1824 02

2Pressure Measurement

Principles of Pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Units of Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Fundamental Constants and Conversion Factors . . . . . . . . . . . . . 32

Examples of Absolute and Gauge Pressure. . . . . . . . . . . . . . . . . . 33

Some Pressure Units and Conversions . . . . . . . . . . . . . . . . . . . . . 34

Additional Pressure Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . 35

kg/mm2 to psi Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

ksi to MPa Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

MPa to ksi Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

ft-lb to Joule Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Joule to ft-lb Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Height Conversions for Liquid Manometers . . . . . . . . . . . . . . . . . 44

Mercury and Distilled Water Density at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Measuring Differential Pressure with Transducers . . . . . . . . . . . . 46

Steam Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

CH 2 pressure.qxd 3/2/2006 8:40 AM Page 29

Chapter 2/Pressure 31

Principles of PressurePressure is the force per unit area afluid or gas exerts on its surround-ings. A container of gas containsnumerous atoms and moleculesconstantly bouncing of its walls.The pressure they create is theaverage force those atoms andmolecules produce on the walls.

Therefore, pressure, P, is a functionof force, F, and area, A.

P = F/A

The SI unit for pressure is thePascal (N/m2). Other frequentlyused units of pressure includeatmospheres (atm), pounds persquare inch (psi), bars, inches ofmercury (in Hg), and millimeters ofmercury (mm Hg).

Pressure measurements are typi-cally described as either static ordynamic. Static pressure occurswhere no motion is involved, suchas air pressure inside a tire or bal-loon. When the motion of a fluid orgas changes the force applied to itssurroundings, the pressure meas-urement is known as dynamic.

Head pressure (or pressure head) isthe measurement of a static pres-sure in a tank or a pipe and is afunction solely on the liquid'sheight and weight density.

Measurement Types andSensorsThere are three types of pressuremeasurements: absolute, differen-tial, and gauge. Absolute pressureis measured relative to a vacuum.Differential pressure measure-ments are taken with respect to aspecific reference pressure, whilegauge pressure is measured rela-tive to ambient atmospheric pres-sure. Pressure sensors come inmany different types of designs.When pressure is converted to anintermediate form such as dis-placement, three universal types ofpressure transducers used are thestrain gauge, variable capacitance,and piezoelectric. Each of thosetypes of sensors convert the dis-placement into an electrical outputsuch as voltage or current.

Perhaps the most common of allpressure sensors are Wheatstonebridge (strain-based) sensors. Theyvary in accuracy, size, ruggedness,and cost. Bridge sensors are usedfor high and low pressure applica-tions and can measure absolute,gauge, or differential pressure.


32 ISA Handbook of Measurement Equations and Tables

Units of Pressure

atm = Atmospheresin H2O = inches of Water columnin Hg = inches of Mercury columnPa = Pascals, also Newtons persquare meterkPa = kiloPascalspsi = pounds per square inchTorr = millimeters of Mercury column (often used to express lowvacuum pressures)

Fundamental Constants and

Conversion Factors

Metric

1 cm = 0.3937 inches

1 meter = 39.37 inches

1 meter = 3.280840 feet

1 cm2 = 0.1550003 in2

1 m2 = 10.76391 ft2

1 cm3 = 0.06102374 in3

1 m3 = 35.31467 ft3

1 kg = 2.204623 lb

1 gm = 0.03527397 oz

1 liter = 1000.028 cm3

1 liter = 61.02545 in3

1 cm3 = 0.9999720 liter

1 gm/cm3 = 62.4280 lb/ft3

1 gm/cm3 = 0.0361273 lb/in3

1 gm/ml = 0.9999730 gm/cm3

1 gm/cm3 = 1.000028 gm/ml

English

1 inch = 2.54 cm

1 foot = 30.48 cm

1 in2 = 6.4516 cm2

1 ft2 = 929.0304 cm2

1 in3 = 16.387064 cm3

1 in3 = 0.01638661 liter

1 ft3 = 0.028316847 m3

1 lb = 453.59237 gm

1 oz = 28.349523 gm

1 lb/ft3 = 0.0160185 gm/cm3

1 lb/in3 = 27.6799 gm/cm3

English / Metric Pressure Units

Quantity English MetricUnits Units

Force Poundal NewtonPressure, ksi, psi, Pascal

Stress psigEnergy, Btu, ft-lb JouleWork



Examples of Absolute and Gauge Pressure

P1 = 28 psia

P1 = 28 psia

Absolute

Pressure

P2 = 20.5 psia

P3 = 8.5 psia

Patm = 14.7 psia

P1 - P2 = 7.5 psig

Differential

Pressure

P3 - Patm = 6.1 psig

Gauge Pressure

P1 - Patm = 13.4 psig

Gauge Pressure

Atmospheric

PressureAbsolute

Pressure

(psia)

(Barometric

Pressure)

P3 = 8.5 psia

Absolute

Pressure

Absolute Zero

(Perfect Vacuum)

30

25

20

15

10

5

0



Pascal bar Newtons per

squaremilli-meter

kp/m2 kp/cm2

(=1 at)atm torr

1 Pa (N/m2)= 1 10-5 10-6 0.102 0.102×10-4

0.987×10-5 0.0075

1 bar (daN/cm2) = 105 1 0.1 10,200 1.02 0.987 750

1 N/ mm2 = 106 10 1 1.02×105 10.2 9.87 7,501

1 kp/m2 = 9.81 9.81×

10-59.81×10-6 1 10-4 0.968×

10-4 0.0736

1 kp/ cm2

(1 atm) =98,100 0.981 0.0981 10,000 1 0.968 736

1 atm (760 torr) = 101,325 1.013 0.1013 10,330 1.033 1 760

1 torr(mmHg) = 133 0.00133 1.33×

10-4 13.6 0.00132 0.00132 1

Some Pressure Units and Conversions



To Convert From To Multiply by:

