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Fresh Water and Seawater Properties

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Updated / Edited by Approved

26
th ITTC

Specialist Committee

on Uncertainty Analysis 26
th ITTC

Date 04/2011 Date 09/2011

FRESH WATER AND SEAWATER

PROPERTIES ........................................ 2

1. INTRODUCTION

................................. 2

2. FRESH WATER PROPERTIES ......... 2

2.1 Uncertainty estimates for fresh water

properties ............................................ 6

2.1.1 Example uncertainty calculation of

fresh water properties ................... 6

3. SALTWATER PROPERTIES ............. 7

3.1 Properties at standard salinity and varying temperature. ......................... 7

3.2 Properties at 15 °C and varying salinity ................................................. 7

3.3 Uncertainty estimates for saltwater

properties ......................................... 12

3.3.1 Example uncertainty calculation of saltwater properties .................... 12

4. SUMMARY .......................................... 13

5. REFERENCES .................................... 14

6.

LIST OF SYMBOLS ........................... 15

APPENDIX A: FRESH WATER

PROPERTIES 0.1 TO 50 °C IN 0.1 °C

INCREMENTS .................................... 16

APPENDIX B: STANDAR

D SALTWATER

PROPERTIES 0.1 TO 50

°C IN 0.1 °C

INCREMENTS .................................... 31

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Fresh Water and Seawater Properties

1.

INTRODUCTION

The international standard for the properties

of fresh water and seawater are specified by the

International Association for the Properties of

Water and Steam (IAPWS). The properties

available include density, viscosity, thermal conductivity, index of refraction, vapour pres- sure, speed of sound, and surface tension.

Those of liquid water are described in IAPWS

(2008a). For this procedure, only the following properties are provided: density, absolute vis- cosity, kinematic viscosity, and vapour pres- sure.

In general, the water properties are a func-

tion of temperature (t), pressure (p), and abso- lute salinity (S A ). For fresh water, S A = 0.0. In this procedure, data are provided at standard pressure of 0.101325 MPa and as a function of temperature. The temperature scale is the In- ternational Temperature Scale 1990 (ITS-90).

At non

-standard conditions, water properties should be computed from computer codes de- scribed in the following paragraphs.

The values

for fresh water were computed via a computer code from NIST (National Insti- tute of Standards and Technology), the Na- tional Metrology Institute (NMI) for the United

States. Harvey, et al. (2008) is the manual for

the computer code.

The sensitivity coefficients

are also provided so that the uncertainty in the property may be computed from the uncer- tainty in temperature per the 25 th ITTC proce-dure on uncertainty analysis. The uncertainties in the IAPWS equations are also provided.

IAWPS (2008b) is the new international

standard for seawater properties. The new stan- dard for seawater has been developed by a group at the United Nations and UNESCO (United Nations Educational, Scientific, and

Cultural Organization) and several other inter-

national organizations. The latest standard for seawater prope rties is the International Ther- modynamic Equation Of Seawater: 2010 (TEOS-10). IOC, et al. (2010) is the manual for the computer code.

The code currently

calc u- lates thermodynamic properties such as density and vapour pressure. IAWPS (2010) has certi- fied a research need for transport properties such as viscosity. In the meantime for this pro- cedure, viscosity and vapour pressure recom- mended by Sharqawy, et al. (2010) is adopted.

Another source of seawater properties is the

SIA (Sea-Ice-Air) library described by Feistel,

et al. (2010) and Wright, et al. (2010). 2.

FRESH WATER PROPERTIES

Fresh water properties were computed at the

standard pressure of 0.101325 MPa. The results for density, absolute viscosity, kin ematic vis- cosity, vapour pressure, and their sensitivity coefficients are shown in the following graph i- cally in Figure 1 through Figure 4 as S A = 0.0.

The properties were produced from

the NIST code of Harvey, et al. (2008) from 0.1 to 50 °C in 0.1

C steps, and the sensitivity coefficients

were computed by a central finite-differencing method from ISO (2008) given by:

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02 Temp t Density /t Viscosity /t = / /t Pressure p v p v /t (°C) (kg/m 3 ) (kg/m 3

°C) (Pas) (Pas/°C) (m

2 /s) (m 2 /s°C) (MPa) (MPa/°C)

