Instrumentation

1. 2
Pressure 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

2. Chapter 2/Pressure 31
Principles of Pressure
Pressure is the force per unit area a
fluid or gas exerts on its surround-ings.
A container of gas contains
numerous atoms and molecules
constantly bouncing of its walls.
The pressure they create is the
average force those atoms and
molecules produce on the walls.
Therefore, pressure, P, is a function
of force, F, and area, A.
P = F/A
The SI unit for pressure is the
Pascal (N/m2). Other frequently
used units of pressure include
atmospheres (atm), pounds per
square inch (psi), bars, inches of
mercury (in Hg), and millimeters of
mercury (mm Hg).
Pressure measurements are typi-cally
described as either static or
dynamic. Static pressure occurs
where no motion is involved, such
as air pressure inside a tire or bal-loon.
When the motion of a fluid or
gas changes the force applied to its
surroundings, the pressure meas-urement
is known as dynamic.
Head pressure (or pressure head) is
the measurement of a static pres-sure
in a tank or a pipe and is a
function solely on the liquid's
height and weight density.
Measurement Types and
Sensors
There are three types of pressure
measurements: absolute, differen-tial,
and gauge. Absolute pressure
is measured relative to a vacuum.
Differential pressure measure-ments
are taken with respect to a
specific reference pressure, while
gauge pressure is measured rela-tive
to ambient atmospheric pres-sure.
Pressure sensors come in
many different types of designs.
When pressure is converted to an
intermediate form such as dis-placement,
three universal types of
pressure transducers used are the
strain gauge, variable capacitance,
and piezoelectric. Each of those
types of sensors convert the dis-placement
into an electrical output
such as voltage or current.
Perhaps the most common of all
pressure sensors are Wheatstone
bridge (strain-based) sensors. They
vary in accuracy, size, ruggedness,
and cost. Bridge sensors are used
for high and low pressure applica-tions
and can measure absolute,
gauge, or differential pressure.

3. 32 ISA Handbook of Measurement Equations and Tables
Units of Pressure
atm = Atmospheres
in H2O = inches of Water column
in Hg = inches of Mercury column
Pa = Pascals, also Newtons per
square meter
kPa = kiloPascals
psi = pounds per square inch
Torr = millimeters of Mercury
column (often used to express low
vacuum 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 Metric
Units Units
Force Poundal Newton
Pressure, ksi, psi, Pascal
Stress psig
Energy, Btu, ft-lb Joule
Work

4. Chapter 2/Pressure 33
P1 = 28 psia
P1 - Patm = 13.4 psig
Gauge Pressure
P1 = 28 psia
Absolute
Pressure
P2 = 20.5 psia
Patm = 14.7 psia
P3 = 8.5 psia
P1 - P2 = 7.5 psig
Differential
Pressure
P3 - Patm = 6.1 psig
Gauge Pressure
Atmospheric
Absolute Pressure
Pressure
(psia)
(Barometric
Pressure)
P3 = 8.5 psia
Absolute
Pressure
Absolute Zero
(Perfect Vacuum)
Examples of Absolute and Gauge Pressure
30
25
20
15
10
5
0

5. 34 ISA Handbook of Measurement Equations and Tables
Some Pressure Units and Conversions
Pascal bar Newtons
per
square
milli-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×
10-5
9.81×
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