Atmosphere Bar 1.01325Atmosphere in. water 406.78@32° FAtmosphere ft. water 33.89854@32° FAtmosphere in. Mercury 22.92126@32° FAtmosphere Kilopascal 101.325Atmosphere mm water 10.3326@4° FAtmosphere Millibar 1013.25Atmosphere mm Mercury 760.000@0° CAtmosphere Micron 760000.000Atmosphere Newton/cm2 10.1325Atmosphere Pascal 101325.000Atmosphere Pound/Force ft2 2116.22Atmosphere psi 14.69595Atmosphere Torr 760.000Bar Atmosphere 0.9869233Bar in. water 401.46@32° FBar ft. water 33.4553@32° FBar in. Mercury 29.53@32° FBar Kilopascal 100.00Bar mm water 0.101972@0° CBar mm Mercury 750.062@0° CBar Newton/cm2 10.00Bar Pascal 100000.00Bar Pound/Force/ft2 2088.54Bar psi 14.50377Bar Torr 750.062cm of Mercury@0° C Atmosphere 0.0131579cm of Mercury@0° C Millibar 13.3322cm of Mercury@0° C mm of water 135.951cm of Mercury@0° C Pascal 1333.22cm of Mercury@0° C psi 0.193368cm of water@0° C Atmosphere 0.000967841cm of water@0° C Millibar 0.980665cm of water@0° C mm of Mercury 0.735559cm of water@0° C Pascal 98.0665cm of water@0° C psi 0.0142233cm3 Atmosphere Joule 0.101325ft3 Atmosphere Foot-Pound (Force) 2116.22ft3 Atmosphere Joule 2869.28Gram (Force)/cm Joule 0.0000980665

Additional Pressure Conversions



Gray Joule/Kilogram 1.000in. of Mercury@32° F Atmosphere 0.0334211in. of Mercury in. of water 13.5951in. of Mercury Millibar 33.8639in. of Mercury@32° F mm of water@32° F 345.316in. of Mercury Pascal 3386.39in. of Mercury psi 0.491154in. of water in. of Mercury 0.0735559in. of water@32° F Millibar 2.49089in. of water mm of Mercury 1.86832in. of water Pascal 249.089in. of water psi 0.0361273KG (Force)/cm2 Atmosphere 0.96784KG (Force)/cm2 ft of water 32.8084KG (Force)/cm2 in. of Mercury 28.9590KG (Force)/cm2 meter of water 10.000KG (Force)/cm2 mm of Mercury 735.559KG (Force)/cm2 Pascal 98066.5KG (Force)/cm2 psi 14.22334KG (Force)/m2 Pascal 9.80665KG (Force)/mm2 MPa 9.80665KG (Force)/mm2 psi 1422.334Kilopascal psi 0.1450377liter-Atmosphere ft3-Atmosphere 0.0353147liter-Atmosphere Joule 101.325liter-Bar Joule 100.000MPa Bar 10.000MPa Newton/mm2 1.000Millibar Pascal 100.000mm of Mercury@0° C Atmosphere 0.001315789mm of Mercury@0° C Dyne/cm2 1333.224mm of Mercury@0° C Millibar 1.333224mm of Mercury@0° C mm of water 13.5951mm of Mercury@0° C Pascal 133.3224mm of Mercury@0° C psi 0.0193368mm of Mercury@0° C Torr 1.000mm of water Millibar 0.0980665mm of water mm of Mercury 0.0735559mm of water Pascal 9.80665mm of water psi 0.00142233Newton/m2 Pascal 1.000Newton/mm2 MPa 1.000

Additional Pressure Conversions (cont.)



Pound (Force)/in2 mm of water 0.00070307Pound (Force)/in2 mm of Mercury 51.7149Pound (Force)/in2 Millibar 68.9476Pound (Force)/in2 Pascal 6894.76Pound (Force) Second/in2 Pascal-Second 6894.76psi in H20 27.679899psi Pound (Force)/in2 1.000Torr Millibar 1.333224Torr mm of Mercury 1.000@0° CTorr Pascal 133.3224

Additional Pressure Conversions (cont.)



Kg/mm2 psi

10 14,22311 15,64612 17,06813 18,49014 19,91315 21,33516 22,75717 24,18018 25,60219 27,02420 28,44721 29,86922 31,29123 32,71424 34,13625 35,55826 36,98127 38,40328 39,82629 41,24830 42,67031 44,09332 45,51533 46,93734 48,36035 49,78236 51,20437 52,62738 54,04939 55,47140 56,89441 58,31642 59,73843 61,16144 62,53845 64,00546 65,42447 66,580

Conversion Table, kg/mm2 to psi

Kg/mm2 psi

48 68,27249 69,69550 71,11751 72,53952 73,96253 75,38454 76,80655 78,22956 79,65157 81,07358 82,49559 83,91860 85,34061 86,76262 88,18563 89,60764 91,02965 92,45266 93,87467 95,29668 96,71969 98,14170 99,56371 100,98672 102,40873 103,83074 105,25375 106,67576 108,09777 109,52078 110,94279 112,36480 113,78781 115,20982 116,63283 118,05484 119,47785 120,899



Kg/mm2 psi

86 122,32187 123,74488 125,16689 126,58890 128,01191 129,43392 130,85593 132,27894 133,70095 135,12296 136,54597 137,96798 139,38999 140,812100 142,234101 143,656102 145,079103 146,501104 147,923105 149,346106 150,767107 152,190108 153,613109 155,035110 156,457111 157,880112 159,302113 160,724114 162,147115 163,569116 164,991117 166,414118 167,836

Conversion Table, kg/mm2 to psi (cont.)

