5 X

10~* V per torr). A uniform sensitivity was obtained

in the frequency range 5 to 50,000 Hz. Dynamic pres- sures as small as 12 dynes per cm^ (0.0009 torr) were

measurable.

44
Arlowe, Dove, and Duggin [6619] have developed

an amplifier for piezoelectric crystal gages which

matches the inherently fast response of the crystal. The

design was particularly adapted to distant indication.

8.1.3. Frustrated Internal Reflection Gage

Ahlborn and Zuzak [6709] describe a gage which is of limited interest here because, at its present state of development, it measures only pressures well above the micromanometer range. The rise time for an indication

is as low as 5 X 10~^ s. Briefly, the aluminum-coated

face of a mylar diaphragm is subjected to pressure, thereby changing its area of contact with a glass prism.

Light incident on the prism is reflected internally from

the aluminum coat in an amount depending on the

contact area and detected by a photocell. The measured voltage output of the photocell is not linear with

pressure.

8.1.4. Frequency Response of Gages

The frequency response of the various designs of micromanometers is summarized in table 1.

It is seen that the best dynamic response is achieved

by piezoelectric crystal gages, followed by the elec- trical resistance and the diaphragm-capacitance gages. The data ascribed to Rony appear to have been ob- tained from the manufacturers; "M" indicates where

this is established. The speed of response decreases

with decrease in the stiffness of the diaphragm of the diaphragm-capacitance gage. If a decrease in the pres- sure range involves the use of a more sensitive dia- phragm, the response time will be increased. Thus, the response time of 10 X 10~'^ s given for the MKS

instrument in table 1 was obtained for a 3-torr step

at 760 torr; for an instrument having a lower range, say 0.03 or 0.003 torr, the response time would be

substantially greater than 10 X 10~^ s.

Table 1. Dynamic response data

Full pressure Described in Frequency or range Design References Section response time % Indication Torr

Diaphragm-Capacitance Gages

MKS [64265] 10XlO-«s 63 M 3

Barocel [64265] 5 X 10-'s(est.) 63 10 Decker [64265] 2XlO-»s 63 1.9 Rony [64265] 5 X 10-° s 63 0.035 Sharpless (Wrede) [61235] 4.5.3.5.1 1 s 100 Transonics [60112] 4.5.3.2.1 5XlO-»s 63 M

Rideal, et al. [5570] 4.5.3.4 lO' Hz 100

Piezoelectric Gages

Willmarth [58151] 8.1.2 50 to 50,000 Hz 100

Arlowe, et al. [6619] 8.1.2 10-«s 100

Barograph (spring force automatically restores null)

Flauraud, et al. [5490] 4.5.3.5.3 0.37 torr/min 100

Vibrating Diaphragm Gage

DimeflF, et al. [6215] 4.5.3.6 0.1 s(est.) 100

Diaphragm-Bonded Strain Gage

Thureau, et al. [62123] 4.7 16,400 Hz nat. freq.

Conducting Liquid Manometer

Pappienheimer [5456] 4.8 12 X lO-'s 95

Conducting Rubber Micromanometer

Massey, et al. [6604] 8.7 20 to 6000 Hz 100

Vibrating Wire (transducer only)

Poindexter [5281] 4.12 5000 Hz 100

45
It is worth noting that the response of diaphragm

gages is governed both by the speed of response of the diaphragm and by that of the amplifier, which may be

either mechanical or electrical in nature.

8.2. Atmospheric Pressure Oscillations

Instruments which measure small changes in either absolute atmospheric pressure or rate of change of pressure are quite generally called microbarographs.

The terms variograph and microbarovariograph have

occasionally been used in practice to designate, perhaps more accurately, the recorder of the rate of change of pressure with time, in a limited frequency range. Only

the latter type of recorder is described in this section. Perhaps it will clarify the concepts to add that the microbarograph records absolute pressure, and the microbarovariograph records differential pressure above or below a mean atmospheric pressure. The

latter is one of the familly of variographs, of which the

aircraft rate-of-climb indicator is another example.

Bowing to custom, the term microbarograph will be

used hereafter in place of the more descriptive term,

microbarovariograph.

In very few cases is the speed of response of the pres- sure element and its associated means of indication an

important factor in measuring atmospheric pressure

oscillations. The period of the fluctuations to be measured lies in the range of one second to several minutes.

To obtain a stable reference pressure, it is necessary

to introduce a restriction between the atmosphere and

the chamber housing the diaphragm or bellows. This

restriction is normally a capillary tube, but in coupling

to the atmosphere for greatest freedom from atmospheric turbulence and high-frequency oscillations, long

pipelines—up to hundreds of feet—are needed. The

design of long lines with spaced holes and varying

cross sections to eliminate fluctuation frequencies above

1 Hz is discussed by Daniels [59198].

The other side of the diaphragm is open to the at- mospheric pressure fluctuations, except that some cutoff of high-frequency fluctuations appears often desirable. For this purpose, an adjustable orifice, usually a valve, or a short-length capillary tube, is inserted. For a more

complicated arrangement see figures 42 and 65. Thus, neither very slow or very rapid changes in at- mospheric pressure are indicated by the pressure ele- ment; only fluctuations within the limits of the estab- lished frequency controls are detected. In principle at least, microbarographs which measure absolute atmospheric pressure could be designed to measure atmospheric pressure fluctuations, but the re- corded data require an inconvenient separation of the microfluctuations from the undesired major fluctua- tions in pressure. Actually, commercially available ca- pacitance-diaphragm gages appear to have the neces- sary sensitivity and frequency response to do the job

if the recorder speed were stepped up. The literature on atmospheric pressure fluctuations

is extensive; up to 1959 Thuronyi [59177] has listed 122 references.

8.2.1. Microbarographs

Most designs depend upon an elastic pressure-sensitive element, and a few upon a liquid column sensor.

8.2.1.1. Elastic Element Microbarographs

One of the two pioneer designs with which an enor- mous amount of fundamental data was accumulated was that developed by Benioff. The other by Shida is described in 8.2.1.2. The Benioff [3911] microbarograph consisted es- sentially of a moving coil-type loud speaker, mounted

in a suitable case with a restriction to air flow to secure the usual reference pressure. The output of the inductance coil was measured on a recording galvanometer, 1 mm deflection of which was produced by

0.001 torr. It was used to measure the low-period, low- amplitude oscillations in atmospheric pressure. Macelwane and Ramirez [3814] designed a microbarograph similar to Benioff's to record rapid atmospheric pressure fluctuations of a period around 7 s. An

inductance coil was fastened to a rubber diaphragm in the vertical plane. A fixed magnet passed through the

center of the coil. The voltage developed in the coil as the diaphragm deflected was measured by a galvan- ometer. The chamber closed by the diaphragm was

connected to the atmosphere through a restriction, ad- justment of which controlled the period of response. Saxer [4501] described an instrument designed to make the same measurements as Benioff's instrument.

