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Air Density and Buoyancy Correction

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Mass Metrology

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 155))

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Abstract

Two weights (standards of mass) are compared usually in air. Upward buoyancy forces act on each weight separately; the values of these upward forces are proportional to the product of the respective volumes of the two weights and air density at the time of comparison. Weights of same nominal value have different volumes if their density is not equal. Volume of a stainless steel 1-kg weight differs from that of the platinum iridium mass standard by about \(85\,\mathrm{cm}^{3}\). Taking average density of air as \(1.2\,\mathrm{mg/cm}^{3}\), correction due to buoyancy effect will be about \(102\,\mathrm{mg}{\,=\,}1.02\times 10^{-4}\,\mathrm{kg}\). Error due to buoyancy correction in a kilogram is of the order 1 in \(10^{4}\). Hence, if we wish to determine the mass of a stainless steel kilogram by comparing it against a Pt. Ir. mass standard with an uncertainty of 1 in \(10^{8}\), we must be able to evaluate buoyancy correction with an uncertainty of 1 part in \(10^{4}\). This means that volume of the weight under test must be measured or known with the uncertainty of not worse than 1 in \(10^{4}\) and the density of air should also be measured with the uncertainty of not worse than 1 in \(10^{4}\).

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Author information

Authors and Affiliations

  1. Sector 8, Rohini 269/B-5, Delhi, 110085, India

    S. V. Gupta (emeritus)

Authors
  1. S. V. Gupta
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Correspondence to S. V. Gupta .

Appendix

Appendix

8.1.1 Air Density (\(\mathrm{kg/m}^{3}\), \(\mathrm{g/dm}^{3}\), \(\mathrm{mg/cm}^{3}\)) in step of \(1\,^{\circ }\mathrm{C}\)

Percentage of carbon \(\mathrm{dioxide}=0.04\), \(\hbox {relative humidity}=0.4\)

Press.

730

735

740

745

750

755

760

Temp.