Kg/mm2 psi

119 169,258120 170,681121 172,103122 173,525123 174,948124 176,370125 177,792126 179,215127 180,637128 182,059129 183,482130 184,904131 186,327132 187,749133 189,171134 190,594135 192,016136 193,438137 194,861138 196,283139 197,705140 199,128141 200,550142 201,972143 203,395144 204,817145 206,239146 207,662147 209,084148 210,506149 211,929150 213,351

Conversion Equation, kg/mm2 to psi

Pressure/inch2 = kg/mm2 (1.42234)



ksi MPa ksi MPa ksi MPa ksi MPa

1 6.895 26 179.264 60 413.685 310 2137.375

2 13.790 27 186.158 70 482.633 320 2206.322

3 20.684 28 193.053 80 551.581 330 2275.270

4 27.579 29 199.948 90 620.528 340 2344.217

5 34.474 30 206.843 100 689.476 350 2413.165

6 41.369 31 213.737 110 758.423 360 2482.113

7 48.263 32 220.632 120 827.371 370 2551.060

8 55.158 33 227.527 130 896.318 380 2620.008

9 62.053 34 234.422 140 965.266 390 2688.955

10 68.948 35 241.316 150 1034.214 400 2757.903

11 75.842 36 248.211 160 1103.161 410 2826.850

12 82.737 37 255.106 170 1172.109 420 2895.798

13 89.632 38 262.001 180 1241.056 430 2964.746

14 96.527 39 268.896 190 1310.004 440 3033.693

15 103.421 40 275.790 200 1378.951 450 3102.641

16 110.316 41 282.685 210 1447.899 460 3171.588

17 117.211 42 289.580 220 1516.847 470 3240.536

18 124.106 43 296.475 230 1585.794 480 3309.483

19 131.000 44 303.369 240 1654.742 490 3378.431

20 137.895 45 310.264 250 1723.689 500 3447.379

21 144.790 46 317.159 260 1792.637 510 3516.326

22 151.685 47 324.054 270 1861.584 520 3585.274

23 159.597 48 330.948 280 1930.532 530 3654.221

24 165.474 49 337.843 290 1999.480 540 3723.169

25 172.369 50 344.738 300 2068.427 550 3792.116

Conversion Table, ksi to MPa



MPa ksi MPa ksi MPa ksi

1 0.145 50 7.252 1300 188.552

2 0.290 100 14.504 1350 195.804

3 0.435 150 21.756 1400 203.056

4 0.580 200 29.008 1450 210.308

5 0.725 250 36.260 1500 217.560

6 0.870 300 43.512 1550 224.812

7 1.015 350 50.764 1600 232.064

8 1.160 400 58.016 1650 239.316

9 1.305 450 65.268 1700 246.568

10 1.450 500 72.520 1750 253.820

11 1.595 550 79.772 1800 261.072

12 1.740 600 87.024 1850 268.324

13 1.886 650 94.276 1900 275.576

14 2.031 700 101.528 1950 282.828

15 2.176 750 108.780 2000 290.080

16 2.321 800 116.032 2050 297.332

17 2.466 850 123.284 2100 304.584

18 2.611 900 130.536 2150 311.836

19 2.756 950 137.788 2200 319.088

20 2.901 1000 145.040 2250 326.340

21 3.046 1050 152.292 2300 333.592

22 3.191 1100 159.544 2350 340.844

23 3.336 1150 166.796 2400 348.096

24 3.481 1200 174.048 2450 355.348

25 3.626 1250 181.300 2500 362.600

Conversion Table, MPa to ksi



ft-lb Joule ft-lb Joule ft-lb Joule ft-lb Joule

1 1.3558 26 35.2513 55 74.5700 180 244.0472

2 2.7116 27 36.6071 60 81.3491 185 250.8263

3 4.0675 28 37.9629 65 88.1282 190 257.6054

4 5.4233 29 39.3187 70 94.9073 195 264.3845

5 6.7791 30 40.6745 75 101.6863 200 271.1636

6 8.1349 31 42.0304 80 108.4654 220 298.2799

7 9.4907 32 43.3862 85 115.2445 240 325.3963

8 10.8465 33 44.7420 90 122.0236 260 352.5126

9 12.2024 34 46.0978 95 128.8027 280 379.6290

10 13.5582 35 47.4536 100 135.5818 300 406.7454

11 14.9140 36 48.8094 105 142.3609 320 433.8617

12 16.2698 37 50.1653 110 149.1400 340 460.9781

13 17.6256 38 51.5211 115 155.9191 360 488.0944

14 18.9815 39 52.8769 120 162.6982 380 515.2108

15 20.3373 40 54.2327 125 169.4772 400 542.3272

16 21.6931 41 55.5885 130 176.2563 420 569.4435

17 23.0489 42 56.9444 135 183.0354 440 596.5599

18 24.4047 43 58.3002 140 189.8145 460 623.6762

19 25.7605 44 59.6560 145 196.5936 480 650.7926

20 27.1164 45 61.0118 150 203.3727 500 677.9090

21 28.4722 46 62.3676 155 210.1518 520 705.0254

22 29.8280 47 63.7234 160 216.9308 540 732.1417

23 31.1838 48 65.0793 165 223.7099 560 759.2581

24 32.5396 49 66.4351 170 230.4890 580 786.3744

25 33.8954 50 67.7909 175 237.2681 600 813.4908

Conversion Table, ft-lb to Joule



Joule ft-lb Joule ft-lb Joule ft-lb Joule ft-lb

1 0.7376 26 19.1766 55 40.5659 180 132.7612

2 1.4751 27 19.9142 60 44.2537 185 136.4490

3 2.2127 28 20.6517 65 47.9415 190 140.1368

4 2.9502 29 21.3893 70 51.6293 195 143.8246

5 3.6878 30 22.1269 75 55.3172 200 147.5124