This was an electrical capacitance-diaphragm instru- ment. The output of a galvanometer was photographically recorded. Theory was presented.

Passechnik and Fedosseenko [58162] describe two

microbarographs, one for laboratory and one for field use. One design was essentially the same as Benioff's,

and both were used for the same purpose. In the design

for field use, the pressure sensitive element consisted

of a number of evacuated diaphragm capsules. A flat response was obtained for oscillation periods from

about 3 to 40 s. Baird and Banwell [4019] desired to record atmospheric pressure oscillations associated with microseisms. Their diaphragm-capacitance design is essentially as shown in figure 29, except for controlled

restrictions added at P and P,, and the addition of a

rectifier. The indications of the galvanometer were re- corded photographically. Normally, pressure oscilla- tions having a period between 4 and 10 s were re- corded; the sensitivity was 0.003 torr for 1 cm

deflection on the photographic record. A microbarograph developed by Cox, Atanasoff,

et al. [4902], has been fully described in section 4.6.3 and shown in figure 42. Reflected explosion waves at frequencies below 1 Hz were to be detected. Their

arrangement of restrictions was such that fluctuations having a frequency of 10 Hz or greater were not in- dicated; at a frequency of 4 Hz, the sensitivity was

reduced 50 percent.

Johnson and Chiles [5784] designed a diaphragmcapacitance instrument to record pressure fluctuations caused at a great distance from explosions on the

46
Figure 62. Jones-Forbes microbarograph.

A, amplifier; B, bridge: Bl, B2, metal bellows; C, capacitance; L,

long-line restriction; P, atmospheric pressure; Po and P'o, reference

pressures; PS, 16 kHz power supply; R, recorder; Tl, T2, TS, valve

restrictions.

earth's surface. These fluctuations were refracted downward from the layer of the atmosphere hotter than at the surface which occurs at an altitude around 50 km.

Their instrument design is essentially as shown in figure

29, except for the frequency-controlling restrictions. A

do electrical recorder was used, which required a rectifier not shown in figure 29. The system recorded large

amplitude pressure waves (infrasonic) , with periods in the range from 60 to 360 s. Theory and considerable

experimental data are presented in their report. Jones and Forbes [6230] designed an elaborate

pressure-sensing system for measuring atmospheric

pressure fluctuations. To obviate the effect of extrane- ous fluctuations in the reference pressure, two metal

bellows were installed as shown in figure 62. The at- mospheric pressure P is transmitted into the interior of the bellows through a line L, 220 m long, and other

restrictions to obtain two reference pressures Po and

P„'. Restricting valve Tl is set to give a pressure lag

of 120 s in bellows Bl and T2, 3 s in bellows B2. Valve

7*3 connects the atmosphere to the case of the instru- ment, and controls the cutoff point for the high-frequency end of the pressure fluctuations. A nearly flat response was obtained for a range in period from 15

to 140 s, for the above adjustments of Tl and T2. Each

of the bellows was rigidly connected to a disk, forming capacitance C, which formed part of a bridge B. The output of B was fed through amplifier A to re- corder R. The power supply PS had a frequency of 16 kHz. Jones and Forbes considered sources of error such as tilt and temperature changes. The sensitivity was 5 X 10-5 mbar (3 3 IQ-Storr).

Cook and Young [62235] summarize the results of measurements of atmospheric pressure fluctuations un- der various circumstances. In detecting long wavelengths, such as caused by an explosion and received

as a reflection from a warm layer high above the ground, the direction of the approach is also desired. To obtain this information, Cook states that four microbarographs were installed about 7 km apart. The microbarographs, which he calls microphones, were of the diaphragm-capacitance type. Their output was a freFicuRE 63. Solion microbarograph.

A, anode leads; B, cathode button; C, cathode leads; Dl and D2, dia- phragms; E, electrolyte; P—Po, differential pressure; V, voltage output.

quency-modulated voltage proportional to the incident

sound pressure, which is transmitted by telephone to a central location for demodulation, amplification, and

recording. Comparison of the different times of arrival of the pressure wave at each microbarograph permitted

the approach direction of the wave to be determined.

It should be noted that short-wavelength fluctuations of the atmospheric pressure must be eliminated from both

sides of the diaphragm, which was done by connecting

the microbarograph inlet to the atmosphere by a long

pipeline. A capillary tube restriction between the two

sides of the diaphragm avoids response to very long

periods but permits obtaining the desired data. Sinclair [65351] designed a microbarograph using

a vacuum tube transducer operated by a diaphragm

capsule. See section 4.10 for a description.

Collins, Richie, and English [64279] propose their "Solion" design as a microbarograph. In figure 63,

diaphragms Dl and D2 enclose a chamber filled with

a water solution of an iodide and iodine. A porous

plug B permits slow liquid flow when a pressure P —

Po is applied, say on diaphragm D2. A dc voltage of

0.9 V is impressed between anode wires A and cathode

wires C. Due to dissociation of the iodide on one side of the cathode button B and recombination on the

other, a voltage develops across V while a flow through

B exists. The output varies from 0.1 to 0.9 V for a pres- sure range from 0.1 to 1000 dynes/cm- (7.5 X 10""^

to 0.75 torr). The frequency range of response was

between 0.003 and 50 Hz.

8.2.1.2. Licpiid Column Microbarographs

The Shida microbarograph, designed in 1918 and

still in use in 1956, is described by Namekawa [3617]

and shown in figure 64. In U-tube manometer U, LI is water and L2 a mineral oil, specific gravity about 0.9 A float F is suspended at the interface of LI and L2

A platinum filament W connects pulley PUl to the float to iron wire M, and to counterweight CI. Electromag

netic damping is provided by coil E and iron wire M. Another filament connects pulleys PUl and PU2, ter minating in counterweight C2. A record of the float motion against time is obtained on smoked paper RS

by pen RP. A reservoir RE, about a cubic meter in

47
IILJ

Po — LI 4>

pL2

Figure 64. Shida microbarograph.