97325

97993

98658

99325

99992

100658

101325

10

1.19569

1.20390

1.21211

1.22032

1.22853

1.23674

1.24495

11

1.19131

1.19949

1.20767

1.21585

1.22403

1.23221

1.24039

12

1.18696

1.19511

1.20326

1.21141

1.21956

1.22771

1.23587

13

1.18262

1.19074

1.19887

1.20699

1.21511

1.22323

1.23136

14

1.17831

1.18640

1.19449

1.20259

1.21068

1.21878

1.22687

15

1.17401

1.18208

1.19014

1.19821

1.20627

1.21434

1.22240

16

1.16973

1.17777

1.18581

1.19384

1.20188

1.20992

1.21796

17

1.16547

1.17348

1.18149

1.18950

1.19751

1.20552

1.21353

18

1.16123

1.16921

1.17719

1.18517

1.19316

1.20114

1.20912

19

1.15700

1.16496

1.17291

1.18086

1.18882

1.19677

1.20473

20

1.15279

1.16072

1.16864

1.17657

1.18450

1.19243

1.20035

21

1.14859

1.15649

1.16439

1.17229

1.18019

1.18809

1.19599

22

1.14441

1.15228

1.16016

1.16803

1.17590

1.18378

1.19165

23

1.14024

1.14809

1.15593

1.16378

1.17163

1.17947

1.18732

24

1.13608

1.14390

1.15172

1.15954

1.16736

1.17518

1.18300

25

1.13193

1.13973

1.14752

1.15532

1.16311

1.17090

1.17870

26

1.12780

1.13557

1.14333

1.15110

1.15887

1.16664

1.17440

27

1.12367

1.13141

1.13916

1.14690

1.15464

1.16238

1.17012

28

1.11955

1.12727

1.13499

1.14270

1.15042

1.15813

1.16585

29

1.11544

1.12313

1.13082

1.13851

1.14620

1.15389

1.16158

30

1.11134

1.11900

1.12667

1.13433

1.14200

1.14966

1.15733

31

1.10724

1.11488

1.12252

1.13016

1.13780

1.14544

1.15308

32

1.10315

1.11076

1.11838

1.12599

1.13361

1.14122

1.14883

33

1.09906

1.10665

1.11424

1.12183

1.12942

1.13701

1.14460

34

1.09498

1.10254

1.11010

1.11767

1.12523

1.13280

1.14036

35

1.09089

1.09843

1.10597

1.11351

1.12105

1.12859

1.13613

36

1.08681

1.09432

1.10184

1.10935

1.11687

1.12438

1.13190

37

1.08272

1.09022

1.09771

1.10520

1.11269

1.12018

1.12767

38

1.07864

1.08611

1.09357

1.10104

1.10851

1.11597

1.12344

39

1.07455

1.08199

1.08944

1.09688

1.10432

1.11176

1.11921

40

1.07046

1.07788

1.08530

1.09272

1.10014

1.10755

1.11497

Diff. T

0.00404

0.00406

0.00409

0.00411

0.00414

0.00417

0.00419

Press.

765

770

775

780

785

790

Diff P

Temp.

101992

102658

103323

103991

104658

105325

 

10

1.25316

1.26137

1.26958

1.27778

1.28599

1.29420

0.00821

11

1.24858

1.25676

1.26494

1.27312

1.28130

1.28948

0.00818

12

1.24402

1.25217

1.26032

1.26847

1.27662

1.28477

0.00815

13

1.23948

1.24760

1.25573

1.26385

1.27197

1.28009

0.00812

14

1.23496

1.24306

1.25115

1.25925

1.26734

1.27544

0.00809

15

1.23047

1.23854

1.24660

1.25467

1.26273

1.27080

0.00807

16

1.22600

1.23403

1.24207

1.25011

1.25815

1.26619

0.00804

17

1.22154

1.22955

1.23756

1.24557

1.25358

1.26159

0.00801

18

1.21710

1.22509

1.23307

1.24105

1.24903

1.25702

0.00798

19

1.21268

1.22064

1.22859

1.23655

1.24450

1.25246

0.00795

20

1.20828

1.21621

1.22414

1.23206

1.23999

1.24792

0.00793

21

1.20389

1.21180

1.21970

1.22760

1.23550

1.24340

0.00790

22

1.19952

1.20740

1.21527

1.22314

1.23102

1.23889

0.00787

23

1.19517

1.20301

1.21086

1.21871

1.22655

1.23440

0.00785

24

1.19082

1.19864

1.20646

1.21428

1.22210

1.22992

0.00782

25

1.18649

1.19429

1.20208

1.20987

1.21767

1.22546

0.00779

26

1.18217

1.18994

1.19771

1.20548

1.21324

1.22101

0.00777

27

1.17786

1.18561

1.19335

1.20109

1.20883

1.21657

0.00774

28

1.17356

1.18128

1.18900

1.19671

1.20443

1.21214

0.00772

29

1.16927

1.17696

1.18466

1.19235

1.20004

1.20773

0.00769

30

1.16499

1.17266

1.18032

1.18799

1.19565

1.20332

0.00766

31

1.16072

1.16836

1.17600

1.18364

1.19128

1.19892

0.00764

32

1.15645

1.16406

1.17168

1.17929

1.18691

1.19452

0.00761

33

1.15219

1.15977

1.16736

1.17495

1.18254

1.19013

0.00759

34

1.14793

1.15549

1.16305

1.17062

1.17818

1.18575

0.00756

35

1.14367

1.15121

1.15875

1.16629

1.17383

1.18137

0.00754

36

1.13941

1.14693

1.15444

1.16196

1.16948

1.17699

0.00752

37

1.13516

1.14265

1.15014

1.15763

1.16512

1.17261

0.00749

38

1.13091

1.13837

1.14584

1.15331

1.16077

1.16824

0.00747

39

1.12665

1.13409

1.14154

1.14898

1.15642

1.16386

0.00744

40

1.12239

1.12981

1.13723

1.14465

1.15207

1.15949

0.00742

Diff. T

0.00422

0.00424

0.00427

0.00429

0.00432

0.00434

\({-}\)

8.1.2 Air Density (\(\mathrm{kg/m}^{3}\), \(\mathrm{g/dm}^{3}\), \(\mathrm{mg/cm}^{3}\)) in step of \(1\,^{\circ }\mathrm{C}\)

Percentage of carbon \(\mathrm{dioxide}=0.04\), \(\hbox {relative humidity}=0.5\)

Press.

730

735

740

745

750

755

760

Temp.