6 4.4254 31 22.8644 80 59.0050 220 162.2637

7 5.1629 32 23.6020 85 62.6928 240 177.0149

8 5.9005 33 24.3395 90 66.3806 260 191.7661

9 6.6381 34 25.0771 95 70.0684 280 206.5174

10 7.3756 35 25.8147 100 73.7562 300 221.2686

11 8.1132 36 26.5522 105 77.4440 320 236.0199

12 8.8507 37 27.2898 110 81.1318 340 250.7711

13 9.5883 38 28.0274 115 84.8196 360 265.5224

14 10.3259 39 28.7649 120 88.5075 380 280.2736

15 11.0634 40 29.5025 125 92.1953 400 295.0248

16 11.8010 41 30.2400 130 95.8831 420 309.7761

17 12.5386 42 30.9776 135 99.5709 440 324.5273

18 13.2761 43 31.7152 140 103.2587 460 339.2786

19 14.0137 44 32.4527 145 106.9465 480 354.0298

20 14.7512 45 33.1903 150 110.6343 500 368.7811

21 15.4888 46 33.9279 155 114.3221 520 383.3532

22 16.2264 47 34.6654 160 118.0099 540 398.2835

23 16.9639 48 35.4030 165 121.6977 560 413.0347

24 17.7015 49 36.1405 170 125.3856 580 427.7860

25 18.4390 50 36.8781 175 129.0734 600 442.5372

Conversion Table, Joule to ft-lb



Height Conversion Equations for

Liquid Manometers

Inches or millimeters of a liquid topounds per square inch or kilo-grams per square centimeter.

P = dh

whereP = pressure, lb/in2 or kg/cm2

d = density, lb/in3 or kg/cm3

h = height, in or cm

Inches of Mercury to pounds persquare inch.

P = 0.48977 h

whereP = pressure, lb/in2

h = height, in0.48977 is the density of Mercuryat 60oF, 15.6oC

Inches of distilled water topounds per square inch.

P = 0.036092 h

whereP = pressure, lb/in2

h = height, in0.036092 is the density of waterat 60oF, 15.6oC

Centimeters of Mercury to kilo-grams per square centimeter.

P = 0.013557 h

whereP = pressure, kg/cm2

h = height, cm0.013557 is the density ofMercury at 60oF, 15.6oC

Centimeters of distilled water tokilograms per square centimeter.

P = 0.0009990 h

whereP = pressure, kg/cm2

h = height, cm0.0009990 = the density of waterat 60oF, 15.6oC

Standard Conditions for

Measuring Pressure Based on the

Height of a Column of Liquid.

[Note: Some vendors, systemdesign firms and other organi-zations use their own “standards,”which may vary from those below.]

Mercury Column

Gravity: 980.665 cm/sec2

32.1740 ft/sec2

Temperature: 0oC, 32oF

Atmosphere: 760 mm of Mercury29.9213 in ofMercury

Water Column

Gravity: 980.665 cm/sec2

32.1740 ft/sec2

Temperature: 20oC, 68oF

Atmosphere: 1035.08 cm of water407.513 in of water



Deg. F Deg. C Mercury,

lb/in3Mercury,

kg/cm3Distilled

Water,

lb/in3

Distilled

Water,

kg/cm3

0 -17.8 0.49275 0.013639

20 -6.7 0.49175 0.013612

32 0.0 0.49116 0.013595

40 4.4 0.49076 0.013584 0.036127 0.0009997

60 15.6 0.48977 0.013557 0.036092 0.0009990

80 26.7 0.48879 0.013530 0.036005 0.0009966

100 37.8 0.48780 0.013502 0.035876 0.0009931

120 48.9 0.48683 0.013475 0.035713 0.0009885

140 60.0 0.48585 0.013448 0.035522 0.0009832

160 71.1 0.48488 0.013421

180 82.2 0.48391 0.013394

200 93.3 0.48293 0.013368 0.034792 0.0009630

Density of Mercury and Distilled Water at Various Temperatures



Measuring Differential Pressure with Transducers.

whereP = pressureCp = capacitance of transducer at operating pressure

C0 = capacitance of transducer at zero pressure

A = current from a constant source

P AC C

Cp

p

=−0



Steam Tables

Standard representations for the thermodynamic properties of waterand steam (commonly known as “steam tables”) are established bythe International Association for the Properties of Water and Steam(IAPWS). The latest IAPWS standard formulation for general andscientific use was adopted in 1995. The numbers in the followingtables were supplied by the Physical and Chemical PropertiesDivision of NIST as calculated from their database (A.H. Harvey, A.P.Peskin, and S.A. Klein, NIST/ASME Steam Properties, NIST StandardReference Database 10, Version 2.2 ([National Institute of Standardsand Technology, Gaithersburg, MD, 20899]) that implements the IAPWS standard. Further information may be found atwww.iapws.org and at www.nist.gov/srd/nist10.htm.

Thermodynamic Properties of Saturated Water and Steam as a

Function of Temperature

t, °C Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)