Cl and C^, counterweights: E, damping coil; F, float; Ll, water; L2,

oil; M, iron rod; P, atmospheric pressure; Po. reference pressure; PUl and PU2, pulleys; R, restriction; RE, ballast volume; RP. pen; RS, smoked chart; U, U-tube manometer; W, platinum wire.

E P

Figure 65. Van Dorn microbarograph.

A, upper chamber; B, lower chamber: E, leads to electric recorder

circuit: M, barometer tube; P, Po, atmospheric and reference pressure; Rl, R2, restrictions; S, wall betwene A and B; SO, silicone oil; T, pressure transducer unit.

volume, is buried underground for temperature stability and is connected to the atmosphere through re- striction R and to one leg of the U-tube, which is maintained at reference pressure Po- The oil surface in the other leg is subjected to atmospheric pressure P. The

natural period of the system was 7 s. Atmospheric pres- sure fluctuations having a period from several minutes

to 30 min were recorded. A pen deflection of 1 mm

corresponded to a pressure change of 0.025 torr. Sources of error were considered in [3617], as indi- cated from the theory governing its operation.

Ericsson [62236] used a magnetic float in a U-tube,

which controlled the inductance in coils installed out- side of the manometer tube. The restrictions to pres- sure equalization in two legs of the U-tube were such

that the microbarograph responded to atmospheric

pressure fluctuations having periods between 2 and

1200 s. The pressure range was from 10""^ to 10""^ of an atmosphere (roughly 10~* to 1 torr).

Van Dorn [60119] designed the microbarograph

shown in figure 65 to determine the correlation of at- mospheric pressure fluctuations with surface water

waves. The fluctuations were measured by a barometric

mercury column M. This was connected to cistern B. Silicone oil filled the space in B below metal separator

5, and had a free surface in chamber A above S.

Figure 66. Donn microbarograph.

A, phase-sensitive circuit: B, amplifier; C, demodulator; D, modulator;

E, microfilm recorder; F, cork float; M, shallow U-tube manometer;

P, atmospheric pressure; Po, reference pressure: Rl, R2, restrictions; V, insulated volume: WT, electrical pressure transducer.

Chamber A and the transducer were connected to the atmospheric pressure at P. An adjustable screw re- striction R\ connected chambers A and B. The bellows

of a commercial pressure transducer T (unbonded

wire strain gage) was connected to the silicone oil in chamber B through restriction R2. E designates the leads to a Wheatstone bridge and a recorder. In operation, the atmospheric pressure P from chamber A

is transmitted to the oil in chamber B through restric- tion Rl, and then to transducer T through R2, to obtain the reference pressure Pq- Restriction jRl cuts off measurement of high frequencies, and R2, low fre- quencies. The entire instrument was mounted in a well, which was packed with diffusers to minimize the effect of turbulence in the atmosphere. The useful range was

5 mbar (3.75 torr) , for which the resolution was ±0.05

mbar, with greater sensitivity possible. The response was linear for fluctuation periods from 15 to 8000 s. Donn [58161] also devised a U-tube manometer for measuring atmospheric pressure fluctuations in order

to correlate them with ocean surface waves. In figure

66, M is the shallow U-tube, shaped somewhat like a doughnut. One leg is entirely closed off except for a

restriction R\ which cuts off all but the slow pressure changes, and thus controls the reference pressure Po- The other leg, much smaller in cross-sectional area, contains a cork float F to which is attached a commercial electrical transducer WT. The U-tube assembly is enclosed in a case, which is connected to the ambient

pressure P through restriction P2, which cuts off un- desired high-frequency fluctuations. An insulated ballast volume V is connected to the reference pressure

side of the manometer to stabilize Po. The manometer

liquid was diethyl sebacate. The output of the trans- ducer was fed to phase-sensitive circuit A, to amplifier

B and modulator D, demodulator C, and recorded on

microfilm recorder E. The response was linear for fluctuations having periods between 10 and 200 s. It

48
was stated that the resolution was 0.002 mbars (0.0015

torr) , which corresponds to about 0.02 mm head of the manometer liquid.

8.3. Elevation From Pressure

Measurement

Since atmospheric pressure varies with elevation (or

altitude), extensive efforts have been made to apply

this fact in making land surveys. One primary diffi- culty exists. The atmospheric pressure varies with time,

and from point to point on the earth's surface. Thus,

in precise work the pressure must be measured simultaneously at the base or reference point and at the point

the elevation of which is desired. A quiescent atmosphere is required. The point-to-point variation in at- mospheric pressure inherently limits the method to small distances from the base. Thus, while instrumentation is available having a

sensitivity of 1 or 2 ft at sea level, equivalent to 0.028

torr per foot, realization of this accuracy in field sur- veys is not easily obtainable. See Kissam [4418]. Most

of the altimeter designs are based on the deflection of an evacuated diaphragm capsule or bellows. Pertinent

designs have been discussed in section 4. One novel design, that described by Stripling. Eroding, and Wir«-elm, [4931] merits a brief description.

A temperature-controlled chamber contains a bellows. The volume of the chamber can be varied by extending or contracting the bellows so as to bring its pressure into equilibrium with atmospheric pressure. The

change in bellows volume, indicative of the change in chamber pressure, is measured through a gear train and a counter attached to the bellows. Pressure equilibrium is indicated by a liquid bubble in a horizontal

tube connecting the chamber with a second chamber

at a stabilized atmospheric pressure attained by the

restriction through which it is connected to the atmosphere. Note that change in ambient pressure, not pressure, is measured. Field tests indicated an average er- ror of 0.8 ft with a maximum of 1.2 ft. This is equivalent to about 0.03 torr.

8.4. Low Vapor Pressure

Consideration in this section is restricted to micromanometers useful only for measuring low vapor pressure. Vane gages primarily used to measure low vapor

pressure may have other applications and therefore are covered separately in section 5. Generally, in the pressure range of interest here, the Knudsen effusion method is used. Two primary designs

are available. In one proposed by Knudsen in 1909,

the mass of vapor effusing from an orifice in unit time

is measured, from which data the vapor pressure is computable. In the other, the vapor effuses so as to produce a torque, w^hich is measured by the angular

deflection of a wire filament. At vapor temperatures

1 above ambient, either method is usable : below ambient,

only the effusion-torque method is practical. In addition to designs based on the effusion from

orifices, a dewpoint design for measuring the vapor

pressure of mercury amalgams will be described. This

is useful only when the effusing vapor temperature is above ambient, and an optical transmission method is available.