6. Chapter 2/Pressure 35
Additional Pressure Conversions
To Convert From To Multiply by:
Atmosphere Bar 1.01325
Atmosphere in. water 406.78@32° F
Atmosphere ft. water 33.89854@32° F
Atmosphere in. Mercury 22.92126@32° F
Atmosphere Kilopascal 101.325
Atmosphere mm water 10.3326@4° F
Atmosphere Millibar 1013.25
Atmosphere mm Mercury 760.000@0° C
Atmosphere Micron 760000.000
Atmosphere Newton/cm2 10.1325
Atmosphere Pascal 101325.000
Atmosphere Pound/Force ft2 2116.22
Atmosphere psi 14.69595
Atmosphere Torr 760.000
Bar Atmosphere 0.9869233
Bar in. water 401.46@32° F
Bar ft. water 33.4553@32° F
Bar in. Mercury 29.53@32° F
Bar Kilopascal 100.00
Bar mm water 0.101972@0° C
Bar mm Mercury 750.062@0° C
Bar Newton/cm2 10.00
Bar Pascal 100000.00
Bar Pound/Force/ft2 2088.54
Bar psi 14.50377
Bar Torr 750.062
cm of Mercury@0° C Atmosphere 0.0131579
cm of Mercury@0° C Millibar 13.3322
cm of Mercury@0° C mm of water 135.951
cm of Mercury@0° C Pascal 1333.22
cm of Mercury@0° C psi 0.193368
cm of water@0° C Atmosphere 0.000967841
cm of water@0° C Millibar 0.980665
cm of water@0° C mm of Mercury 0.735559
cm of water@0° C Pascal 98.0665
cm of water@0° C psi 0.0142233
cm3 Atmosphere Joule 0.101325
ft3 Atmosphere Foot-Pound (Force) 2116.22
ft3 Atmosphere Joule 2869.28
Gram (Force)/cm Joule 0.0000980665

7. 36 ISA Handbook of Measurement Equations and Tables
Additional Pressure Conversions (cont.)
Gray Joule/Kilogram 1.000
in. of Mercury@32° F Atmosphere 0.0334211
in. of Mercury in. of water 13.5951
in. of Mercury Millibar 33.8639
in. of Mercury@32° F mm of water@32° F 345.316
in. of Mercury Pascal 3386.39
in. of Mercury psi 0.491154
in. of water in. of Mercury 0.0735559
in. of water@32° F Millibar 2.49089
in. of water mm of Mercury 1.86832
in. of water Pascal 249.089
in. of water psi 0.0361273
KG (Force)/cm2 Atmosphere 0.96784
KG (Force)/cm2 ft of water 32.8084
KG (Force)/cm2 in. of Mercury 28.9590
KG (Force)/cm2 meter of water 10.000
KG (Force)/cm2 mm of Mercury 735.559
KG (Force)/cm2 Pascal 98066.5
KG (Force)/cm2 psi 14.22334
KG (Force)/m2 Pascal 9.80665
KG (Force)/mm2 MPa 9.80665
KG (Force)/mm2 psi 1422.334
Kilopascal psi 0.1450377
liter-Atmosphere ft3-Atmosphere 0.0353147
liter-Atmosphere Joule 101.325
liter-Bar Joule 100.000
MPa Bar 10.000
MPa Newton/mm2 1.000
Millibar Pascal 100.000
mm of Mercury@0° C Atmosphere 0.001315789
mm of Mercury@0° C Dyne/cm2 1333.224
mm of Mercury@0° C Millibar 1.333224
mm of Mercury@0° C mm of water 13.5951
mm of Mercury@0° C Pascal 133.3224
mm of Mercury@0° C psi 0.0193368
mm of Mercury@0° C Torr 1.000
mm of water Millibar 0.0980665
mm of water mm of Mercury 0.0735559
mm of water Pascal 9.80665
mm of water psi 0.00142233
Newton/m2 Pascal 1.000
Newton/mm2 MPa 1.000

8. Chapter 2/Pressure 37
Additional Pressure Conversions (cont.)
Pound (Force)/in2 mm of water 0.00070307
Pound (Force)/in2 mm of Mercury 51.7149
Pound (Force)/in2 Millibar 68.9476
Pound (Force)/in2 Pascal 6894.76
Pound (Force) Second/in2 Pascal-Second 6894.76
psi in H20 27.679899
psi Pound (Force)/in2 1.000
Torr Millibar 1.333224
Torr mm of Mercury 1.000@0° C
Torr Pascal 133.3224