p, MPa ρρL ρρV hL hV ∆∆h sL sV ∆∆s

0.01 0.000 612 999.79 0.004 855 0.00 2500.9 2500.9 0.000 00 9.1555 9.1555

5 0.000 873 999.92 0.006 802 21.02 2510.1 2489.0 0.076 25 9.0248 8.9486

10 0.001 228 999.65 0.009 407 42.02 2519.2 2477.2 0.151 09 8.8998 8.7487

15 0.001 706 999.06 0.012 841 62.98 2528.3 2465.4 0.224 46 8.7803 8.5558

20 0.002 339 998.16 0.017 314 83.91 2537.4 2453.5 0.296 48 8.6660 8.3695

25 0.003 170 997.00 0.023 075 104.83 2546.5 2441.7 0.367 22 8.5566 8.1894

30 0.004 247 995.61 0.030 415 125.73 2555.5 2429.8 0.436 75 8.4520 8.0152

35 0.005 629 993.99 0.039 674 146.63 2564.5 2417.9 0.505 13 8.3517 7.8466

40 0.007 385 992.18 0.051 242 167.53 2573.5 2406.0 0.572 40 8.2555 7.6831

45 0.009 595 990.17 0.065 565 188.43 2582.4 2394.0 0.638 61 8.1633 7.5247

50 0.012 352 988.00 0.083 147 209.34 2591.3 2381.9 0.703 81 8.0748 7.3710

55 0.015 762 985.66 0.104 56 230.26 2600.1 2369.8 0.768 02 7.9898 7.2218

60 0.019 946 983.16 0.130 43 251.18 2608.8 2357.7 0.831 29 7.9081 7.0769

t = temperature

p, MPa = pressure

ρL = liquid density

ρV = vapor density

hL = liquid enthalpy

hV = vapor enthalpy

∆h = enthalpy of vaporization

sL = liquid entropy

sV = vapor entropy

∆s = entropy of vaporization




65 0.025 042 980.52 0.161 46 272.12 2617.5 2345.4 0.893 65 7.8296 6.9359

70 0.031 201 977.73 0.198 43 293.07 2626.1 2333.0 0.955 13 7.7540 6.7989

75 0.038 595 974.81 0.242 19 314.03 2634.6 2320.6 1.0158 7.6812 6.665

80 0.047 414 971.77 0.293 67 335.01 2643.0 2308.0 1.0756 7.6111 6.5355

85 0.057 867 968.59 0.353 88 356.01 2651.3 2295.3 1.1346 7.5434 6.4088

90 0.070 182 965.30 0.423 90 377.04 2659.5 2282.5 1.1929 7.4781 6.2853

95 0.084 608 961.88 0.504 91 398.09 2667.6 2269.5 1.2504 7.4151 6.1647

100 0.101 42 958.35 0.598 17 419.17 2675.6 2256.4 1.3072 7.3541 6.0469

105 0.120 90 954.70 0.705 03 440.27 2683.4 2243.1 1.3633 7.2952 5.9318

110 0.143 38 950.95 0.826 93 461.42 2691.1 2229.6 1.4188 7.2381 5.8193

115 0.169 18 947.08 0.965 40 482.59 2698.6 2216.0 1.4737 7.1828 5.7091

120 0.198 67 943.11 1.1221 503.81 2705.9 2202.1 1.5279 7.1291 5.6012

125 0.232 24 939.02 1.2987 525.07 2713.1 2188.0 1.5816 7.0770 5.4955

130 0.270 28 934.83 1.4970 546.38 2720.1 2173.7 1.6346 7.0264 5.3918

135 0.313 23 930.54 1.7190 567.74 2726.9 2159.1 1.6872 6.9772 5.2900

140 0.361 54 926.13 1.9667 589.16 2733.4 2144.3 1.7392 6.9293 5.1901

145 0.415 68 921.62 2.2423 610.64 2739.8 2129.2 1.7907 6.8826 5.0919

150 0.476 16 917.01 2.5481 632.18 2745.9 2113.7 1.8418 6.8371 4.9953

155 0.543 50 912.28 2.8863 653.79 2751.8 2098.0 1.8924 6.7926 4.9002

160 0.618 23 907.45 3.2596 675.47 2757.4 2082.0 1.9426 6.7491 4.8066

165 0.700 93 902.51 3.6707 697.24 2762.8 2065.6 1.9923 6.7066 4.7143

170 0.792 19 897.45 4.1222 719.08 2767.9 2048.8 2.0417 6.6650 4.6233

175 0.892 60 892.28 4.6172 741.02 2772.7 2031.7 2.0906 6.6241 4.5335

180 1.0028 887.00 5.1588 763.05 2777.2 2014.2 2.1392 6.5840 4.4448

185 1.1235 881.60 5.7504 785.19 2781.4 1996.2 2.1875 6.5447 4.3571

190 1.2552 876.08 6.3954 807.43 2785.3 1977.9 2.2355 6.5059 4.2704

195 1.3988 870.43 7.0976 829.79 2788.8 1959.0 2.2832 6.4678 4.1846

200 1.5549 864.66 7.8610 852.27 2792.0 1939.7 2.3305 6.4302 4.0996



t, °C Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)p, MPa ρρL ρρV hL hV ∆∆h sL sV ∆∆s