8.4.1. Effusion-Weight Method

Douglas [5441] designed an apparatus for measuring the vapor pressure of calcium in the temperature

range from 800 to 900 °C, where the vapor ranged

from 1.2 X 10— to 41 X 10"^ torr. The design is shown schematically in figure 67. Here F is the furnace;

5. the calcium, sample: SL\ and SL2 are slits to guide

the effusing vapor to cover glass C. A shutter SH is operated to control the time interval of depositing

vapor on C. Any one of eight cover glasses can be

placed to receive vapor deposits by means of rotatable

table R. The time interval during which vapor is de- posited on C must be measured. Douglas obtained the mass of vapor deposited by means of titration. The

accuracy in measuring vapor pressure was ± 5 percent.

The mass of the deposited vapor can also be ob- tained by means of a microbalance, as in the design de- veloped by Herlet and Reich [5788] indicated in figure

68. Here the sample S is in furnace F. heated elec- trically by coil E. The effusing vapor impinges on disk

D, hung from beam B, in turn attached to spiral

spring SP. The deflection of beam B as the vapor de- posits on D is indicated on scale SC. Not shown in the

figure is a photocell and feedback arrangement by

which the beam B is maintained in the null position,

Figure 67. Effusion-weight vapor-pressure gage.

C, cover glass receptacle: F, furnace; Po, vacuum; R, rotatable table;

S, calcium sample; SH, rotatable shield; SLl, SL2, flow directing

slits.

SC 1_

- SP

D

F

3

E

Figure 68. Effusion-microbalance vapor-pressure gage.

B, microbalance; D. disk receptacle; E, electrical heater; F, furnace;

Po, vacuum pump connection; S, evaporating sample; SC, scale; SP,

spiral spring.

49
and the electrically generated balancing force measured

on an electrical recorder. The sensitivity obtained was

10~" torr. The vapor pressure of pump oils was measured in the range from 10""^ to 10""^ torr in the temperature range from 40 to 160 °C. Habermann and Daane [64202] applied the microbalance, nulled electromagnetically, designed by Edwards and Baldwin [5176] to measure the vapor pres- sure of substances at temperatures up to 2000 °C. Their

paper dwells mainly on the furnace design required to function at this temperature.

In all of the above described designs, the mass of the effused vapor was measured. Alternatively, the mass lost by the sample as a function of time can be

measured.

Carrera, Walker, et al. [63346], and Suzuki and

Wahlbeck [6625], describe microbalances in which the

effusion cell is weighed by a microbalance against time

while evaporation takes place. From such measurements

the vapor pressure of pure substances is computable.

Suzuki and Wahlbeck measured vapor pressure as low

as 10~^ torr, at sample temperatures up to 1500 °C. Carrera et al. were interested in vapor pressure meas- urements in the temperature range 1600-2500 °C. They discuss an improvement in sensitivity by allow- ing the balance beam to deflect and measuring the

deflection by an electrical capacitor, one plate of which was attached to the beam. The associated electronic

circuit to obtain the beam deflection is described, but

development of the design had not reached the test stage. Ditchburn and Gilmour [4115] published a review

and bibliography (93 references) on vapor pressure measurement in 1941, which may even now be of in- terest. A later survey was made in 1966 by Cooper

and Stranks [6628].

Theoretically, as first given by Knudsen:

_^ /2^NV.

KAt \ M )

^

'

where P is the vapor pressure in dynes per square

centimeter if all other terms are in cgs units; m is the mass of vapor effused in time interval t; A is the cross- sectional area of the orifice; R is the universal gas constant; T is the temperature in kelvins; M is the molecular weight in the vapor phase; and K is the sticking

probability.

Witman [5268], and others also, discusses the as- sumptions underlying eq (17), and sources of error:

(a) Free molecular flow of the vapor must exist. The mean free path must be at least 10 times the smallest dimension, usually that of the orifice or slits. Practically, this limits the method to measuring vapor pres- sures above about lO"^ torr. (b) The reflection of the molecules in the furnace

must be diffuse. (c) The molecules must enter the orifice or slits with

a cosine distribution of directions. (d) The molecules must enter uniformly over the

face of the orifice or slits. Usually the sticking coefficient is assumed to be

unity.

Douglas [5441] substituted a narrow rectangular

slit in cases where the circular slit was too large in comparison with the mean free path. He, as well as other experimenters, pointed out that the vapor must

be monatomic; otherwise, fractionation may occur. The indicated vapor pressures will be in error to the degree that the evaporating substance contains volatile impurities.

Birks and Bradley [4930] mention the cooling of the evaporating substance as evaporation proceeds as

a source of error. This is intensified by the necessity of maintaining vacuum conditions surrounding the

furnace. Cooke [5649] presents theory for the drop in the vapor pressure along the path of the vapor from the evaporating substance to the orifice through which it effuses. This pressure drop is a function of the cross- sectional area of the orifice. Experimental data on the

effect of various orifice areas were presented to establish the validity of the calculation, and to give a method for applying a correction.

8.4.2. Effusion-Torque Method

The design presented by Pratt and Aldred [59179],

and shown schematically in figure 69, is essentially that

first proposed by Volmer [3112]. In the figure, C is a graphite effusion cell containing the evaporating substance. The vapor effuses through two holes, 180 de- grees apart, causing a torque to act on the cell which

angularly deflects tungsten filament Fl. Tantalum fila- ment F2 is rigid in comparison with Fl. On rod R is mounted a mirror M, which reflects a light beam pass- ing through window W to a scale, by which the deflec- tion of Fl is measured. An aluminum disk D mounted

on R is in the field of alnico magnet DM to provide

damping. A silica tube T is the furnace. The highest

furnace temperature was 1000 °C. The vapor pressure was measurable in the range from 10~^ to 10""^ torr, with an accuracy at low pressures of ± 10 percent,

and at high, ± 1 percent.

Wessel [5175] improved Volhner's furnace design

to obtain a maximum temperature of 1500 °C, Searcy

and Freeman [5494], to 1900 °C, and Peleg and Al1

71

|o ,-.|—

Figure 69. Effusion-torque vapor-pressure gage.

C, graphite effusion cell; D, aluminum disk; DM, damping magnet;

Fl, F2, flexible and stiff wire filaments; M, mirror; Po, vaeuuB iwmp

connection; R, rod; T, silica tube; W, window.