9. 38 ISA Handbook of Measurement Equations and Tables
Conversion Table, kg/mm2 to psi
Kg/mm2 psi
10 14,223
11 15,646
12 17,068
13 18,490
14 19,913
15 21,335
16 22,757
17 24,180
18 25,602
19 27,024
20 28,447
21 29,869
22 31,291
23 32,714
24 34,136
25 35,558
26 36,981
27 38,403
28 39,826
29 41,248
30 42,670
31 44,093
32 45,515
33 46,937
34 48,360
35 49,782
36 51,204
37 52,627
38 54,049
39 55,471
40 56,894
41 58,316
42 59,738
43 61,161
44 62,538
45 64,005
46 65,424
47 66,580
Kg/mm2 psi
48 68,272
49 69,695
50 71,117
51 72,539
52 73,962
53 75,384
54 76,806
55 78,229
56 79,651
57 81,073
58 82,495
59 83,918
60 85,340
61 86,762
62 88,185
63 89,607
64 91,029
65 92,452
66 93,874
67 95,296
68 96,719
69 98,141
70 99,563
71 100,986
72 102,408
73 103,830
74 105,253
75 106,675
76 108,097
77 109,520
78 110,942
79 112,364
80 113,787
81 115,209
82 116,632
83 118,054
84 119,477
85 120,899

10. Chapter 2/Pressure 39
Conversion Table, kg/mm2 to psi (cont.)
Kg/mm2 psi
86 122,321
87 123,744
88 125,166
89 126,588
90 128,011
91 129,433
92 130,855
93 132,278
94 133,700
95 135,122
96 136,545
97 137,967
98 139,389
99 140,812
100 142,234
101 143,656
102 145,079
103 146,501
104 147,923
105 149,346
106 150,767
107 152,190
108 153,613
109 155,035
110 156,457
111 157,880
112 159,302
113 160,724
114 162,147
115 163,569
116 164,991
117 166,414
118 167,836
Kg/mm2 psi
119 169,258
120 170,681
121 172,103
122 173,525
123 174,948
124 176,370
125 177,792
126 179,215
127 180,637
128 182,059
129 183,482
130 184,904
131 186,327
132 187,749
133 189,171
134 190,594
135 192,016
136 193,438
137 194,861
138 196,283
139 197,705
140 199,128
141 200,550
142 201,972
143 203,395
144 204,817
145 206,239
146 207,662
147 209,084
148 210,506
149 211,929
150 213,351
Conversion Equation, kg/mm2 to psi
Pressure/inch2 = kg/mm2 (1.42234)

11. 40 ISA Handbook of Measurement Equations and Tables
Conversion Table, ksi to MPa
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

12. Chapter 2/Pressure 41
Conversion Table, MPa to ksi
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

13. 42 ISA Handbook of Measurement Equations and Tables
Conversion Table, ft-lb to Joule
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

14. Chapter 2/Pressure 43
Conversion Table, Joule to ft-lb
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

15. 44 ISA Handbook of Measurement Equations and Tables
Height Conversion Equations for
Liquid Manometers
Inches or millimeters of a liquid to
pounds per square inch or kilo-grams
per square centimeter.
P = dh
where
P = pressure, lb/in2 or kg/cm2
d = density, lb/in3 or kg/cm3
h = height, in or cm
Inches of Mercury to pounds per
square inch.
P = 0.48977 h
where
P = pressure, lb/in2
h = height, in
0.48977 is the density of Mercury
at 60oF, 15.6oC
Inches of distilled water to
pounds per square inch.
P = 0.036092 h
where
P = pressure, lb/in2
h = height, in
0.036092 is the density of water
at 60oF, 15.6oC
Centimeters of Mercury to kilo-grams
per square centimeter.
P = 0.013557 h
where
P = pressure, kg/cm2
h = height, cm
0.013557 is the density of
Mercury at 60oF, 15.6oC
Centimeters of distilled water to
kilograms per square centimeter.
P = 0.0009990 h
where
P = pressure, kg/cm2
h = height, cm
0.0009990 = the density of water
at 60oF, 15.6oC
Standard Conditions for
Measuring Pressure Based on the
Height of a Column of Liquid.
[Note: Some vendors, system
design 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 Mercury
29.9213 in of
Mercury
Water Column
Gravity: 980.665 cm/sec2
32.1740 ft/sec2
Temperature: 20oC, 68oF
Atmosphere: 1035.08 cm of water
407.513 in of water