205 1.7243 858.76 8.6898 874.88 2794.8 1919.9 2.3777 6.3930 4.0154

210 1.9077 852.72 9.5885 897.63 2797.3 1899.6 2.4245 6.3563 3.9318

215 2.1058 846.54 10.562 920.53 2799.3 1878.8 2.4712 6.3200 3.848

220 2.3196 840.22 11.615 943.58 2800.9 1857.4 2.5177 6.2840 3.7663

225 2.5497 833.75 12.755 966.80 2802.1 1835.4 2.5640 6.2483 3.6843

230 2.7971 827.12 13.985 990.19 2802.9 1812.7 2.6101 6.2128 3.6027

235 3.0625 820.33 15.314 1013.8 2803.2 1789.4 2.6561 6.1775 3.5214

240 3.3469 813.37 16.749 1037.6 2803.0 1765.4 2.7020 6.1423 3.4403

245 3.6512 806.22 18.297 1061.5 2802.2 1740.7 2.7478 6.1072 3.3594

250 3.9762 798.89 19.967 1085.8 2800.9 1715.2 2.7935 6.0721 3.2785

255 4.3229 791.37 21.768 1110.2 2799.1 1688.8 2.8392 6.0369 3.1977

260 4.6923 783.63 23.712 1135.0 2796.6 1661.6 2.8849 6.0016 3.1167

265 5.0853 775.66 25.809 1160.0 2793.5 1633.5 2.9307 5.9661 3.0354

270 5.5030 767.46 28.073 1185.3 2789.7 1604.4 2.9765 5.9304 2.9539

275 5.9464 759.00 30.520 1210.9 2785.2 1574.3 3.0224 5.8944 2.8720

280 6.4166 750.28 33.165 1236.9 2779.9 1543.0 3.0685 5.8579 2.7894

285 6.9147 741.25 36.028 1263.2 2773.7 1510.5 3.1147 5.8209 2.7062

290 7.4418 731.91 39.132 1290.0 2766.7 1476.7 3.1612 5.7834 2.6222

295 7.9991 722.21 42.501 1317.3 2758.7 1441.4 3.2080 5.7451 2.5371

300 8.5879 712.14 46.168 1345.0 2749.6 1404.6 3.2552 5.7059 2.4507

305 9.2094 701.64 50.167 1373.3 2739.4 1366.1 3.3028 5.6657 2.3629

310 9.8651 690.67 54.541 1402.2 2727.9 1325.7 3.3510 5.6244 2.2734

315 10.556 679.18 59.344 1431.8 2715.1 1283.2 3.3998 5.5816 2.1818

320 11.284 667.09 64.638 1462.2 2700.6 1238.4 3.4494 5.5372 2.0878

325 12.051 654.33 70.506 1493.5 2684.3 1190.8 3.5000 5.4908 1.9908

330 12.858 640.77 77.050 1525.9 2666.0 1140.2 3.5518 5.4422 1.8903

335 13.707 626.29 84.407 1559.5 2645.4 1085.9 3.6050 5.3906 1.7856

340 14.601 610.67 92.759 1594.5 2621.8 1027.3 3.6601 5.3356 1.6755





345 15.541 593.63 102.36 1631.5 2594.9 963.4 3.7176 5.2762 1.5586

350 16.529 574.71 113.61 1670.9 2563.6 892.7 3.7784 5.2110 1.4326

355 17.570 553.14 127.09 1713.7 2526.6 812.9 3.8439 5.1380 1.294

360 18.666 527.59 143.90 1761.7 2481.5 719.8 3.9167 5.0536 1.1369

365 19.821 495.74 166.35 1817.8 2422.9 605.2 4.0014 4.9497 0.9483

370 21.044 451.43 201.84 1890.7 2334.5 443.8 4.1112 4.8012 0.6901

tc 22.064 322.00 322.00 2084.3 2084.3 0. 4.4070 4.4070 0.

(tc = 373.946 °C)

50 ISA Handbook of Measurement Equations and TablesChapter 3/Pressure 50



Thermodynamic Properties of Saturated Water and Steamas a Function of Pressure

Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)

p, MPa

t, °C ρL ρV hL hV ∆h sL sV ∆s

611.657 Pa 0.01 999.79 0.004 855 0.00 2500.9 2500.9 0.000 00 9.1555 9.15550.0008 3.761 999.92 0.006 264 15.81 2507.8 2492.0 0.057 48 9.0567 8.99920.0010 6.970 999.86 0.007 741 29.30 2513.7 2484.4 0.105 91 8.9749 8.86900.0012 9.654 999.68 0.009 202 40.57 2518.6 2478.0 0.145 95 8.9082 8.76230.0014 11.969 999.46 0.010 650 50.28 2522.8 2472.5 0.180 15 8.8521 8.67190.0016 14.010 999.20 0.012 086 58.83 2526.5 2467.7 0.210 04 8.8035 8.59350.0018 15.837 998.93 0.013 511 66.49 2529.9 2463.4 0.236 62 8.7608 8.52410.0020 17.495 998.64 0.014 928 73.43 2532.9 2459.4 0.260 56 8.7226 8.4620

0.0025 21.077 997.93 0.018 437 88.42 2539.4 2451.0 0.311 82 8.6420 8.33020.0030 24.079 997.24 0.021 904 100.98 2544.8 2443.9 0.354 29 8.5764 8.22210.0035 26.672 996.56 0.025 338 111.82 2549.5 2437.7 0.390 61 8.5211 8.13050.0040 28.960 995.92 0.028 743 121.39 2553.7 2432.3 0.422 39 8.4734 8.05100.0045 31.012 995.30 0.032 122 129.96 2557.4 2427.4 0.450 69 8.4313 7.98060.0050 32.874 994.70 0.035 480 137.75 2560.7 2423.0 0.476 20 8.3938 7.9176

0.0060 36.159 993.59 0.042 135 151.48 2566.6 2415.2 0.520 82 8.3290 7.80820.0070 39.000 992.55 0.048 722 163.35 2571.7 2408.4 0.559 03 8.2745 7.71540.0080 41.509 991.59 0.055 252 173.84 2576.2 2402.4 0.592 49 8.2273 7.63480.0090 43.761 990.69 0.061 731 183.25 2580.2 2397.0 0.622 30 8.1858 7.56350.010 45.806 989.83 0.068 166 191.81 2583.9 2392.1 0.649 20 8.1488 7.4996

0.012 49.419 988.26 0.080 917 206.91 2590.3 2383.4 0.696 28 8.0849 7.38870.014 52.547 986.82 0.093 535 219.99 2595.8 2375.8 0.736 64 8.0311 7.29450.016 55.313 985.50 0.106 04 231.57 2600.6 2369.1 0.772 01 7.9846 7.21260.018 57.798 984.28 0.118 44 241.96 2605.0 2363.0 0.803 55 7.9437 7.14020.020 60.058 983.13 0.130 75 251.42 2608.9 2357.5 0.832 02 7.9072 7.0752

0.025 64.963 980.54 0.161 21 271.96 2617.4 2345.5 0.89319 7.8302 6.93700.030 69.095 978.25 0.191 26 289.27 2624.5 2335.3 0.94407 7.7675 6.82340.035 72.681 976.19 0.220 99 304.30 2630.7 2326.4 0.98774 7.7146 6.72690.040 75.857 974.30 0.250 44 317.62 2636.1 2318.4 1.0261 7.6690 6.64290.045 78.715 972.56 0.279 65 329.62 2640.9 2311.2 1.0603 7.6288 6.56860.050 81.317 970.94 0.308 64 340.54 2645.2 2304.7 1.0912 7.5930 6.5018

