NAME

ASME Steam Table Library

USER GUIDE

The Westinghouse ASME Steam Table library has been in existence for many years. This library of well-tested functions is available for those who need to perform calculations involving the various properties of steam. Users are responsible (as always) for verifying the accuracy of their results.

Menu-Driven Steam Table Program

ASME Steam Table User Guide

 Section Title
 

 1.0     Introduction

 2.0     Validation of the ASME Steam Property
         Procedures

 3.0     Basis for the Westinghouse 7600 Steam
         Property Procedures and Certain Limitations

 4.0     Use of the ASME Steam Property Procedures

     4.1 Nomenclature
     4.2 The Three Calculational Regions
     4.3 Regions of Applicability
     4.4 Description of Steam Property Functions

         CONDL  CONDV  CPL     CPV
         CRFLO  CRVEL  HCL     HSL
         HSS    HSSICL HSSISS  HSV
         PRLIQ  PRSTM  PSL     PSV
         SSL    SSSICL SSSISS  TSL
         TSLH   VCL    VISL    VISV
         VSL

     4.5 Input Argument Limits for Specific Enthalpy, H

     4.6 Input Argument Limits for Specific Entropy, S

     4.7 Procedures Grouped by Output Property - Table 1

     4.8 Procedures Grouped by Region - Table 2

     4.9 Alphabetic Listing of Steam Property Procedures - Table 3

 5.0     References

 6.0     STEAMV67 routine should be called to document the
         pedigree of the library being used.

 7.0     Document Revision Record

SYNOPSIS

This document describes the Westinghouse ASME Steam Table FORTRAN library procedures. The library is a set of well-tested functions that dates back many years. It is available for those who need to work with calculations involving the various properties of steam.

Note that this library is all double precision.

Users are responsible (as always) for verifying the accuracy of their results.

MANUAL USAGE

This is actually a rather lengthy manual. New users of the WCCS Steam Table routines might find it easier to print a copy of this manual for study rather than just trying to scan it on-line.

The fastest way to look up a specific procedure's information is to go to one of the hyper-text tables in sections 4.7, 4.8, and 4.9, and click on a routine name.

1.0 Introduction

The following quotations, taken directly from the "1967 ASME Steam Tables" published by the American Society of Mechanical Engineers, are thought to be of significant value both as background, and for proper use of the ASME Steam Table subroutines. The entire introduction is taken from the "1967 ASME Steam Tables" reference, except for the headings for Sections 1.1, 1.2. and 1.3.

1.1 From the Foreword:

The publication of these new ASME Steam Tables represents the culmination of an ASME project which had its origin in 1954 when, at the Fourth International Conference on Properties of Steam held in Philadelphia, Pa., it was decided that the time had come to update our knowledge of the thermodynamic properties of steam. Fortunately, the Society was able to take advantage of the experience of a number of its members who were involved in a similar venture more than thirty years earlier.

Just as occurred previously, the project required fund raising, identification and technical supervision of new experimental research, extensive international cooperation, and the adoption of internationally accepted skeleton tables. This time, however, the demand for standardization of design and performance calculations could not be satisfied by skeleton tables alone. International agreement had to be reached on a set of equations which would reproduce these skeleton tables, provide a suitable interpolation scheme, and yet give reasonable computer efficiency when incorporated in the already complex computer programs used day after day for design and performance calculations.

1.2 From the Introduction:

The First International Conference on Properties of Steam, London, England, 1929, concerned itself with a detailed examination of the tables of specific volume and enthalpy submitted by the various national delegations. The skeleton tables compiled at that conference served as the basis for the 1930 ASME Steam Tables, prepared by Professor J. H. Keenan and published by ASME. This conference recognized that considerable additional measurements would be required before a truly satisfactory representation of these properties could be agreed upon.