50
cock [6622], to 2500 °C. All used torsion suspension

filaments. Klumb and Lueckert [5946] describe a design similar to that shown in figure 69, and stated its pressure range to be 10~^ to 10~* torr. Balson [4728] modified the Volmer design by adding a cold trap in the space above the furnace in order

to condense the effusing vapor. He constructed six ef- fusion cells of varying sensitivity, with the most sensitive having a sensitivity of 5 X 10~^ torr per milli- meter of scale deflection. Rosen [60188] added an electromagnet to control the position of rod D, figure 69, by which the filament

Fl was kept in the null position. The nulling electric current was measured to obtain the vapor pressure. He noted that by use of a photocell and feedback, the

null position of Fl could be maintained automatically.

No performance data were given. Peters and Herrick [6714] applied their automated

optical system for measuring angular deflection to measuring the torque produced by a diffusion cell. The theory for the effusion-torque method is given

by both Neumann and Voelker [3210] and Pratt and

Aldred [59179]. By the latter

oi^i/i + 02^2/2 ^^^^

where P is the vapor pressure in dynes per square centi- meter if all other terms are in cgs units; K is the tor- sion constant of the suspending filament; a. its angular

deflection; ai and Oo are the cross-sectional area of the two effusion holes respectively; q-i and go. their dis- tance from the suspension axis; and /i and /2 are cor- rection factors developed by Clausing [Dushman B491]

to take care of end effects. The underlying assumptions and sources of error are those discussed in section 8.4.1.

8.4.3. Dewpoint Pressure Divider

Kapff and Jacobs [4724] devised a dewpoint method

of securing vapor pressures at temperatures below

which the effusion-weight method took too long to obtain a measurement. The idea is to obtain the dewpoint

of the vapor at a temperature lower than that in the

furnace. If the vapor pressure at the higher temperature

is known, that at the lower dewpoint temperature can

M P2,T2

SPU

N

PIT I

be computed. In figure 70, L is the liquid sample,

temperature controlled. The vapor effuses through nozzle A^, through slit S to chrome-plated mirror M. The

mirror on which the vapor condenses is viewed through

window W. Theoretically,

P2 o /

7^2 \ H

(19)

where PI is the vapor pressure of the liquid at temperature T\; P2 is the vapor pressure at mirror temperature T2 when the impinging and evaporating vapor

are in balance; 6, a, and d. are physical dimensions as indicated in the figure. The pressure of other gases in the system must be held to pressures below lO""* torr. The pressure PI exceeds P2, which justifies the designation of pressure divider. The instrument was used to obtain vapor pressure P2 for pump oils from measured

values of P2/P1. For the particular geometrj' used,

P2/P1 was about lO-^; Th about 360 K: and 72,

about 300 K. To determine P2, PI must be measured,

which was done by the effusion-weight method in the range 10""* to 10~^ torr. Values of the vapor pressure

in the region of 10~^ torr are obtainable by the pres- sure divider. The accuracy was estimated at ± 30 percent. The values of P2 obtained were significantly

lower than those obtained with ionization gages, by as such as 100 percent. The source of the discrepancy was

not investigated.

8.4.4. Optical Transmission Gage

Morgolis [6621] developed a method for measuring

the vapor pressure of mercury amalgams. In figure 71,

^1 and Q2 are quartz optical cells, Q2 contains a drop

of pure mercury and ^1 contains a small quantity of

the mercury amalgam. These cells were installed in chamber T, the temperature of which could be controlled in the range 25 to 125 °C. The cells were illumi- nated by a mercury vapor lamp L with the 2537 °A

line, which is strongly absorbed by mercury vapor. The light transmitted through the cells was received by

a spectrophotometer S. At a given temperature the transmission through Ql was measured; the temperature was then adjusted to obtain the same transmission

through Q2. Thus, the vapor pressure of the amalgam

at the adjusted temperature equaled the vapor pressure

of the mercury. The latter is kno^NTi. The pressure range covered by the temperature control was 0.0017

to 0.9 torr.

1_

r

-0-

D

Q2

Figure 70. Dew-point vapor-pressure gage.

L, evaporating liquid; M, mirror; N, nozzle, Pi, P2, pressures; PU, pump connection; S, slit; Tl, T2, temperatures; W, window.

Figure 71. Optical transmission gage.

L, mercury vapor lamp; Ql, Q2, quartz transmission cells; S. spectro- photometer; T, temperature controlled chamber.

51
8.5. Low Differential Pressure at High Pressure

Ring gages capable of withstanding high pressure have been mentioned in section 2.11.3 and are dis- cussed by Schmidt [3601].

A null-type U-tube manometer developed by Reamer

and Sage [6008], in which the null position of a dia- phragm was detected by a linear differential trans- former, is described in section 2.6.2. Up to 15,000 psi

absolute, the differential pressure was measurable with

a precision of 0.05 torr, with an accuracy of 0.25 torr. Bell [65348] developed a null type U-tube manometer, also described in section 2.6.2. An inductance de- tector controlled a servomotor which moved one leg of the U-tube vertically to bring the liquid surface to a

null position. The differential pressure range was from

0.02 to 100 in of liquid column for absolute pressure

to 2500 psi.

8.6. Corrosive Gases

The problem here is to avoid using materials which

corrode when in contact with the fluid, the pressure

of which is to be measured. Elastic elements, dia- phragms or metal bellows, and connecting lines, can

be made of materials which do not corrode. Then any

of the transducers, in contact with the elastic element

but external to the corrosive fluid, can be used to make

the measurement. One design for the purpose is that

of Sancier and Richeson [5617], described in section

4.6.1. Another is that of Spence [4021], described in section 4.3.2, where avoidance of interaction of gases with mercury is its only virtue.

8.7. Distant Indication

This section concerns situations where the indication of the pressure is desired at a location at some

distance from the source of the pressure. One solution

is to connect the instrument to the source of the pres- sure by tubing. The lag may be high so that the dynamic response is poor, but the use of connecting tub- ing is practical in many cases. The tubing lag has been

discussed in section 8.1. Another solution is to place the pressure-sensitive

element close to the pressure source, use an electrical transducer, and transmit its output by electrical leads to the desired location. This is much more satisfactory

where rapid dynamic response is required. In general,

transmission of a modulated frequency is the ultimate

solution, since amplification of the signal does not

interfere with the modulated frequency. The pressure element and its transducer are placed close to the pressure source, as is the electrical circuit producing

the frequency modulation signal. Electrical leads may

connect to the indicating means, or in the ultimate,

may be telemetered by radio, as in the case of the radiosonde.