97325

97993

98658

99325

99992

100658

101325

10

1.19512

1.20333

1.21154

1.21975

1.22796

1.23617

1.24438

11

1.19071

1.19889

1.20707

1.21525

1.22343

1.23161

1.23979

12

1.18631

1.19446

1.20261

1.21076

1.21891

1.22707

1.23522

13

1.18193

1.19006

1.19818

1.20630

1.21442

1.22255

1.23067

14

1.17757

1.18567

1.19376

1.20186

1.20995

1.21804

1.22614

15

1.17323

1.18130

1.18936

1.19743

1.20549

1.21356

1.22162

16

1.16890

1.17694

1.18498

1.19302

1.20105

1.20909

1.21713

17

1.16459

1.17260

1.18061

1.18862

1.19663

1.20464

1.21265

18

1.16029

1.16828

1.17626

1.18424

1.19222

1.20020

1.20819

19

1.15601

1.16396

1.17192

1.17987

1.18783

1.19578

1.20374

20

1.15174

1.15967

1.16759

1.17552

1.18345

1.19138

1.19930

21

1.14748

1.15538

1.16328

1.17118

1.17908

1.18698

1.19488

22

1.14323

1.15110

1.15897

1.16685

1.17472

1.18260

1.19047

23

1.13899

1.14683

1.15468

1.16253

1.17037

1.17822

1.18607

24

1.13476

1.14258

1.15040

1.15822

1.16604

1.17386

1.18168

25

1.13053

1.13833

1.14612

1.15391

1.16171

1.16950

1.17730

26

1.12632

1.13408

1.14185

1.14962

1.15739

1.16515

1.17292

27

1.12210

1.12985

1.13759

1.14533

1.15307

1.16081

1.16855

28

1.11790

1.12561

1.13333

1.14104

1.14876

1.15648

1.16419

29

1.11369

1.12138

1.12907

1.13676

1.14445

1.15214

1.15983

30

1.10949

1.11716

1.12482

1.13248

1.14015

1.14781

1.15548

31

1.10529

1.11293

1.12057

1.12821

1.13585

1.14349

1.15113

32

1.10109

1.10870

1.11632

1.12393

1.13155

1.13916

1.14677

33

1.09689

1.10448

1.11207

1.11966

1.12724

1.13483

1.14242

34

1.09268

1.10025

1.10781

1.11538

1.12294

1.13051

1.13807

35

1.08848

1.09602

1.10356

1.11109

1.11863

1.12617

1.13371

36

1.08426

1.09178

1.09929

1.10681

1.11432

1.12184

1.12935

37

1.08004

1.08753

1.09503

1.10252

1.11001

1.11750

1.12499

38

1.07582

1.08328

1.09075

1.09822

1.10568

1.11315

1.12062

39

1.07158

1.07902

1.08647

1.09391

1.10135

1.10880

1.11624

40

1.06734

1.07476

1.08217

1.08959

1.09701

1.10443

1.11185

Diff. T

0.00412

0.00414

0.00417

0.00419

0.00422

0.00425

0.00427

Press.

765

770

775

780

785

790

Diff P

Temp.

101992

102658

103323

103991

104658

105325

 