Progress was reviewed at the Second International Conference, held in Berlin, Germany, in 1930, at which time, significant modifications were made in the skeleton tables. The time, however, was not ripe for full agreement. Such agreement was reached in 1934 at the Third International Conference held in Washington, D.C., Cambridge, Mass., and New York, N.Y., with the adoption of skeleton tables giving the specific volume and enthalpy along the saturation line and at round values of temperature and pressure for the compressed liquid and superheated vapor. In addition, each entry in the tables had associated with it a tolerance so that the two values would "constitute a criterion, internationally agreed upon, by which, the reliability of steam tables may be judged". The skeleton tables and the experimental measurements which led up to them served as the basis for a number of publications, the most prominent of which was the Keenan and Keyes Steam Tables which had served as the vade mecum of engineers these past 30 years.

The need was recognized for continued research on properties of steam and water by the Third International Conference, to an extent that solicitations and even recorded assurances from various delegations and institutions assured that the work on steam would be continued and extended.

The plan to hold a Fourth International Conference in Prague, Czechoslovakia gave way in time to more pressing problems brought on by the Second World War. Almost twenty years elapsed before the thermodynamic properties of steam again became an active concern of the Society and the international scientific and engineering community. When the Fourth International Conference was held in Philadelphia, PA in 1954, it was evident that technological advances made in intervening years would require thermodynamic information outside of the temperature and pressure range of the existing steam tables. The Society established a research committee on the Properties of Steam, and charged it with the task of arranging for new research and reestablishing the program of international coordination, which had proved so fruitful two decades earlier. The Society also accepted the invitation to serve as the permanent Secretariat for the International Conferences on Properties of Steam.

By this time, interest had developed in Japan and the U.S.S.R. in thermodynamic tables for steam having the status of an international standard. Moreover, a considerable body of new experimental measurements had been reported by a number of institutions in the Soviet Union. Thus, at the time of the Fifth International Conference, London, 1956, it was evident that the work of examining the published data and supervising the then current research could be handled best by national commissions from the four countries in which the major experimental research was being carried on. It was further agreed, that the national Commissions (Federal Republic of Germany, United Kingdom. Union of Soviet Socialist Republics, and the United States) would constitute the International Coordinating Committee - the working group of the Fifth International Conference.

The labors of the International Coordinating Committee were rewarded at a plenary session of the Sixth International Conference on the Properties of Steam, New York, N. Y., 1963. when the tables were adopted as "The International Skeleton Tables of 1963". The temperature range of the skeleton tables is from 0 to 800 C and the pressure extends to 1000 bars - a considerable extension over the range of the 1934 Skeleton Tables. Where new experimental data reflected refined experimental techniques, they are in turn, reflected in the narrower "tolerance" limits of the new tables. The skeleton tables adopted by 16 member nations of the Sixth International Conference, are the bases for the equations from which these ASME Steam Tables have been computed.

Long before the work of the International Coordinating Committee was completed, it was clear to most members of the working groups that the skeleton tables alone did not insure the degree of reproducibility originally envisioned for design and performance calculations owing to the relatively coarse grid of the skeleton tables and to the requirements of performing numerical differentiation and integration. It became important to ensure that each country handled the numbers in the same way when it came to compiling detailed tables such as the following, or, when incorporating the skeleton tables into a computer program for design and performance calculations. The Sixth International Conference was cognizant of this problem and established an International Formulation Committee (IFC) to:

"Develop at the earliest practical date a formulation for use with computers of the properties of steam as they are represented by the International Skeleton Tables of 1963. This formulation shall provide values that are, at all points, within the tolerances stated in the International Skeleton Tables of 1963, and shall be thermodynamically consistent."

After two years of sustained effort, during which delegates from Japan and Czechoslovakia joined those of the Federal Republic of Germany, United Kingdom, United States of America, and the Union of Soviet Socialist Republics, a conference was held in Prague, at which agreement was reached concerning the form and characteristics of the equations which would meet the requirements laid down by the Sixth International Conference. A year later (March 1966), the IFC met in Glasgow, Scotland. After much deliberation, unanimous agreement was reached among the six national delegations on a formulation, which, after some post-conference modifications. was recommended to the members of the Sixth International Conference.