10 999.7025 -0.08791 0.001306 -3.760E-05 1.3063E-06 -3.749E-08 1.2282E-03 8.230E-05

11 999.6079 -0.10112 0.001269 -3.591E-05 1.2697E-06 -3.580E-08 1.3130E-03 8.728E-05

12 999.5004 -0.11399 0.001234 -3.433E-05 1.2347E-06 -3.420E-08 1.4028E-03 9.252E-05

13 999.3801 -0.12653 0.001200 -3.284E-05 1.2012E-06 -3.271E-08 1.4981E-03 9.802E-05

14 999.2474 -0.13877 0.001168 -3.144E-05 1.1692E-06 -3.130E-08 1.5990E-03 1.038E-04

15 999.1026 -0.15071 0.001138 -3.012E-05 1.1386E-06 -2.997E-08 1.7058E-03 1.099E-04

16 998.9461 -0.16237 0.001108 -2.887E-05 1.1093E-06 -2.872E-08 1.8188E-03 1.162E-04

17 998.7780 -0.17376 0.001080 -2.769E-05 1.0811E-06 -2.754E-08 1.9384E-03 1.229E-04

18 998.5986 -0.18489 0.001053 -2.658E-05 1.0542E-06 -2.642E-08 2.0647E-03 1.299E-04

19 998.4083 -0.19578 0.001027 -2.553E-05 1.0283E-06 -2.537E-08 2.1983E-03 1.372E-04

20 998.2072 -0.20644 0.001002 -2.453E-05 1.0034E-06 -2.437E-08 2.3393E-03 1.449E-04

21 997.9955 -0.21687 0.000978 -2.359E-05 9.7950E-07 -2.343E-08 2.4882E-03 1.530E-04

22 997.7735 -0.22708 0.000954 -2.270E-05 9.5653E-07 -2.253E-08 2.6453E-03 1.614E-04

23 997.5414 -0.23709 0.000932 -2.185E-05 9.3442E-07 -2.168E-08 2.8111E-03 1.702E-04

24 997.2994 -0.24691 0.000911 -2.104E-05 9.1315E-07 -2.088E-08 2.9858E-03 1.794E-04

25 997.0476 -0.25653 0.000890 -2.028E-05 8.9266E-07 -2.011E-08 3.1699E-03 1.890E-04

26 996.7864 -0.26597 0.000870 -1.955E-05 8.7291E-07 -1.938E-08 3.3639E-03 1.990E-04

27 996.5158 -0.27524 0.000851 -1.886E-05 8.5388E-07 -1.869E-08 3.5681E-03 2.095E-04

28 996.2360 -0.28434 0.000832 -1.820E-05 8.3552E-07 -1.803E-08 3.7831E-03 2.205E-04

29 995.9471 -0.29327 0.000814 -1.757E-05 8.1781E-07 -1.740E-08 4.0092E-03 2.319E-04

30 995.6495 -0.30206 0.000797 -1.697E-05 8.0071E-07 -1.681E-08 4.2470E-03 2.438E-04

31 995.3431 -0.31069 0.000781 -1.640E-05 7.8419E-07 -1.624E-08 4.4969E-03 2.562E-04

32 995.0281 -0.31918 0.000764 -1.586E-05 7.6823E-07 -1.569E-08 4.7596E-03 2.692E-04

33 994.7048 -0.32753 0.000749 -1.534E-05 7.5280E-07 -1.517E-08 5.0354E-03 2.826E-04

34 994.3731 -0.33574 0.000734 -1.484E-05 7.3788E-07 -1.467E-08 5.3251E-03 2.967E-04

35 994.0333 -0.34383 0.000719 -1.436E-05 7.2344E-07 -1.420E-08 5.6290E-03 3.113E-04

36 993.6855 -0.35179 0.000705 -1.391E-05 7.0947E-07 -1.375E-08 5.9479E-03 3.265E-04

37 993.3298 -0.35963 0.000691 -1.347E-05 6.9595E-07 -1.331E-08 6.2823E-03 3.424E-04

38 992.9663 -0.36736 0.000678 -1.305E-05 6.8285E-07 -1.289E-08 6.6328E-03 3.588E-04

39 992.5951 -0.37497 0.000665 -1.265E-05 6.7015E-07 -1.250E-08 7.0002E-03 3.759E-04

40 992.2164 -0.38248 0.000653 -1.227E-05 6.5785E-07 -1.211E-08 7.3849E-03 3.937E-04

Table 1 : Fresh water properties at 1 °C increment

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02 )2/()(/ 11 txxdtdx ii (1) where x is a water property, t is the temperature

ǻt = 0.1 °C.

Water property numerical values at 1 °C in-

crement from 10 to 40 °C are listed in Table 1.

A more detailed list at 0.1 °C increments from

0.1 to 50 °C is located in

Appendix A.