Tsukakoshi, et al. [64276], in their semiconductor

strain gage manometer, described in section 4.7, trans- mitted a dc signal from 2 to 300 m with no difficulty.

They avoided the transmission of high-frequency ac

current. Attention is also called to the vibrating wire gage

described in section 4.12, which is useful primarily for

distant indication of the pressure.

8.8. IVIiniature Pressure Cells

Although mainly suitable for measuring pressure

just above the micromanometer range, reference to de- velopments of small elastic element pressure cells may

be of interest. In some measure these developments

give an idea of the minimum diameter of the pressure

cell achievable for use in the micromanometer range. Wrathall [5280] describes diaphragm gages which are

to 1/2 in in diameter, with three different types of transducers: (a) resistance wire strain gage bonded

to the diaphragm, pressure range l/o and psi; elec- trical capacity, pressure range 2 and 8 psi; and variable reluctance, lowest pressure ranges 1 and 8 psi.

The resonant frequency of the various elements was

in the range 2300 to 30,000 Hz. Delmonte [5279] describes a miniature diaphragm

element, with an unbonded resistance wire strain gage

as the transducer, which was % in in outside diameter,

and could be made to have a pressure range as low as

1 psi. Pettersson and Clemedson [5059] used a silver dia- phragm in a transducer unit, 8 mm in diameter by 20

mm long, to measure fluctuations in blood pressure. The limiting sensitivity was 1 to 2 mm of water (0.07

to 0.15 torr).

Dimeff, et al. [6215], in their vibrating diaphragm

instrument described in section 4.11, used in a wind

tunnel, had a diaphragm as small as 0.28 in in diameter. Pressures as low as 10"~* torr were measurable.

Massey and Kavrak (6604) designed a miniature

pressure gage with a fast response. In figure 72, T is a

steel tube 0.04 in (1 mm) in diameter. A platinum

wire PT passes through the tube. One end of the tube

is cut away and shaped to obtain a flat, rigid surface,

at which location the platinum wire is also flattened. A disk of conducting rubber, as small as 0.045 in in diameter and 0.020 in thick, is placed between the

flattened sections of the tube and wire. Since the flat- tened platinum wire is flexible, changes in ambient

pressure compress or expand the rubber insert, which

changes the electrical resistance of the rubber. The

electrical resistance is measured by the output of

B A S

P '\ I *—p

^e3=fe^— CR

PT D

Figure 72. Miniature dynamic micromanometer.

A, amplifier; B, Wheatstone bridge: CR, conducting rubber; D, rigid

disk; P, pressure; PT, platinum wire; S, oscilloscope; T. steel tube.

52
Wheatstone bridge B, amplified and displayed on os- cilloscope 5. The sensitivity obtained was 0.04 torr; the indications were independent of frequency in the range 20 to 6000 Hz. The resistance of the rubber

decreased 1 percent per degree Celsius rise in temperature in the interval 10 to 50 °C.

8.9. Oxygen Partial Pressure

The measurement of oxygen pressure in a gas mixture is particularly important in respiration studies. This necessity stimulated the development of the Pauling oxygen meter [4631]. While its sensitivity probably does not quite qualify it as a micromanometer, its unique operating principle justifies its description. The

Pauling instrument is based on the fact that oxygen is paramagnetic, while other gases commonly mixed with

it in the atmospher are diamagnetic. In figure 73, a

small glass dumbbell G is hung from quartz fiber F

which carries mirror M. The dumbbell is in the field of a strong magnet MA. The glass balls are hollow and

filled with either air or an inert gas. As the partial pres- sure of oxygen in a gas at pressure P entering the cell changes, the dumbbell rotates, the torsion of which is balanced by the quartz fiber. A light beam reflected from mirror M to a scale measures the balancing

torque. Generally, the scale is graduated in percent oxygen, as low as 0 to 5 percent with an accuracy of

1 percent of the range, but it can also be calibrated in pressure units. Assuming a total gas pressure of 760

torr, the 5 percent meter would have an accuracy of about 0.4 torr, probably limited at lower total pressures

to about 0.1 torr. The force on the dumbbell is proportional to the product of two factors, the magnetic field gradient, and the difference in magnetic susceptibility

(between the dumbbell and the surrounding gas) . Later developments have included the application of an elec- trostatic voltage, to maintain the dumbbell in a null position and to provide a feedback to maintain the null automatically. A recorder of the electrostatic nulling

voltage has also been added.

Weissbart and Ruka [6113] tested successfully the

feasibility of an oxygen meter using an electrolytic ele- ment, and developed its theory. It operated at temperatures above 500 °C. The test setup is shown in figure

74, where E is the solid electrolyte (ZrO-j) .nr, fCaO).i5. r is a tube kept evacuated ; Tl is the inlet tube for the gas mixture, and T2 is the output tube. Furnace F is temperature controlled. The two sides of E are con- nected to a potentiometer. The output emf was found

to be proportional to the logarithm of the oxygen

pressure at a given temperature in the range 611 to 649 °C for mixtures of stable gases. When reactions

occurred in a gas mixture, the residual oxygen pressure was indicated. The emf was in the range 0.05 to 0.20 V

for oxygen pressures from 0.2 to 100 torr.

P G

Figure 73. Pauling oxygen meter.

F, quartz filament; G, glass dumbbell; M, miror; MA, magnet; P, entrance.

FO

Figure 74. Weissbart and Ruka oxygen meter.

E, solid electrolyte; F, furnace; PO, potentiometer; T, tube; Tl. gas mixture inlet tube; T2. gas outlet; V, vacuum source.

9. Calibration Techniques

Two principal techniques exist: static calibration and that for determining the dynamic response. Factors

affecting the static performance (mainly those due to temperature change) usually can be determined by

controlled variation of the affecting condition, and will not be considered further.

9.1. Static Calibration

Calibration is required of very few types of micromanometers, mainly those dependent on an elastic element, piezoelectric gages, and the effusion^iype vaporpressure gage.

Generally, calibration of an instrument involves comparison of its readings with those of a standard instru- ment, both subjected to the same pressure. A standard

instrument is here defined as one where the pressure can be calculated from easily made measurements and

without ambiguity. In many cases, only determination

of length and mass are required. The production of a computable pressure is another way of obtaining a

calibration.

53
There follows a discussion of standard instruments

which are, or could be, used as a calibration standard.