While it was the general feeling of the IFC that the formulation did indeed satisfy the requirement for international standardization of steam tables for industrial use, it left much to be desired as a definitive equation of state for steam; thus, The "1967 IFC Formulation for Industrial Use: A Formulation of the Thermodynamic Properties of Ordinary Water Substance." Several of the countries participating in the Sixth International Conference are using this formulation to prepare more detailed tables for steam and water. This formulation is the basis for the thermodynamic tables and figures in these new ASME Steam Tables.

The Sixth International Conference expanded the scope of its activity by establishing a panel of experts to develop skeleton tables for transport properties (viscosity and thermal conductivity of steam and water). That panel completed its work at a meeting in Paris, France, in June 1964 and the transport properties given here are based on the skeleton tables and the empirical equations which they developed.

1.3 From the 1967 Formulation for Industrial Use:

The canonical functions provide the definitive expression of the formulation. The derived functions are for practical use and are secondary to the canonical functions.

The formulation presented herein describes the thermodynamic properties of ordinary water substance throughout the whole of the region that extends pressure from the ideal-gas limit (at zero pressure) to a pressure of 10**8 N/m**2 (1000 bar), and that extends in temperature from 273.16 K (0.01 C) to 1073.15 K(800 C).

DISCONTINUITIES AT BOUNDARIES BETWEEN SUBREGIONS
(See Figure 2 on next page)

PRECAUTIONS TO BE OBSERVED IN NUMERICAL COMPUTATION

1. It will be clearly evident that, in order to attain an adequately precise result from numerical inversion in subregions 3 and 4, it is necessary to control the pressure error or the volume error, or both, within appropriate bounds. When pressure alone is controlled, very severe conditions must be imposed (possibly as fine as 1 part in 10**6 or, near the critical point, much finer).
2. Note should be taken of the fact that errors may arise if finite-different techniques be used with too small an interval.

This figure is taken from "1967 ASME Steam Tables"

2.0 Validation of the ASME Steam Property Sub-Programs

1. To compare sub-program results with the skeleton tables which appear in "1967 ASME Steam Tables", and to determine the quality of the results over their full range of applicability.
2. To provide the necessary computer programs for the continued Quality Assurance of the ASME sub-programs. The results of these programs will continue to be analyzed following ASME sub-program corrections, and other critical System changes.
3. To provide the necessary information for new user documentation.

Two computer programs which have evolved from this study are:

1. A program which calculates steam properties at ASME skeleton table values of temperature and pressure, compares the sub-program results with the published skeleton table values, and tests to see that the difference between the sub-program result and the skeleton table value is within tolerance. The program also produces plots of sub-program and skeleton table results. In what follows this program will be referred to as the Skeleton Table Program.
2. A program which produces three dimensional plots of the steam properties as functions of temperature and pressure. This program will be called the 3-D Plot Program.

2.1 The Skeleton Table Program

1. Calculation of steam properties at skeleton values of pressure and temperature, and comparison of sub-program results with the published ASME values. When more than one sub-program may be used to calculate the property, all sub-programs are tested. In all cases, the original inputs for the calculation are pressure and temperature, so that when the function requires other inputs, an intermediate step is performed. Thus, to calculate the enthalpy using the function sub-program HSSISS[*], the following steps are used:

   C=HSS(P,T,S,V) to calculate S using P and T
   H=HSSISS(P,S,T1,V1,X) to calculate the enthalpy, H, using P and S.
   

   *See Section 4 for a description of usage of the steam property sub-programs. Specifically see sections 4.4.9 and 4.4.11 for descriptions of HSS and HSSISS, respectively.

2. Using each of the skeleton table pressures, each property is calculated at small increments of temperature - normally increments of 2 C. Plots are produced using the character period (".") at 2 C increments, and using the character ("T") to represent ASME skeleton table values.

   Note that in Figure 1, an example of such a plot, the T's of the skeleton table values rest on the line generated by the periods, and hence agreement is perfect.