2.1

Uncertainty estimates for fresh water properties

The uncertainties in the IAWPS equations

are summarized in

Table 2 for an expanded un-

certainty with a coverage factor o f 2. For den- sity and viscosity, the uncertainties are from

IAWPS (2008a). The uncertainty in vapour

pressure is from Harvey, et al. (2008) Figure B-

4. The value of ±0.02 % is actually the maxi-

mum value over the ambient temperature range and is recommended for simplicity.

Property Symbol U

95
Units

Density 1 ppm

Viscosity 1 %

Vapour Pressure p

v

0.02 %

Table 2: Uncertainty in water properties at 95 %

confidence limit [ppm: parts per million (0.0001 %)]

The combined uncertainty then includes

both the influence of the uncertainty in tem- perature and the uncertainty in the IAWPS equations. The combin ed expanded uncertainty is then 2 ,2 c ttxx

UcUU (2)

where U x is the uncertainty in the water prop- erty equation from

Table 2, U

t the uncertainty in temperature, and c x,t = t the sensitivity coefficient from

Table 1 or Appendix A. The

uncertainty in temperature should include both

Type A and Type B uncertainty estimates from

ISO (2008).

2.1.1

Example uncertainty calculation of fresh

water properties

From the previous

section, the following are specific examples of fresh water properties at 20 °C. For U t

±1.0 °C:

Density:

998.21 ±0.21 kg/m

3 (±0.021 %)

Absolute viscosity:

0.001002

± 0.000026 Pas (±2.6 %)

Kinematic viscosity:

(1.003 ±0.026) x 10 -6 m 2 /s (±2.6 %)

Vapour pressure:

2.34 ±0.14 kPa (6.2 %)

In this example, most of the uncertainty is from

the uncertainty in temperature. For U t

±0.10 °C:

Density:

998.2
07

±0.

0

21 kg/m

3 (±0.0 0 21 %)

Absolute viscosity:

0.001002 ± 0.000010 Pas (±1.0 %)

Kinematic viscosity:

(1.003 ±0.010) x 10 -6 m 2 /s (±1.0 %)

Vapour pressure:

2.3 39

±0.014 kPa (0.62 %)

In this case, most of the uncertainty in density

and vapour pressure is from temperature while most of the uncertainty in viscosity is from the viscosity equation (±1.0 %).

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3. SALTWATER PROPERTIES

In the new international standard for seawa-

ter properties, IOC, et al. (2010) absolute salin- ity is mass based. In the previous standard, sa- linity was practical salinity, S P , which is meas- ured as conductivity and has no units. The practical salinity scale is valid over the range, 2 < S P < 42. For standard seawater, practical sa- linity has a value of 35 while absolute salinity has a value of 35.16504 ±0.007 g/kg. Refer- ence salinity is defined as PR )35/16504.35(SS (3)

Absolute Salinity

may then be computed from a conductivity measurement ARA

SSS (4)

where į A is the absolute salinity anomaly. In general, the absolute salinity anomaly is a func- tion of latitude, longitude, and pressure. Add i- tional detai ls are described in IOC, et al. (2010). 3.1 Properties at standard salinity and va-rying temperature.

Saltwater properties were computed at the

standard pressure of 0.101325 MPa and stan- dard absolute salinity, S A = 35.16504 ±0.007 g/kg. The results for density, absolute viscosi- ty, kinematic viscosity, vapour pressure, and their sensitivity coefficients for temperature are presented in Figure 1 through Figure 4. The density was computed from the TEOS-10 code

MatLab Version 2, IOC, et al. (2010) while

viscosity and vapour pressure were computed from Sharqawy, et al. (2010) from 0.1 to 50 °C in 0.1 °C steps, and the sensitivity coefficients were computed by the central finite differenc- ing method of Equation (1) with ǻt = 0.1 °C.

From Sharqawy, et al.

(2010) the equation for absolute viscosity is )1(

AAfwsw

BSAS (5)

where 25

1052.901998.0541.1ttA

25

10724.407561.0974.7ttB

The equation for vapour pressure is

)1000/(57357.01/

AAswv,fwv,

SSpp (6)

The fresh water prope

rties (fw) are computed from Harvey, et al. (2008) as described in Sec- tion 2. When S A = 0.0, the values of vapour pressure and absolute viscosity in Equations (5) and (6) are the same as in Section 2.

Seawater property numerical values at 1 °C

increment from 1 to 30 °C are listed in Table 3.

A more detailed list at 0.1 °C increments from

0.1 to 50

C is located in Appendix B.

3.2

Properties at 15 °C and varying salin-

ity

As an example and for comparison, results

for varying absolute salinity and temperature of

15 °C are presented in Figure 5 through Figure

8 and Table 4. The derivatives of absolute sa- linity were computed from Equation (1) with S A = 0.1 g/kg substituted for temperature.