16. Chapter 2/Pressure 45
Density of Mercury and Distilled Water at Various Temperatures
Deg. F Deg. C Mercury,
lb/in3
Mercury,
kg/cm3
Distilled
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

17. 46 ISA Handbook of Measurement Equations and Tables
Measuring Differential Pressure with Transducers.
=
P A
− 0
C C
C
p
p
where
P = pressure
Cp = capacitance of transducer at operating pressure
C0 = capacitance of transducer at zero pressure
A = current from a constant source

18. Chapter 2/Pressure 47
Steam Tables
Standard representations for the thermodynamic properties of water
and steam (commonly known as “steam tables”) are established by
the International Association for the Properties of Water and Steam
(IAPWS). The latest IAPWS standard formulation for general and
scientific use was adopted in 1995. The numbers in the following
tables were supplied by the Physical and Chemical Properties
Division of NIST as calculated from their database (A.H. Harvey, A.P.
Peskin, and S.A. Klein, NIST/ASME Steam Properties, NIST Standard
Reference Database 10, Version 2.2 ([National Institute of Standards
and Technology, Gaithersburg, MD, 20899]) that implements
the IAPWS standard. Further information may be found at
www.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 ρL ρV hL hV Δh sL sV Δs
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
Δh = enthalpy of
vaporization
sL = liquid entropy
sV = vapor entropy
Δs = entropy of
vaporization

19. 48 ISA Handbook of Measurement Equations and Tables
t, °C Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa ρL ρV hL hV Δh sL sV Δs
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

20. Chapter 2/Pressure 49
t, °C Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa ρL ρV hL hV Δh sL sV Δs
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

21. 50 ISA Handbook of Measurement Equations aCnhda pTtaebr l3e/sPressure 50
t, °C Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa ρL ρV hL hV Δh sL sV Δs
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)

22. Chapter 2/Pressure 51
Thermodynamic Properties of Saturated Water and Steam
as a Function of Pressure
Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa
t, °C ρL ρV hL hV Δh sL sV Δs
611.657 Pa 0.01 999.79 0.004 855 0.00 2500.9 2500.9 0.000 00 9.1555 9.1555
0.0008 3.761 999.92 0.006 264 15.81 2507.8 2492.0 0.057 48 9.0567 8.9992
0.0010 6.970 999.86 0.007 741 29.30 2513.7 2484.4 0.105 91 8.9749 8.8690
0.0012 9.654 999.68 0.009 202 40.57 2518.6 2478.0 0.145 95 8.9082 8.7623
0.0014 11.969 999.46 0.010 650 50.28 2522.8 2472.5 0.180 15 8.8521 8.6719
0.0016 14.010 999.20 0.012 086 58.83 2526.5 2467.7 0.210 04 8.8035 8.5935
0.0018 15.837 998.93 0.013 511 66.49 2529.9 2463.4 0.236 62 8.7608 8.5241
0.0020 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 8.3302
0.0030 24.079 997.24 0.021 904 100.98 2544.8 2443.9 0.354 29 8.5764 8.2221
0.0035 26.672 996.56 0.025 338 111.82 2549.5 2437.7 0.390 61 8.5211 8.1305
0.0040 28.960 995.92 0.028 743 121.39 2553.7 2432.3 0.422 39 8.4734 8.0510
0.0045 31.012 995.30 0.032 122 129.96 2557.4 2427.4 0.450 69 8.4313 7.9806
0.0050 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 7.8082
0.0070 39.000 992.55 0.048 722 163.35 2571.7 2408.4 0.559 03 8.2745 7.7154
0.0080 41.509 991.59 0.055 252 173.84 2576.2 2402.4 0.592 49 8.2273 7.6348
0.0090 43.761 990.69 0.061 731 183.25 2580.2 2397.0 0.622 30 8.1858 7.5635
0.010 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 7.3887
0.014 52.547 986.82 0.093 535 219.99 2595.8 2375.8 0.736 64 8.0311 7.2945
0.016 55.313 985.50 0.106 04 231.57 2600.6 2369.1 0.772 01 7.9846 7.2126
0.018 57.798 984.28 0.118 44 241.96 2605.0 2363.0 0.803 55 7.9437 7.1402
0.020 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 6.9370
0.030 69.095 978.25 0.191 26 289.27 2624.5 2335.3 0.94407 7.7675 6.8234
0.035 72.681 976.19 0.220 99 304.30 2630.7 2326.4 0.98774 7.7146 6.7269
0.040 75.857 974.30 0.250 44 317.62 2636.1 2318.4 1.0261 7.6690 6.6429
0.045 78.715 972.56 0.279 65 329.62 2640.9 2311.2 1.0603 7.6288 6.5686
0.050 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 6.3857
0.07 89.932 965.34 0.422 87 376.75 2659.4 2282.7 1.1921 7.4790 6.2869
0.08 93.486 962.93 0.479 14 391.71 2665.2 2273.5 1.2330 7.4339 6.2009
0.09 96.687 960.70 0.534 94 405.20 2670.3 2265.1 1.2696 7.3943 6.1246
0.10 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 5.9367
0.14 109.292 951.49 0.808 69 458.42 2690.0 2231.6 1.4110 7.2461 5.8351
0.16 113.297 948.41 0.916 29 475.38 2696.0 2220.7 1.4551 7.2014 5.7463
0.18 116.911 945.57 1.0230 490.70 2701.4 2210.7 1.4945 7.1621 5.6676
0.20 120.210 942.94 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
Δh = enthalpy of
vaporization
sL = liquid entropy
sV = vapor entropy
Δs = entropy of
vaporization