9.1.1. U-Tube Micromanometer

Of the many forms of measuring liquid column

heights in U-tubes which have been described in section

2, the simple design by Thomas and Cross described in section 2.2.1 is preferable, if the high-accuracy micromanometers are to be calibrated. This is a U-tube with

legs at least 2 in in diameter, with an index attached

to a micrometer in each leg to measure the displacement

of the two liquid surfaces. Either mercury or a lowdensity fluid can be used ; either differential or absolute pressure can be measured. With mercury as the liquid, the uncertainty with 2-in legs was 4 X 10~^ torr, and

with an oil, 4 X 10~* torr [6701]. Further improvement in performance is believed possible.

Other accurate means of measuring the liquid col- umn height which could be used in a standard instru- ment are: (a) optical interferometers (sect. 2.5), and

(b) the electrical capacitance transducer (sect. 2.6.1).

9.1.2. McLeod Gage

Some experimenters have used a McLeod gage to calibrate micromanometers measuring absolute pressure. The chief advantage of its use is that its range ex- tends downward well into the high-vacuum region

(10~^ to 10~^ torr). However, the uncertainty in the measured pressure is likely to be as great as 10 to 20

percent. Discussion in detail is out of place here, since the McLeod gage is classed as a vacuum gage and not

as a micromanometer.

9.1.3. Piston Gage

As a standard for measuring differential pressure at absolute pressures above about 1 torr, the air-lubri- cated, tilting piston gage is suitable down to about

0.01 torr, with an uncertainty of 1 or 2 X 10~^ torr. See section 5. For measuring absolute pressures, Douslin and Osborn [6596], section 5.1, have lowered the range to 0.01 torr, with an uncertainty at that pressure

of 1 X 10~^ torr. Further development work is needed

to set the pressure limits within which this gage is useful as a standard.

9.1.4. Gas Column Manometers

The standards described in the next four paragraphs

involve the production of a known pressure which can

be applied in some manner to a micromanometer which

is to be calibrated. The first of these is the gas column

manometer, useful only for low differential pressure at atmospheric pressure or above (see sect. 3). Sensitivities as good as 3 X 10~® torr have been obtained, but

the device has been rarely used.

9.1.5. Gas Volume Expansion

Here a gas at a higher and easily measured pressure and volume is expanded into an evacuated chamber of known volume from which the final pressure can be

computed. It is primarily used to calibrate vacuum

gages. Arney and Henderson [6813] describe a mobile

calibrator of this type to secure pressures in the range

10~^ to 30 torr. In the range 10~^ to 1 torr the ac- curacy was ±1.3 percent.

9.1.6. Vapor Pressure

The vapor pressure of a pure substance is a function

of temperature only and can be used to calibrate absolute micromanometers if the temperature of a closed system is closely controlled. For this application, the vapor pressure-temperature curve must be known and,

of course, must be in the required pressure range. The

difficulty is to locate substances with conveniently us- able vapor pressure-temperature curves, so that there has been practically no development of the method.

Strictly speaking, the pressure produced in the de- vice proposed by Pappas [6620] is not a vapor pressure, but it is akin to it. The complex Na2UF8 dis- sociates to give a gas uranium hexafluoride UFe, and

a solid NaF. The gas pressure varies with the temperature of the solid in accord with the relation

log P = 10.88 - 5.09 X (20)

where T is the absolute temperature in degrees Kelvin

and P the pressure in torr. At a pressure of 0.001 torr the temperature is 95 °C; at 0.01 torr, 123 °C; at 0.05 torr, 145 °C. While the given pressure-temperature

relation may be in question and precautions must be

taken to use pure Na2UFs, as pointed out by Pappas,

the dissociation pressures may be useful as a calibra- tion standard for absolute pressures in the rather diffi- cult calibration region between 0.01 and 0.001 torr. Further experimentation is required to determine more

accurately the dissociation pressures and the possible

errors. Futch [6130] used the vapor pressure of ice from — 100 to —40 °C to calibrate ionization gages in the pressure range from 10"* to 10""^ torr. It could equally

well be used to calibrate micromanometers.

9.1.7. Centrifugal Micromanometer

A known differential pressure in the vicinity of at- mospheric pressure is produced by the centrifugal mi- cromanometer. The best design is that proposed by

Kemp [5955], described in section 7. The range of pressures produced was from 3.6 X 10""* to 1.5 torr, with an accuracy of 1 percent.

9.1.8. Elastic Element Gage

The micromanometer based upon a diaphragmcapacitance, pressure-sensitive element has practical application as a calibration standard. Drawin [6081]

considers its application for measuring absolute pres- sures in the range from 10~^ to 1 torr, and Ryzhov

[63345] for the range from 0.001 to 0.1 torr. The chief

difficulty is in obtaining a valid pressure-deflection

relation for the diaphragm, usually flat and under

tension. However, both Drawin and Ryzhov avoided

this difficulty by developing theory for the case where

54
the diaphragm was maintained in the null position. See section 4.5.1. Drawin checked his computed sensitivity for one instrument against a McLeod gage and

found deviations within -|-3.0 and —2.7 percent, for 22

observations and 8 different gases. Within these deviations, only one source of error is significant, that due to instrument temperature change, which can be

avoided by maintaining the micromanometer at constant temperature. See section 4.5.4. Ryzhov stated that

the error in his design was 1 percent.

If the diaphragm is of uniform thickness and is free

to deflect, the instrument sensitivity can be obtained by

computation in another way. Tilting the diaphragm,

say 90° and 180°, changes the indication by an amount

equivalent to a pressure which is computable from the weight and dimensions of the diaphragm. In any event, checks on the constancy of the sensitivity can be obtained when desired by the tilting procedure.

In view of the need for an alternative to the McLeod

gage in the absolute pressure range 10~^ to 10~^ torr, further development of the capacitance gage as a working standard is worthwhile. See section 4.5.

9.2. Dynamic Calibration

In general, the response of micromanometers to fluctuating pressure or a rapid change in pressure can

be determined either by subjecting it to a varying pres- sure of known frequency and amplitude, or to a step

change in pressure made in a time interval which is

I small compared to the response time of the instrument.

The calibration is simplified if a micromanometer is available which has a response time greatly superior

to that of the instrument under test. As has been

previously stated, ordinarily dynamic calibration is

1 of practical importance only for elastic-element gages.

I In the case of microbarographs, the problem is to reI strict indications to pressures varying within a selected band of rather low frequencies for which calibration

offers no great difficulty.