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Temp t Density /t Viscos /t /t Pressure p

v p v /t (°C) (kg/m 3 ) (kg/m 3

°C) (Pas) (Pas/°C) (m

2 /s) (m 2 /s°C) (MPa) (MPa/°C)

1 1028.0941 -0.0680 0.001843 -6.186E-05 1.7926E-06 -6.005E-08 6.4363E-04 4.639E-05

2 1028.0197 -0.0810 0.001783 -5.862E-05 1.7341E-06 -5.689E-08 6.9153E-04 4.944E-05

3 1027.9327 -0.0930 0.001726 -5.561E-05 1.6787E-06 -5.395E-08 7.4256E-04 5.265E-05

4 1027.8336 -0.1050 0.001671 -5.282E-05 1.6262E-06 -5.122E-08 7.9689E-04 5.604E-05

5 1027.7225 -0.1170 0.001620 -5.021E-05 1.5762E-06 -4.867E-08 8.5471E-04 5.962E-05

6 1027.6000 -0.1280 0.001571 -4.777E-05 1.5288E-06 -4.630E-08 9.1620E-04 6.340E-05

7 1027.4662 -0.1390 0.001524 -4.549E-05 1.4836E-06 -4.408E-08 9.8157E-04 6.738E-05

8 1027.3214 -0.1500 0.001480 -4.337E-05 1.4406E-06 -4.200E-08 1.0510E-03 7.156E-05

9 1027.1659 -0.1605 0.001438 -4.137E-05 1.3995E-06 -4.006E-08 1.1248E-03 7.597E-05

10 1027.0000 -0.1710 0.001397 -3.950E-05 1.3604E-06 -3.823E-08 1.2030E-03 8.061E-05

11 1026.8238 -0.1815 0.001359 -3.774E-05 1.3230E-06 -3.652E-08 1.2861E-03 8.550E-05

12 1026.6376 -0.1915 0.001322 -3.609E-05 1.2873E-06 -3.492E-08 1.3741E-03 9.063E-05

13 1026.4416 -0.2010 0.001286 -3.454E-05 1.2532E-06 -3.341E-08 1.4674E-03 9.601E-05

14 1026.2360 -0.2105 0.001252 -3.308E-05 1.2205E-06 -3.198E-08 1.5662E-03 1.017E-04

15 1026.0210 -0.2195 0.001220 -3.170E-05 1.1892E-06 -3.064E-08 1.6709E-03 1.076E-04

16 1025.7967 -0.2290 0.001189 -3.040E-05 1.1592E-06 -2.938E-08 1.7816E-03 1.139E-04

17 1025.5633 -0.2380 0.001159 -2.918E-05 1.1304E-06 -2.819E-08 1.8987E-03 1.204E-04

18 1025.3210 -0.2470 0.001131 -2.801E-05 1.1028E-06 -2.706E-08 2.0225E-03 1.272E-04

19 1025.0700 -0.2555 0.001103 -2.692E-05 1.0763E-06 -2.599E-08 2.1533E-03 1.344E-04

20 1024.8103 -0.2640 0.001077 -2.588E-05 1.0508E-06 -2.498E-08 2.2914E-03 1.419E-04

21 1024.5421 -0.2725 0.001051 -2.489E-05 1.0263E-06 -2.402E-08 2.4373E-03 1.498E-04

22 1024.2656 -0.2805 0.001027 -2.396E-05 1.0027E-06 -2.312E-08 2.5912E-03 1.581E-04

23 1023.9808 -0.2890 0.001004 -2.307E-05 9.8002E-07 -2.226E-08 2.7535E-03 1.667E-04

24 1023.6881 -0.2970 0.000981 -2.223E-05 9.5818E-07 -2.144E-08 2.9247E-03 1.757E-04

25 1023.3873 -0.3050 0.000959 -2.143E-05 9.3713E-07 -2.066E-08 3.1050E-03 1.851E-04

26 1023.0788 -0.3125 0.000938 -2.067E-05 9.1683E-07 -1.993E-08 3.2950E-03 1.949E-04

27 1022.7626 -0.3200 0.000918 -1.995E-05 8.9726E-07 -1.922E-08 3.4950E-03 2.052E-04

28 1022.4389 -0.3275 0.000898 -1.926E-05 8.7837E-07 -1.856E-08 3.7056E-03 2.159E-04

29 1022.1078 -0.3345 0.000879 -1.860E-05 8.6014E-07 -1.792E-08 3.9271E-03 2.271E-04

30 1021.7694 -0.3420 0.000861 -1.798E-05 8.4253E-07 -1.731E-08 4.1600E-03 2.388E-04

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