23. 52 ISA Handbook of Measurement Equations and Tables
Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa
t, °C ρL ρV hL hV Δh sL sV Δs
0.22 123.250 940.47 1.2345 517.63 2710.6 2193.0 1.5628 7.0951 5.5323
0.24 126.072 938.13 1.3393 529.64 2714.6 2185.0 1.5930 7.0661 5.4731
0.26 128.708 935.93 1.4436 540.87 2718.3 2177.4 1.6210 7.0394 5.4184
0.28 131.185 933.83 1.5474 551.44 2721.7 2170.3 1.6471 7.0146 5.3675
0.30 133.522 931.82 1.6508 561.43 2724.9 2163.5 1.6717 6.9916 5.3199
0.35 138.857 927.15 1.9077 584.26 2732.0 2147.7 1.7274 6.9401 5.2128
0.40 143.608 922.89 2.1627 604.65 2738.1 2133.4 1.7765 6.8955 5.1190
0.45 147.903 918.96 2.4161 623.14 2743.4 2120.2 1.8205 6.8560 5.0356
0.50 151.831 915.29 2.6680 640.09 2748.1 2108.0 1.8604 6.8207 4.9603
0.55 155.456 911.85 2.9189 655.76 2752.3 2096.6 1.8970 6.7886 4.8916
0.60 158.826 908.59 3.1687 670.38 2756.1 2085.8 1.9308 6.7592 4.8284
0.65 161.980 905.51 3.4177 684.08 2759.6 2075.5 1.9623 6.7322 4.7699
0.70 164.946 902.56 3.6660 697.00 2762.8 2065.8 1.9918 6.7071 4.7153
0.75 167.749 899.74 3.9137 709.24 2765.6 2056.4 2.0195 6.6836 4.6641
0.80 170.406 897.04 4.1608 720.86 2768.3 2047.4 2.0457 6.6616 4.6160
0.85 172.936 894.43 4.4074 731.95 2770.8 2038.8 2.0705 6.6409 4.5704
0.90 175.350 891.92 4.6536 742.56 2773.0 2030.5 2.0940 6.6213 4.5272
0.95 177.661 889.48 4.8995 752.74 2775.1 2022.4 2.1165 6.6027 4.4862
1.0 179.878 887.13 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 4.3735
1.2 187.957 878.35 6.1251 798.33 2783.7 1985.4 2.2159 6.5217 4.3058
1.3 191.605 874.28 6.6144 814.60 2786.5 1971.9 2.2508 6.4936 4.2428
1.4 195.039 870.39 7.1034 829.97 2788.8 1958.9 2.2835 6.4675 4.1839
1.5 198.287 866.65 7.5924 844.56 2791.0 1946.4 2.3143 6.4430 4.1286
1.6 201.370 863.05 8.0815 858.46 2792.8 1934.4 2.3435 6.4199 4.0765