10

1.25259

1.26080

1.26900

1.27721

1.28542

1.29363

0.00821

11

1.24797

1.25615

1.26433

1.27251

1.28069

1.28887

0.00818

12

1.24337

1.25152

1.25967

1.26782

1.27597

1.28413

0.00815

13

1.23879

1.24691

1.25504

1.26316

1.27128

1.27940

0.00812

14

1.23423

1.24233

1.25042

1.25851

1.26661

1.27470

0.00809

15

1.22969

1.23776

1.24582

1.25389

1.26196

1.27002

0.00807

16

1.22517

1.23321

1.24124

1.24928

1.25732

1.26536

0.00804

17

1.22066

1.22867

1.23668

1.24469

1.25270

1.26071

0.00801

18

1.21617

1.22415

1.23213

1.24012

1.24810

1.25608

0.00798

19

1.21169

1.21965

1.22760

1.23556

1.24351

1.25147

0.00795

20

1.20723

1.21516

1.22309

1.23101

1.23894

1.24687

0.00793

21

1.20278

1.21068

1.21858

1.22648

1.23438

1.24228

0.00790

22

1.19834

1.20622

1.21409

1.22196

1.22984

1.23771

0.00787

23

1.19392

1.20176

1.20961

1.21746

1.22530

1.23315

0.00785

24

1.18950

1.19732

1.20514

1.21296

1.22078

1.22860

0.00782

25

1.18509

1.19288

1.20068

1.20847

1.21627

1.22406

0.00779

26

1.18069

1.18846

1.19622

1.20399

1.21176

1.21953

0.00777

27

1.17630

1.18404

1.19178

1.19952

1.20726

1.21500

0.00774

28

1.17191

1.17962

1.18734

1.19505

1.20277

1.21049

0.00772

29

1.16752

1.17521

1.18290

1.19059

1.19828

1.20597

0.00769

30

1.16314

1.17081

1.17847

1.18614

1.19380

1.20147

0.00766

31

1.15877

1.16641

1.17404

1.18168

1.18932

1.19696

0.00764

32

1.15439

1.16200

1.16962

1.17723

1.18485

1.19246

0.00761

33

1.15001

1.15760

1.16519

1.17278

1.18037

1.18796

0.00759

34

1.14563

1.15320

1.16076

1.16833

1.17589

1.18346

0.00756

35

1.14125

1.14879

1.15633

1.16387

1.17141

1.17895

0.00754

36

1.13687

1.14438

1.15190

1.15942

1.16693

1.17445

0.00752

37

1.13248

1.13997

1.14746

1.15495

1.16244

1.16993

0.00749

38

1.12808

1.13555

1.14302

1.15048

1.15795

1.16542

0.00747

39

1.12368

1.13112

1.13857

1.14601

1.15345

1.16089

0.00744

40

1.11927

1.12669

1.13411

1.14152

1.14894

1.15636

0.00742

Diff. T

0.00430

0.00432

0.00435

0.00437

0.00440

0.00442

\({-}\)

8.1.3 Air Density (\(\mathrm{kg/m}^{3}\), \(\mathrm{g/dm}^{3}\), \(\mathrm{mg/cm}^{3}\)) in step of \(1\,^{\circ }\mathrm{C}\)

Percentage of carbon \(\mathrm{dioxide}=0.04\), \(\hbox {relative humidity}=0.6\)

Press.

730

735

740

745

750

755

760

Temp.

