**Numerical
Consistency of ES_StableIF97 Steam Table Functions**

For each region, the numerical consistency is verified in three steps as below.

Step 1) shows IAPWS-IF97 test data. IAPWS-IF97 documents provide the test data with the title of "Computer-program verification". Step 1) is the image captured from IAPWS-IF97 documents. For the abbreviated title of IAPWS-IF97 documents and region boundary, pleaser refer to IAPWS-IF97 (Basis of ES_StableIF97).

Step 2) shows ES_StableIF97 AddIn output data, which were calculated in a MS Excel sheet by ES_StableIF97 AddIn functions for verification of IAPWS-IF97 test data of Step 1). Step 2) is the image captured from the MS Excel sheet.

Step 3) summarizes about consistency. If ES_StableIF97 AddIn data are consistent with the IAPWS-IF97 test data in significant digits, just "OK" is written.

__Region
1 Functions__

How to make MS Excel sheet for Region 1 using ES_StableIF97 AddIn is presented in a separate page as linked below. For numerical consistency for Region 1, the separate page is referred.

Please note that the Unit Legend for the ES_StableIF97 AddIn output data here was put into a separate sheet named as "Unit", in contrast to the Example 1 in which the Unit Legend was put into the same sheet and sp the cell addresses of unit arguments do not have the sheet identifier "Unit!".

1) IAPWS-IF97 Test Data : Table 5

Please refer to Example 1 : Numerical Consisency of ES_StableIF97 Steam Table Functions in Region 1, Table 5.

** **2)
ES_StableIF97 Output Data

Please refer to Example 1 : Numerical Consisency of ES_StableIF97 Steam Table Functions in Region 1, ES_StableIF97 data.

3) Consistency : OK

** **

__Region
2 Functions__

1) IAPWS-IF97 Test Data : Table 15

2) ES_StableIF97 Output Data

3) Consistency : OK

** **

__Metastable
Vapor Functions (Region 2)__

1) IAPWS-IF97 Test Data : Table 18

2) ES_StableIF97 Output Data

3) Consistency : OK

__Region
3 Functions__

1) IAPWS-IF97 Test Data : Table 33

2) ES_StableIF97 Output Data

3) Consistency :

IAPWS-IF97 provides the basic equations for Region 3 with temperature and density given, and the test data(Table 33) are also provided with temperature and density given, as shown in Step 1) above.

ES_StableIF97 uses IAPWS-IF97 basic equations for Region 3 calculation and the numerical consistency of the Region 3 basic equations was verified by ENGSoft internally.

However,
the functions of ES_StableIF97 should cover all regions with a given set of input
arguments given by the user. Region 3 should not be different from
other regions in terms of input arguments. Therefore, ES_StableIF97
takes iteration method for Region 3 functions, and so there is **very small
inconsistency in the final digit **between IAPWS-IF97 test data(Step 1)) and ES_StableIF97
output data(Step 2)). **Therefore, it can be said that ES_StableIF97
functions in Region 2 are consistent with IAPWS-IF97 equations.**

__Region
4 Functions__

1) IAPWS-IF97 Test Data :

** Table
35 : Saturation Pressure Equation (Basic Equation)**

** Table
36 : Saturation Temperature Equation (Backward Equation)**

2) ES_StableIF97 Output Data

3) Consistency : OK

** **

__Region
5 Functions__

__ __1)
IAPWS-IF97 Test Data : Table 42

2) ES_StableIF97 Output Data

3) Consistency : OK

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