   Similar plots are produced by fixing temperature at each of the skeleton values, and varying pressure in small increments, over the entire pressure range.

   For purposes of Quality Assurance, checksums are calculated by summing plotted results for each fixed pressure and temperature. A total checksum for all properties is also calculated.

3. Using the curves which are generated in 2), sub-program results are searched for local maximums and minimums. (A local maximum is a point where the function value is greater than the two values immediately to the left and to the right, but which is not a genuine maximum of the property. These maximum and minimums are actually small discontinuities. All of the sub-programs produce such local variations when the pressure and temperature increments are 0.1. However, most variations disappear when increments of 1.0 are used.)

   Microfiche print and plot output of this program is available from Customer Services.

2.2 The 3-D Plot Program

1. Calculates sub-program results over a rectangular region, using input limits and increments of pressure and temperature. In all cases, the original input arguments for the calculation are pressure and temperature.
2. Plots the results of 1) three-dimensionally, using pressure and temperature as independent variables, and sub-program results as the dependent variable. Figure 2 is the surface for Specific Isobaric Heat Capacity.
3. If the sub-program outputs temperature, the original input temperature is compared with the output temperature. Maximum differences of approximately .1% have been found for values of temperature near 32 F, although normal differences are .001% and less. Microfiche print and plot outputs of this program are available. The program, itself, is also available to users who wish to study results in their regions of applicability.

2.3 The following routines are validated by one or both of the above programs.

 2.3.1  For Specific Volume

        VSL,HSV,VCL,HSS,HSSISS,SSSISS,CPV

 2.3.2  For Specific Enthalpy

        HSL,HCL,HSSICL,HSS,HSV,HSSISS

 2.3.3  For Specific Entropy

        SSL,HCL,SSSICL,HSS,HSV,SSSISS

 2.3.4  For Thermal Conductivity

        CONDL,CONDV

 2.3.5  For Viscosity

        VISL,VISV

 2.3.6  For Specific Isobaric Heat Capacity

        CPL,CPV

 2.3.7  For Temperature

        TSL,TSLH,HSV,HSSICL,HSSISS,SSSICL,SSSISS

 2.3.8  For Pressure

        PSL,PSV

 2.3.9  For Prandtl Number

        PRLIQ and PRSTM

 2.3.10 CRVEL which calculates critical velocity.

 2.3.11 CRFLO which calculates Critical Mass Flow Rate.

 2.4    The following outputs have not been validated:

 2.4.1  Isentropic Exponent from CRVEL.

 2.4.2  Quality, as output by HSSISS and SSSISS.

SPECIFIC ISOBARIC HEAT CAPACITY

3.0
Basis for the Westinghouse PSCC 7600 Steam Property Sub-programs, and certain limitations.

3.1

The properties of specific volume, enthalpy, and entropy are calculated as described in "1967 ASME Steam Tables" published by the American Society of Mechanical Engineers.

3.2

Viscosity is calculated as described in Reference 3.

3.3

The thermal conductivity subroutine represents the latest work of the Westinghouse Steam Division. It is a modification of the approximation which is described in Reference 2. The routine returns values which are well within tolerance at all skeleton table values. However, for pressures greater than 400 bars. thermal conductivity has the following general shape when it is plotted for fixed pressure and varying temperatures.

The oscillations in the circled region occur at approximately 360 C = 680 F

---

3.4

Heat capacity is, in most cases, calculated by a numerical approximation of the derivative of enthalpy with respect to temperature. However, in three small rectangular regions where this approximation undergoes non-trivial oscillations, linear interpolation of nearby values of heat capacity is used. In addition, there are a few other regions where the numerical derivative displays gaps of as much as 8% from neighboring values, although the overall effect of the approximation is quite satisfactory.

The calculation of heat capacity by numerical differentiation demonstrates two possible characteristics which must be considered for all of the ASME steam properties:

1. There may be regions where the numerical derivative of the properties are discontinuous, or where the numerical derivative undergoes non-trivial oscillations. Therefore, users are advised to investigate the behavior of the properties in their regions of application, before making use of a numerical derivative. Programs are available to aid in these investigations (See Section 2.2).