0.06 85.926 967.99 0.366 07 359.91 2652.9 2292.9 1.1454 7.5311 6.38570.07 89.932 965.34 0.422 87 376.75 2659.4 2282.7 1.1921 7.4790 6.28690.08 93.486 962.93 0.479 14 391.71 2665.2 2273.5 1.2330 7.4339 6.20090.09 96.687 960.70 0.534 94 405.20 2670.3 2265.1 1.2696 7.3943 6.12460.10 99.606 958.63 0.590 34 417.50 2674.9 2257.4 1.3028 7.3588 6.0561

0.12 104.784 954.86 0.700 10 439.36 2683.1 2243.7 1.3609 7.2977 5.93670.14 109.292 951.49 0.808 69 458.42 2690.0 2231.6 1.4110 7.2461 5.83510.16 113.297 948.41 0.916 29 475.38 2696.0 2220.7 1.4551 7.2014 5.74630.18 116.911 945.57 1.0230 490.70 2701.4 2210.7 1.4945 7.1621 5.66760.20 120.210 942.94 1.1291 504.70 2706.2 2201.5 1.5302 7.1269 5.5967

t = temperature

p, MPa = pressure

ρL = liquid density

ρV = vapor density

hL = liquid enthalpy

hV = vapor enthalpy

∆h = enthalpy of vaporization

sL = liquid entropy

sV = vapor entropy

∆s = entropy of vaporization



p, MPa


0.22 123.250 940.47 1.2345 517.63 2710.6 2193.0 1.5628 7.0951 5.53230.24 126.072 938.13 1.3393 529.64 2714.6 2185.0 1.5930 7.0661 5.47310.26 128.708 935.93 1.4436 540.87 2718.3 2177.4 1.6210 7.0394 5.41840.28 131.185 933.83 1.5474 551.44 2721.7 2170.3 1.6471 7.0146 5.36750.30 133.522 931.82 1.6508 561.43 2724.9 2163.5 1.6717 6.9916 5.31990.35 138.857 927.15 1.9077 584.26 2732.0 2147.7 1.7274 6.9401 5.21280.40 143.608 922.89 2.1627 604.65 2738.1 2133.4 1.7765 6.8955 5.11900.45 147.903 918.96 2.4161 623.14 2743.4 2120.2 1.8205 6.8560 5.03560.50 151.831 915.29 2.6680 640.09 2748.1 2108.0 1.8604 6.8207 4.96030.55 155.456 911.85 2.9189 655.76 2752.3 2096.6 1.8970 6.7886 4.89160.60 158.826 908.59 3.1687 670.38 2756.1 2085.8 1.9308 6.7592 4.82840.65 161.980 905.51 3.4177 684.08 2759.6 2075.5 1.9623 6.7322 4.76990.70 164.946 902.56 3.6660 697.00 2762.8 2065.8 1.9918 6.7071 4.71530.75 167.749 899.74 3.9137 709.24 2765.6 2056.4 2.0195 6.6836 4.66410.80 170.406 897.04 4.1608 720.86 2768.3 2047.4 2.0457 6.6616 4.61600.85 172.936 894.43 4.4074 731.95 2770.8 2038.8 2.0705 6.6409 4.57040.90 175.350 891.92 4.6536 742.56 2773.0 2030.5 2.0940 6.6213 4.52720.95 177.661 889.48 4.8995 752.74 2775.1 2022.4 2.1165 6.6027 4.48621.0 179.878 887.13 5.1450 762.52 2777.1 2014.6 2.1381 6.5850 4.4470

1.1 184.062 882.62 5.6354 781.03 2780.6 1999.6 2.1785 6.5520 4.37351.2 187.957 878.35 6.1251 798.33 2783.7 1985.4 2.2159 6.5217 4.30581.3 191.605 874.28 6.6144 814.60 2786.5 1971.9 2.2508 6.4936 4.24281.4 195.039 870.39 7.1034 829.97 2788.8 1958.9 2.2835 6.4675 4.18391.5 198.287 866.65 7.5924 844.56 2791.0 1946.4 2.3143 6.4430 4.12861.6 201.370 863.05 8.0815 858.46 2792.8 1934.4 2.3435 6.4199 4.07651.7 204.307 859.58 8.5708 871.74 2794.5 1922.7 2.3711 6.3981 4.02701.8 207.112 856.22 9.0606 884.47 2795.9 1911.4 2.3975 6.3775 3.98001.9 209.798 852.96 9.5508 896.71 2797.2 1900.5 2.4227 6.3578 3.93512.0 212.377 849.80 10.042 908.50 2798.3 1889.8 2.4468 6.3390 3.8923

2.2 217.249 843.72 11.026 930.87 2800.1 1869.2 2.4921 6.3038 3.81162.4 221.789 837.92 12.013 951.87 2801.4 1849.6 2.5343 6.2712 3.73692.6 226.046 832.37 13.004 971.67 2802.3 1830.7 2.5736 6.2409 3.66722.8 230.057 827.04 14.000 990.46 2802.9 1812.4 2.6106 6.2124 3.60183.0 233.853 821.90 15.001 1008.3 2803.2 1794.8 2.6455 6.1856 3.54003.2 237.459 816.92 16.006 1025.4 2803.1 1777.7 2.6787 6.1602 3.48153.4 240.897 812.10 17.018 1041.8 2802.9 1761.0 2.7102 6.1360 3.42583.6 244.182 807.41 18.036 1057.6 2802.4 1744.8 2.7403 6.1129 3.37263.8 247.330 802.83 19.059 1072.8 2801.7 1728.9 2.7691 6.0908 3.32174.0 250.354 798.37 20.090 1087.5 2800.8 1713.3 2.7968 6.0696 3.27284.2 253.264 794.00 21.127 1101.7 2799.8 1698.1 2.8234 6.0491 3.22574.4 256.070 789.73 22.172 1115.5 2798.6 1683.1 2.8490 6.0293 3.18034.6 258.780 785.53 23.224 1128.9 2797.3 1668.4 2.8738 6.0102 3.13644.8 261.402 781.42 24.284 1141.9 2795.8 1653.9 2.8978 5.9917 3.09395.0 263.941 777.37 25.351 1154.6 2794.2 1639.6 2.9210 5.9737 3.05275.2 266.403 773.39 26.427 1167.0 2792.5 1625.5 2.9435 5.9561 3.01265.4 268.795 769.46 27.512 1179.1 2790.7 1611.5 2.9654 5.9391 2.97365.6 271.120 765.59 28.605 1191.0 2788.7 1597.8 2.9868 5.9224 2.93565.8 273.382 761.77 29.707 1202.6 2786.7 1584.1 3.0075 5.9061 2.89856.0 275.585 758.00 30.818 1213.9 2784.6 1570.7 3.0278 5.8901 2.86236.2 277.733 754.27 31.940 1225.1 2782.4 1557.3 3.0476 5.8745 2.82696.4 279.829 750.58 33.070 1236.0 2780.1 1544.1 3.0669 5.8592 2.79236.6 281.875 746.93 34.211 1246.7 2777.7 1530.9 3.0858 5.8441 2.75836.8 283.874 743.31 35.363 1257.3 2775.2 1517.9 3.1043 5.8293 2.7250