97325

97993

98658

99325

99992

100658

101325

10

1.19455

1.20276

1.21097

1.21918

1.22739

1.23560

1.24381

11

1.19010

1.19828

1.20646

1.21464

1.22282

1.23100

1.23918

12

1.18566

1.19381

1.20196

1.21012

1.21827

1.22642

1.23457

13

1.18124

1.18937

1.19749

1.20561

1.21373

1.22186

1.22998

14

1.17684

1.18493

1.19303

1.20112

1.20922

1.21731

1.22540

15

1.17245

1.18052

1.18858

1.19665

1.20471

1.21278

1.22085

16

1.16807

1.17611

1.18415

1.19219

1.20023

1.20826

1.21630

17

1.16371

1.17172

1.17973

1.18774

1.19575

1.20376

1.21177

18

1.15936

1.16734

1.17532

1.18331

1.19129

1.19927

1.20725

19

1.15502

1.16297

1.17093

1.17888

1.18684

1.19479

1.20275

20

1.15069

1.15861

1.16654

1.17447

1.18240

1.19032

1.19825

21

1.14636

1.15426

1.16216

1.17006

1.17796

1.18586

1.19376

22

1.14205

1.14992

1.15779

1.16567

1.17354

1.18141

1.18929

23

1.13774

1.14558

1.15343

1.16128

1.16912

1.17697

1.18482

24

1.13343

1.14125

1.14907

1.15689

1.16471

1.17253

1.18035

25

1.12913

1.13692

1.14472

1.15251

1.16031

1.16810

1.17589

26

1.12483

1.13260

1.14037

1.14813

1.15590

1.16367

1.17144

27

1.12053

1.12828

1.13602

1.14376

1.15150

1.15924

1.16698

28

1.11624

1.12395

1.13167

1.13939

1.14710

1.15482

1.16253

29

1.11194

1.11963

1.12732

1.13501

1.14270

1.15039

1.15808

30

1.10764

1.11530

1.12297

1.13063

1.13830

1.14596

1.15363

31

1.10334

1.11098

1.11862

1.12625

1.13389

1.14153

1.14917

32

1.09903

1.10664

1.11426

1.12187

1.12948

1.13710

1.14471

33

1.09471

1.10230

1.10989

1.11748

1.12507

1.13266

1.14025

34

1.09039

1.09795

1.10552

1.11308

1.12065

1.12821

1.13578

35

1.08606

1.09360

1.10114

1.10868

1.11622

1.12376

1.13130

36

1.08172

1.08923

1.09675

1.10426

1.11178

1.11929

1.12681

37

1.07736

1.08485

1.09234

1.09983

1.10732

1.11482

1.12231

38

1.07299

1.08046

1.08793

1.09539

1.10286

1.11033

1.11779

39

1.06861

1.07605

1.08349

1.09094

1.09838

1.10582

1.11326

40

1.06421

1.07163

1.07905

1.08646

1.09388

1.10130

1.10872

Diff. T

0.00420

0.00422

0.00425

0.00427

0.00430

0.00433

0.00435

Press.

765

770

775

780

785

790

Diff P

Temp.

101992

102658

103323

103991

104658

105325

 

10

1.25201

1.26022

1.26843

1.27664

1.28485

1.29306

0.00821

11

1.24736

1.25554

1.26372

1.27190

1.28008

1.28826

0.00818

12

1.24272

1.25087

1.25902

1.26718

1.27533

1.28348

0.00815

13

1.23810

1.24622

1.25435

1.26247

1.27059

1.27872

0.00812

14

1.23350

1.24159

1.24969

1.25778

1.26588

1.27397

0.00809

15

1.22891

1.23698

1.24504

1.25311

1.26118

1.26924

0.00807

16

1.22434

1.23238

1.24042

1.24845

1.25649

1.26453

0.00804

17

1.21978

1.22779

1.23580

1.24381

1.25182

1.25983

0.00801

18

1.21524

1.22322

1.23120

1.23918

1.24717

1.25515

0.00798

19

1.21070

1.21866

1.22661

1.23457

1.24252

1.25048

0.00795

20

1.20618

1.21411

1.22203

1.22996

1.23789

1.24582

0.00793

21

1.20167

1.20957

1.21747

1.22537

1.23327

1.24117

0.00790

22

1.19716

1.20503

1.21291

1.22078

1.22866

1.23653

0.00787

23

1.19266

1.20051

1.20836

1.21620

1.22405

1.23190

0.00785

24

1.18817

1.19599

1.20381

1.21163

1.21945

1.22727

0.00782

25

1.18369

1.19148

1.19928

1.20707

1.21486

1.22266

0.00779

26

1.17921

1.18697

1.19474

1.20251

1.21028

1.21804

0.00777

27

1.17473

1.18247

1.19021

1.19795

1.20569

1.21344

0.00774

28

1.17025

1.17796

1.18568

1.19340

1.20111

1.20883

0.00772

29

1.16577

1.17346

1.18115

1.18884

1.19653

1.20422

0.00769

30

1.16129

1.16896

1.17662

1.18429

1.19195

1.19962

0.00766

31

1.15681

1.16445

1.17209

1.17973

1.18737

1.19501

0.00764

32

1.15233

1.15994

1.16756

1.17517

1.18278

1.19040

0.00761

33

1.14784

1.15543

1.16302

1.17061

1.17819

1.18578

0.00759

34

1.14334

1.15091

1.15847

1.16603

1.17360

1.18116

0.00756

35

1.13884

1.14638

1.15392

1.16146

1.16900

1.17654

0.00754

36

1.13432

1.14184

1.14935

1.15687

1.16438

1.17190

0.00752

37

1.12980

1.13729

1.14478

1.15227

1.15976

1.16725

0.00749

38

1.12526

1.13273

1.14019

1.14766

1.15513

1.16259

0.00747

39

1.12071

1.12815

1.13559

1.14304

1.15048

1.15792

0.00744

40

1.11614

1.12356

1.13098

1.13840

1.14582

1.15323

0.00742

Diff. T

0.00438

0.00440

0.00443

0.00445

0.00448

0.00450

\({-}\)

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Gupta, S.V. (2019). Air Density and Buoyancy Correction. In: Mass Metrology. Springer Series in Materials Science, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-030-12465-6_8

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