2. The steam property sub-program results are generally very smooth, as evident from maximum discontinuities of only 8% in the heat capacity, over (almost) the entire range of temperature and pressure. The irregularities of enthalpy, which cause the anomalies in heat capacity are so slight that they cannot be detected by close scrutiny of plots of enthalpy for constant pressure, and temperatures which vary in 1 C increments from 0 to 700 C (32 to 1292 F).

One further word on heat capacity is required. Heat capacity should be considered to be undefined at the critical point, since it is unbounded within any neighborhood of the critical point. The subroutines CPL and CPV, however, produce results which are continuous and comparatively large at and near the critical point.

3.5

There are four combinations of subroutines which may be used to calculate the specific volume over its full range of values. These combinations are the use of VCL in the liquid region, and the use of CPV, HSS, HSSISS, or SSSISS in the steam and gas regions. There are also four combinations which may be used to calculate enthalpy and entropy. Generally, the property values which are calculated from these different combinations have been found to agree to six decimal places. The significance of this agreement is best illustrated by an example.

The specific volume V1 which is calculated by

             C = HSS(P,T.S,V1)           to calculate V1

and the specific volume V2 which is calculated by

             Q = HSS(P,T,S,V1)           to calculate S
                                         for P and T.

             C = HSSISS(P,S,T1,V2,M)     using above
                                         output S to
                                         calculate V2.

agree to six decimal places. This example demonstrates a rather remarkable consistency of the results produced by HSS and HSSISS, a consistency which has been found to be generally true of the ASME sub-programs.

---

3.6

Areas of slight fluctuation of results have been discovered in all of the properties. These fluctuations are characterized by the occurrence of local maximums and minimums within very small intervals of temperature or pressure. Again, these fluctuations cannot be detected by viewing a plot which covers the entire range of temperature or pressure. As an example, the specific entropy at 550 C = 1022 F, has a local minimum of 5.06412 at 779.3 bars pressure, and a local maximum of 5.06424 bars at 779.4 bars pressure. However small these variations might appear, they could cause difficulties if the derivative is being approximated in this region as (S1-S0)/(P1-P0)[ editor's note: read this as "change-in-S/change-in-P"], and (P1-P0) is very small. Generally these difficulties may be avoided by selecting a sufficiently large (P1-P0) or (T1-T0). For example a (T1-T0)= 2 degrees F was selected to calculate values of specific heat as the derivative of enthalpy with respect to temperature.

3.7

It is possible that a user may encounter problems with calculating property values near the critical point. However, no difficulties have been encountered when using critical point values of 3208.234 psia pressure and 705.47 degrees F temperature, and calculating the properties as described in Section 4.

3.8

The function PSV returns zero values for negative values of entropy. This results in answers which are slightly out of tolerance when both the temperature and pressure are near zero.

3.9

The functions which calculate enthalpy have been found to fail for zero values of pressure. A pressure of .001 has been found to be acceptable.

3.10

The results have been found to be within skeleton tables tolerances in almost every case. The maximum value of |D/S|, where D is the variation from tolerance and S is the skeleton table value, is less than .15%. An exception to this is the property of entropy near pressures of zero, where the entropy has nearly zero (and sometimes negative) values. In this case |D/S| can be as high as 50%.

3.11

Critical flow values calculated by the subprogram CRFLO have been compared with plotted curve values of Figure 14, Reference 1. The total region of comparison is defined by the following figure.

The corners of this region are (P=.2, H=600), (P=1000, H=600), (P=1000, H=700), (P=2000 H,700), (P=2000 H=1700), and (P=.2, H=1700). Agreement with the Reference 1 values is well within graph reading error limits, and the CRFLO-generated curves are remarkably smooth.

---

3.12

Critical velocity values calculated by the sub-program CRVEL have been compared with the curves plotted in Figure 12 and 13 of Reference 1 (except for the curve, Pressure=15000 psia). The total region of comparison is defined by the following figure.