p, MPa


7.0 285.829 739.72 36.525 1267.7 2772.6 1505.0 3.1224 5.8148 2.69247.2 287.741 736.17 37.698 1277.9 2770.0 1492.1 3.1402 5.8004 2.66037.4 289.614 732.64 38.883 1287.9 2767.3 1479.3 3.1576 5.7863 2.62877.6 291.448 729.14 40.079 1297.9 2764.5 1466.6 3.1747 5.7723 2.59767.8 293.245 725.66 41.287 1307.7 2761.6 1454.0 3.1915 5.7586 2.56718.0 295.008 722.20 42.507 1317.3 2758.7 1441.4 3.2081 5.7450 2.53698.2 296.737 718.76 43.740 1326.8 2755.7 1428.8 3.2243 5.7316 2.50728.4 298.434 715.34 44.985 1336.3 2752.6 1416.3 3.2403 5.7183 2.47798.6 300.100 711.93 46.244 1345.6 2749.4 1403.9 3.2561 5.7051 2.44908.8 301.737 708.54 47.517 1354.8 2746.2 1391.5 3.2717 5.6921 2.42049.0 303.345 705.16 48.804 1363.9 2742.9 1379.1 3.2870 5.6791 2.39229.2 304.926 701.80 50.105 1372.9 2739.6 1366.7 3.3021 5.6663 2.36429.4 306.481 698.44 51.421 1381.8 2736.2 1354.4 3.3170 5.6536 2.33669.6 308.010 695.09 52.753 1390.6 2732.7 1342.0 3.3317 5.6410 2.30929.8 309.516 691.76 54.100 1399.4 2729.1 1329.7 3.3463 5.6284 2.2822

10.0 310.997 688.42 55.463 1408.1 2725.5 1317.4 3.3606 5.6160 2.2553

10.5 314.603 680.11 58.946 1429.4 2716.1 1286.7 3.3959 5.5851 2.189211.0 318.079 671.81 62.541 1450.4 2706.3 1255.9 3.4303 5.5545 2.124211.5 321.433 663.51 66.257 1471.1 2696.1 1225.0 3.4638 5.5241 2.060312.0 324.675 655.18 70.106 1491.5 2685.4 1194.0 3.4967 5.4939 1.997212.5 327.813 646.81 74.097 1511.6 2674.3 1162.7 3.5290 5.4638 1.934813.0 330.854 638.37 78.245 1531.5 2662.7 1131.2 3.5608 5.4336 1.872813.5 333.803 629.85 82.563 1551.3 2650.5 1099.3 3.5921 5.4032 1.811114.0 336.666 621.22 87.069 1571.0 2637.9 1066.9 3.6232 5.3727 1.749514.5 339.449 612.45 91.783 1590.6 2624.6 1034.0 3.6539 5.3418 1.687915.0 342.155 603.52 96.727 1610.2 2610.7 1000.5 3.6846 5.3106 1.626015.5 344.789 594.38 101.93 1629.9 2596.1 966.2 3.7151 5.2788 1.563616.0 347.355 584.99 107.42 1649.7 2580.8 931.1 3.7457 5.2463 1.500616.5 349.855 575.29 113.25 1669.7 2564.6 894.9 3.7765 5.2130 1.436417.0 352.293 565.21 119.46 1690.0 2547.5 857.5 3.8077 5.1787 1.371017.5 354.671 554.66 126.12 1710.8 2529.3 818.5 3.8394 5.1431 1.303818.0 356.992 543.54 133.30 1732.1 2509.8 777.7 3.8718 5.1061 1.234218.5 359.259 531.70 141.13 1754.1 2488.8 734.7 3.9053 5.0670 1.161819.0 361.473 519.00 149.76 1777.2 2466.0 688.9 3.9401 5.0256 1.085519.5 363.636 505.25 159.43 1801.4 2440.8 639.4 3.9767 4.9808 1.004120.0 365.749 490.19 170.50 1827.2 2412.3 585.1 4.0156 4.9314 0.915820.5 367.813 473.34 183.63 1855.3 2379.2 523.9 4.0579 4.8753 0.817421.0 369.827 453.41 200.16 1887.6 2338.6 451.0 4.1064 4.8079 0.701521.5 371.791 426.11 223.54 1929.5 2283.1 353.6 4.1698 4.7181 0.548222.0 373.705 369.77 274.16 2011.3 2173.1 161.7 4.2945 4.5446 0.2501

22.064 373.946 322.00 322.00 2084.3 2084.3 0. 4.4070 4.4070 0.



1824 02

Engineering

head pressure

whilegauge pressure

pressure measurements

pressure 33p1

tablessome pressure

static pressure occurswhere

aspecific reference

suchas air pressure