1.7 204.307 859.58 8.5708 871.74 2794.5 1922.7 2.3711 6.3981 4.0270
1.8 207.112 856.22 9.0606 884.47 2795.9 1911.4 2.3975 6.3775 3.9800
1.9 209.798 852.96 9.5508 896.71 2797.2 1900.5 2.4227 6.3578 3.9351
2.0 212.377 849.80 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 3.8116
2.4 221.789 837.92 12.013 951.87 2801.4 1849.6 2.5343 6.2712 3.7369
2.6 226.046 832.37 13.004 971.67 2802.3 1830.7 2.5736 6.2409 3.6672
2.8 230.057 827.04 14.000 990.46 2802.9 1812.4 2.6106 6.2124 3.6018
3.0 233.853 821.90 15.001 1008.3 2803.2 1794.8 2.6455 6.1856 3.5400
3.2 237.459 816.92 16.006 1025.4 2803.1 1777.7 2.6787 6.1602 3.4815
3.4 240.897 812.10 17.018 1041.8 2802.9 1761.0 2.7102 6.1360 3.4258
3.6 244.182 807.41 18.036 1057.6 2802.4 1744.8 2.7403 6.1129 3.3726
3.8 247.330 802.83 19.059 1072.8 2801.7 1728.9 2.7691 6.0908 3.3217
4.0 250.354 798.37 20.090 1087.5 2800.8 1713.3 2.7968 6.0696 3.2728
4.2 253.264 794.00 21.127 1101.7 2799.8 1698.1 2.8234 6.0491 3.2257
4.4 256.070 789.73 22.172 1115.5 2798.6 1683.1 2.8490 6.0293 3.1803
4.6 258.780 785.53 23.224 1128.9 2797.3 1668.4 2.8738 6.0102 3.1364
4.8 261.402 781.42 24.284 1141.9 2795.8 1653.9 2.8978 5.9917 3.0939
5.0 263.941 777.37 25.351 1154.6 2794.2 1639.6 2.9210 5.9737 3.0527
5.2 266.403 773.39 26.427 1167.0 2792.5 1625.5 2.9435 5.9561 3.0126
5.4 268.795 769.46 27.512 1179.1 2790.7 1611.5 2.9654 5.9391 2.9736
5.6 271.120 765.59 28.605 1191.0 2788.7 1597.8 2.9868 5.9224 2.9356
5.8 273.382 761.77 29.707 1202.6 2786.7 1584.1 3.0075 5.9061 2.8985
6.0 275.585 758.00 30.818 1213.9 2784.6 1570.7 3.0278 5.8901 2.8623
6.2 277.733 754.27 31.940 1225.1 2782.4 1557.3 3.0476 5.8745 2.8269
6.4 279.829 750.58 33.070 1236.0 2780.1 1544.1 3.0669 5.8592 2.7923
6.6 281.875 746.93 34.211 1246.7 2777.7 1530.9 3.0858 5.8441 2.7583
6.8 283.874 743.31 35.363 1257.3 2775.2 1517.9 3.1043 5.8293 2.7250