The corners of this region are (P=.25, H=800), (P=600, H=800), (P=2000, H=935) (P=2000, H=1100), (P=12000, H=1100), (P=12000, H=1700), and (P=.25, H=1700). Agreement with the Reference 1 values is well within graph reading limits, and the CRVEL generated curves are remarkably smooth. However, along the lines Ll and L2, discontinuities of less than 1% do occur in CRVEL calculated results. Ll passes through the points (P=2000, H=1245), (P=5000, H=1125), (P=8000, H=1137), (P=10000, H=1157), and (P=12000, H=1183). L2 passes through the points (P=8000, H=1270), (P=10000, H=1288), and (P=12000, H=1390).

4.0 Use of the ASME Steam Property Sub-Programs

4.1 Nomenclature

P[min], P[max]

The minimum and maximum pressures for which a property may be calculated. For pressures outside this range, the value of the property is undefined by the ASME tables.

T[min], T[max]

The minimum and maximum temperatures for which a property may be calculated. For temperatures outside this range, the value of the property is undefined by the ASME tables.

P[sat]

Saturation pressure for a given temperature

T[sat]

Saturation temperature for a given pressure

P[crit], T[crit]

Critical point pressure and temperature (3208.234 psia, 705.47 F).

CP

Specific Isobaric Heat Capacity, BTU/lb-F

FC

Critical Flow, lb/hr-in**2

H

Specific Enthalpy, BTU/lb

K

Thermal Conductivity, BTU/hr-ft-F

P

Pressure, psia

PR

Prandtl Number

S

Specific Entropy, BTU/lb-F

T

Temperature, F

V

Specific Volume, ft**3/lb

VC

Critical Velocity, ft/sec

VISC

Viscosity, lb/ft-sec

X

Quality, %/100

4.2 The Three Calculational Regions.

Region 3: THE SATURATION LINE.

The Saturation Line extends from (.0886 psia, 32 F) to the critical point. In a portion of what follows, the curve is considered to have two sides: The liquid side, and the gas or vapor side.

Region 1: THE LIQUID SIDE

            T[min] .le. T .le. T[crit]
                      and
      and   P[sat](T) .le. P .le. P[max]

            Note that Region 1 includes the liquid side of Region 3.

Region 2: THE STEAM OR GAS SIDE

            P[min] .le. P .le. P[max]
                      and
             T[sat](P) .le. T .le. T[max]   when  P .le. P[crit]
            T[crit](P) .le. T .le. T[max]   when  P   >  P[crit]

Note that Region 2 includes the steam/gas side of Region 3.

4.3 Regions of Applicability

1. The regions of applicability defined by "1967 ASME Steam Tables" published by the American Society of Mechanical Engineers.
2. The regions over which most of the sub-programs have been tested and quality assured by the programs described in Section 2.
3. Regions beyond which the 1967 ASME tables do not define the behavior of the results.

1. Regions outside of which error messages are or are not printed.
2. Regions beyond which results are correct or incorrect.

4.4 Description of the Steam Property Functions (listed alphabetically).

It is generally true that functions with two input arguments and which end in L, must be used to compute property values in Region 1. Similarly, functions with two input arguments and which end in S or V, must be used in Region 2.

In the descriptions which follow, Definition and Purpose define input and output arguments of the function. When more than one variable appears on the left of the = sign, the first variable is the function value, and the remaining variables are output arguments. The values in parentheses to the right of the = sign are the input arguments.

4.5 Input Argument Limits for Specific Enthalpy, H.

4.5.1 Region 1 (Liquid)

For any temperature T in Region 1, let P[sat] = PSL(T). The H must lie between the specific enthalpy values, HCL(P[sat],T) and HCL(P[max],T). The approximate magnitudes of these limits may be obtained by dividing result of Table 1.3 (Appendix 4, Reference 1) by 2.326.