, It is obvious that the micromanometer as a whole

has to be calibrated, but that the speed of response is

I determined chiefly by the slowest element, either the

I elastic element, the transducer, the amplifying circuits,

' or the recorder. The fastest response is obtainable

j with electrical transducers, in which case, with ordij nary care in designing the electrical circuits, the limit- ing element is the elastic element. There is an immense literature on methods of dynamic calibration of instrumentation measuring presj sures above the micromanometer range, but this for the most part is not applicable to micromanometers.

I However, the monograph by Schweppe, Eichberger,

et al. [63343], covers a wide variety of dynamic cali- bration methods and should be mentioned.

A number of methods used to produce pressure osI cillations of known amplitude and frequency in the

1 micromanometer will next be described.

9.2.1. Pressure Step Produced

Thureau and Lemiere [62123] had two chambers,

one with a volume of 2 cm^, the other 1000 cm^,

separated by a fragile diaphragm. The diaphragm pres- sure element was installed in the larger chamber which was initially at a lower pressure. Rupturing the dia- phragm subjected the micromanometer to about 1/500

of the initial pressure difference in the two chambers.

Reflected pressure waves in the large chamber gave a vibratory response with a frequency of about 16,000

Hz on an oscilloscope, later confirmed as the natural frequency of the micromanometer. These reflections were reduced by modifying the installation of the micromanometer in the test chamber. The pressure step can be calculated and compared with the static and

dynamic response of the micromanometer to give the needed information.

The above is a variation of the quick opening valve

between two spaces at different pressures, and of the shock tube commonly used to obtain a pressure step

at pressures above the range of interest here. The rupturing of a soap bubble by pressure has been

used to obtain a pressure step in the micromanometer

range. Pressure steps of 0.1 mbar (0.07 torr) are obtainable but are hard to reproduce. This method pro- vides an excellent quick check of the frequency re- sponse of microbarographs.

9.2.2. Fluctuating Pressures Produced

A number of widely different methods of producing

fluctuating pressures of known amplitude and fre- quency will be described. None appear to be applicable

at low absolute pressures. The pistonphone was developed to determine the performance of microphones and has been similarly

applied to elastic element micromanometers. It is de- scribed by Beranek [4932]. The theory involved in computing the pressure amplitude is described by Biagi

and Cook [5495] and Gerber [64280, 64281]. Simply,

the pistonphone consists of a small chamber, at one end

of which is a small diameter piston installed in a hole

in the chamber wall and the instrument under test at the other end. This piston is driven at known frequencies and measured amplitudes by an elecromagnetic

driver. As the piston oscillates the pressure in the chamber varies by an amount which can be calculated from the air volume changes in the chamber and from

assumptions made as to the degree the pressure change

is adiabatic. Rideal and Robertson [5570] used a loudspeaker

to impinge pressures of controlled frequency on a capacitance-diaphragm micromanometer. The output

of the micromanometer, and the input to the loud- speaker indicative of the frequency, were displayed on

an oscilloscope. The response of the micromanometer

was frequently independent up to 10^ Hz.

Miles [64273] developed a method of determining

the dynamic response of diaphragms, which is equally

useful for elastic element micromanometers. A piezoelectric oscillator was devised to obtain adequate amplitude of the pressure. Two polarized disks of ceramic

lead zirconium titanate, one of which expands and the other contracts when frequency-controlled voltage is

55
imposed, were cemented together. The disk assembly was installed in one end of a small volume and the diaphragm under test at the other end. Oscillations of the disk act like a pump in producing a pressure fluct- uation. The natural frequency of the disk used was

8600 Hz, which limited the frequency which could be

imposed. The diaphragm was connected to a wire

strain-gage transducer, the output of which was dis- played on an oscilloscope together with information on

the frequency of oscillation of the disk. Incidentally,

Miles gives data on the natural frequency of a number

of sizes and thicknesses of flat diaphragms.

Massey and Kavrak [6604] had the problem of determining the dynamic response of a miniature micromanometer depending on the electrical conductivity

of a rubber. A water column was kept in vibration at measured frequencies by a moving coil drive. The fre- quency range was from 1 to 10* Hz, and the amplitude

from 10-* to 0.5 in of water (1.9 X 10"* to 0.9 torr)

the latter measured by a vibration transducer. The

micromanometer unit was installed at the lower end

of the water column. An oscilloscope indicated both

the output of the micromanometer and of the vibration

amplitude transducer. The response was independent

of frequency in the range from 20 to 6000 Hz.

Fehr, Ben-Ary, and Ryan [67r3] modified a loud- speaker to obtain a piston action, and used it to pro- duce pressure oscillations in a chamber to which the instrument to be calibrated was connected. They deter- mined the relation between power input and pressure

oscillations at known frequencies. A microbarograph

which was calibrated had a flat response in the fre- quency range from 0.001 to 22 Hz in the range from

10-2 to iQi dynes/cm^ (roughly, 7 X 10-*' to 0.7

torr). The calibration procedures and techniques were

covered in considerable detail.

10. References

The number of the references are conveniently the same as those given in the bibliography, NBS Monograph 35 [6101], and its supplement [6708], to which

readers are referred for titles and indexed content. Quite a few references, some previous to 1960 and all subsequent to 1965, are not listed in Monograph 35. This method of identification accounts for the fact that the reference number listed below for any one year are not consecutive. In the list, book numbers are prefixed by B, the first two digits indicate the year of issue, and the last digit

distinguishes those listed for any one year. Papers in journals or reports have numbers the first two of which identify the year of issue, and the remaining digits distinguish those listed for any one year. Thus, [5955] indicates publication in 1959 and 55 the

identifying number.

[B271] Sosman, R. B., The Properties of Silica. Am. Chem.

Soc. Monogr. 37 (1927). [B301] Diedrichs, H., and Andrae, W. C, Experimental Mech.

Eng. VI, Eng. Instruments, p. 86 (1930). [B491] Dushman, S., Scientific Foundations of Vacuum Technique. John Wiley & Sons, New York, 882 p. (1949)

[496] Ower, E., The Measurement of Air Flow. (Chapter on manometers). Chapman & Hall, London, 293 p. (1949). [B533] Reilly, J., and Rae, W. N., Physico-Chemical Methods.

Vol. 1, (Chapter on Pressure measurement, p. 233-258)

D. Van Nostrand, 5th ed., 760 p. ( 1953)

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