24. Chapter 2/Pressure 53
Density, kg/m3 Enthalpy, kJ/kg Entropy, kJ/(kg·K)
p, MPa
t, °C ρL ρV hL hV Δh sL sV Δs
7.0 285.829 739.72 36.525 1267.7 2772.6 1505.0 3.1224 5.8148 2.6924
7.2 287.741 736.17 37.698 1277.9 2770.0 1492.1 3.1402 5.8004 2.6603
7.4 289.614 732.64 38.883 1287.9 2767.3 1479.3 3.1576 5.7863 2.6287
7.6 291.448 729.14 40.079 1297.9 2764.5 1466.6 3.1747 5.7723 2.5976
7.8 293.245 725.66 41.287 1307.7 2761.6 1454.0 3.1915 5.7586 2.5671
8.0 295.008 722.20 42.507 1317.3 2758.7 1441.4 3.2081 5.7450 2.5369
8.2 296.737 718.76 43.740 1326.8 2755.7 1428.8 3.2243 5.7316 2.5072
8.4 298.434 715.34 44.985 1336.3 2752.6 1416.3 3.2403 5.7183 2.4779
8.6 300.100 711.93 46.244 1345.6 2749.4 1403.9 3.2561 5.7051 2.4490
8.8 301.737 708.54 47.517 1354.8 2746.2 1391.5 3.2717 5.6921 2.4204
9.0 303.345 705.16 48.804 1363.9 2742.9 1379.1 3.2870 5.6791 2.3922
9.2 304.926 701.80 50.105 1372.9 2739.6 1366.7 3.3021 5.6663 2.3642
9.4 306.481 698.44 51.421 1381.8 2736.2 1354.4 3.3170 5.6536 2.3366
9.6 308.010 695.09 52.753 1390.6 2732.7 1342.0 3.3317 5.6410 2.3092
9.8 309.516 691.76 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 2.1892
11.0 318.079 671.81 62.541 1450.4 2706.3 1255.9 3.4303 5.5545 2.1242
11.5 321.433 663.51 66.257 1471.1 2696.1 1225.0 3.4638 5.5241 2.0603
12.0 324.675 655.18 70.106 1491.5 2685.4 1194.0 3.4967 5.4939 1.9972
12.5 327.813 646.81 74.097 1511.6 2674.3 1162.7 3.5290 5.4638 1.9348
13.0 330.854 638.37 78.245 1531.5 2662.7 1131.2 3.5608 5.4336 1.8728
13.5 333.803 629.85 82.563 1551.3 2650.5 1099.3 3.5921 5.4032 1.8111
14.0 336.666 621.22 87.069 1571.0 2637.9 1066.9 3.6232 5.3727 1.7495
14.5 339.449 612.45 91.783 1590.6 2624.6 1034.0 3.6539 5.3418 1.6879
15.0 342.155 603.52 96.727 1610.2 2610.7 1000.5 3.6846 5.3106 1.6260
15.5 344.789 594.38 101.93 1629.9 2596.1 966.2 3.7151 5.2788 1.5636
16.0 347.355 584.99 107.42 1649.7 2580.8 931.1 3.7457 5.2463 1.5006
16.5 349.855 575.29 113.25 1669.7 2564.6 894.9 3.7765 5.2130 1.4364
17.0 352.293 565.21 119.46 1690.0 2547.5 857.5 3.8077 5.1787 1.3710
17.5 354.671 554.66 126.12 1710.8 2529.3 818.5 3.8394 5.1431 1.3038
18.0 356.992 543.54 133.30 1732.1 2509.8 777.7 3.8718 5.1061 1.2342
18.5 359.259 531.70 141.13 1754.1 2488.8 734.7 3.9053 5.0670 1.1618
19.0 361.473 519.00 149.76 1777.2 2466.0 688.9 3.9401 5.0256 1.0855
19.5 363.636 505.25 159.43 1801.4 2440.8 639.4 3.9767 4.9808 1.0041
20.0 365.749 490.19 170.50 1827.2 2412.3 585.1 4.0156 4.9314 0.9158
20.5 367.813 473.34 183.63 1855.3 2379.2 523.9 4.0579 4.8753 0.8174
21.0 369.827 453.41 200.16 1887.6 2338.6 451.0 4.1064 4.8079 0.7015
21.5 371.791 426.11 223.54 1929.5 2283.1 353.6 4.1698 4.7181 0.5482
22.0 373.705 369.77 274.16 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.