4.5.2 Region 2 (Steam or Gas)

4.5.2.1

For a temperature T in Region 2 such that T .le. T[crit], let P[sat] = PSL(T). Then HSS(P[sat],T) .le. H .le. HSS(P = .01,T). The approximate magnitude of these limits may be obtained by dividing results of Table 1.3 (Appendix 4, Reference 1) by 2.326.

4.5.2.2

For a temperature T in Region 2 such that T > T[crit], HSS(P[max],T).le. H .le. HSS(P=.01,T). The approximate magnitude of these limits may be obtained by dividing results of Table 1.3 (Appendix 4, Reference 1) by 2.326.

4.6 Input Argument Limits for Specific Entropy, S.

4.6.1 Region 1 (Liquid)

For a temperature T in Region 1, let P[sat] = PSL(T). Let S1 = value of specific entropy given by calling HCL(P[max],T), and S2 = value of specific entropy given by calling HCL(P[sat],T). Then the specific entropy S must approximately satisfy S1 < S < S2. Approximate values of S1 and S2 may be obtained by dividing results of Table 8 (Appendix 3, Reference 1) by 4.1868.

4.6.2 Region 2 (Steam or Gas)

4.6.2.1

For a temperature T in Region 2 such that T .le. T[crit], let P[sat]=PSL(T), and S1 be the value of specific entropy given by calling HSS(P[sat],T). Let S2 be the value of specific entropy given by calling HSS(P = .01,T). The approximate limits on the specific entropy S are S1 .le. S .le. S2. Values for S1 and S2 may be obtained by dividing results of Table 8 (Appendix 3, Reference 1) by 4.1868.

4.6.2.2

For a temperature T in Region 2 such that T > T[crit], let S1 and S2 be values of specific entropy obtained by calling HSS(P[max],T) and HSS(P= .01,T). Then S1 .le. S .le. S2. Approximate values of S1 and S2 may be obtained by dividing results of Table 8 (Appendix 3, Reference 1) by 4.1868.

4.7
Table 1 [see note 1]

1. This table displays what sub-programs may be used to calculate each of the Steam Properties.
2. These statements should not be used in Fortran, since K is an integer variable.

4.8
Table 2 [see note 1]

1. This table displays the regions in which each of the Steam Property Sub-Programs is valid.
2. These statements should not be used in Fortran, since K is an integer variable.
3. In this table, enthalpy and entropy are specific enthalpy and entropy.

4.9
Table 3

5.0 References [1]

1. "1967 ASME Steam Tables, Thermodynamic and Transport Properties of Steam"

   Published by the American Society of Mechanical Engineers

2. "Formulation of Thermal Conductivity for Water Substance as a action of Temperature and Density"

   Authorized by Ichimatsu Tanishita, Koichi Watanabi, and Kosei Oguchi of Keio University, in Tokyo Japan

3. "Formulation of Viscosity for Water Substance as a Function of Temperature and Density"

   Authorized by Ichimatsu Tanishita, Koichi Watanabi, and Kosei Oguchi of Keio University, in Tokyo Japan

4. "Fortran Subroutines for Calculating the 1967 ASME Steam Tables" W Steam Division Report EM-1035, June 1969, William Steltz and George Silvestri

6.0 Use The STEAMV routine to verify the pedigree of the steam library

A routine called STEAMV identifies the origin of the steam library being used. The first parameter identifies which FORTRAN unit number to write the output on (values less than 0 cause the output to be suppressed).

7.0 Document Revision Record

                                RECORD OF REVISIONS

 NO.        DATE

 1          08/21/87 - First release of document on-line for COS in DOCLIB.
 2          07/01/91 - First release of document on UNICOS as a PRE-RELEASE.
 3          08/20/93 - added STEAMV67 routine to allow workstation users to
                       more easily identify which library they are using.
 4          09/06/93 - Corrected f77 command example and minor carriage
                       control changes.
 5          09/06/93 - Document put onto WWW, main document is still a text file.
 6          12/19/95 - Actual conversion to HTML and added scanned graphics.

• Created: 19971231