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ASME's Mechanical Engine…ing Toolkit 1997 December
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STEAM93/PC
Properties of Steam and Water
Interactive Desk Reference
NBS/NRC IAPS'84 Formulations
"The most accurate properties of water and steam in the world"
By:
Benjamin R. (Ray) Strong, Jr. and
IMPULSE Engineering
415 Arch Street
San Francisco, CA 94132
(415) 239-0940 Voice
(415) 229-2354 Fax
Internet:
76260,1200@CIS.COM (weekly)
Thermo@hooked.net (daily)
ThermoRay@AOL.com (weekly)
Copyright 1984 through 1994
Benjamin R. Strong, Jr. P.E.
License Agreement
This manual and software is protected by both United States
Copyright law and international copyright treaty provisions.
You are granted a 30 day trial license. If you use the software
for more that 30 days you MUST purchase a license to continue
using the program. One license is required for every copy of
the program. If the program will be used on a network, an
additional license is required for each additional person who
uses the program.
Your licenses registration is not extended to anyone else.
You may not distribute your registration number and if your
registration number is distributed, your license will be revoked.
This version of STEAM93/PC is shareware. You may distribute
this program to others for their evaluation. Each additional
copy you distribute is also bound to a 30 day trial period beginning
from their receipt.
You may copy this software to your computer. Also, to protect your
investment from loss, you may make archival copies for the
sole purpose of backing up the software.
Network License
If more than one user will be allowed to use the software on
a computer network at the same time, additional users need to
be authorized by paying for an additional fee for each
additional user. By computer network, we mean any
configuration of electronically linked computers where two or
more users have access to the same computer program.
Requirements, Transportability and Compatibility
STEAM93/PC will run on all IBM/PC's and compatibles with 356k
of memory or above also running PC/MS-DOS 1.1 or above. A
graphics card and video monitor that supports IBM standard
text is required. An 80i87 NDP is strongly recommended: operation
without an NDP may be excessively slow.
STEAM93/PC may not function properly in every hardware/-
software environment, particularly in modified versions of
the operating system. Graphics characters showing on the
screen may not be displayable on all printers.
ACKNOWLEDGEMENTS
IBM (TM) of International Business Machines, Inc.
Microsoft (TM) of Microsoft, Inc.
1-2-3 (TM) of Lotus Development Corporation.
Sidekick is a tradename of Borlund International.
GETTING STARTED
Check for Completeness
The program is found as part of the self-extract compressed file
STEAMDOS.exe. (If you're reading this manual, you've likely
already expended this file.) Just execute it to uncompress the
files. The files in the package are:
STEAM.EXE The STEAM93/PC program
DUMMY.DAT A practice data set
DUMMY.PRN The practice data set for use by 1-2-3
STEAMAN.TXT This manual
Before running the program, make a copy (see your DOS manual)
and use the copy for general use and practice session.
Notes on your System
STEAM93/PC will run on many different color or monochrome
monitors with composite or RGB signals, and the Compaq and
IBM portables. It was written for MGA, CGA, EGA, Compaq, and
compatible graphics cards.
STEAM93 has been tested in a variety of 8086/8088/80286 and
high-speed CPU enhancements including ultra-high-speed co-
processor accelerator cards and machines. However, the
addition of an 80i87 to your system will make much more
difference than a faster or newer CPU.
For best results, a color monitor is recommended: STEAM93
uses color enhancements to increase the information content
and for ease on the eyes. If you have a Compaq with an
external monitor, remember to turn it on using the Ctrl-Alt-<
keys.
The program will run with or without a NDP chip, but runs
much faster with it installed. This especially applies to P-
h, P-s, and some transports calls which can be quite time
consuming. If you are using an 80i87, STEAM93 will use it
extensively. This can be used as a test of the 80i87 - if an
inconsistency or program abort occurs during calculation, it
is our experience that this is most likely an 80i87 problem:
that the 80i87 is operating too "hot", or at too high a
speed. If you have a switchable system clock, try slowing the
clock down. If problems occur with a cold/slow system, call
us immediately.
If the version of your program is copy protected, you will
only be able to use the program on the diskette provided to
you. We hope this doesn't provide too much of an
inconvenience to you. If you have damaged the diskette,
please send it back and we'll send you a new one.
Post Processing the STEAM93 Properties Data
For follow-on calculations, data logging, and/or plotting we
suggest Lotus 1-2-3. This spread sheet program can be used to
automatically perform some quite complex calculations. (More
about 1-2-3 later.)
You can also use 1-2-3 to convert STEAM93/PC data for use by
dBASE-II/III. For on-line calculations, we recommend
Sidekick.
Table of Contents
Getting Started
Check for Completeness
Notes on your System
Post Processing the STEAM93 Properties Data
Table of Contents
List of Figures
List of Tables
INTRODUCTION
About Steam93/PC
Related Products
About IMPULSE Engineering
STEAM93/PC USAGE OVERVIEW
Starting the Program
Loading the Program
Practice Session
EXIT'ing, Ending your Session
Screen Layout and Use
Properties Screen
Additional Transports Screen
Messages and Indicators
On-Line Helps
Inputting and Deleting Data
Inputting Property Data
Inputting Property Combinations
Copying Data
Deleting Data
F3 Key, Finding State Values
Opps! = ESC and Recovery
Calculation Options
Critical Region Toggle
Transport Calculation Toggle
Printing
Units
USING THE STEAM TABLES
Finding Saturation Values
Isentropic Searches and Efficiencies
Availability
SAVING AND RETRIEVING YOUR SESSION DATA ON DISK
Saving Your Session
Saving To Your Default File
Retrieving a Data File
Merging Partial Data Sets
USING STEAM93 WITH LOTUS 1-2-3
ENGINEERING NOTES
Critical Mass Flux
Speed of Sound in the Two-Phase Region
Thermodynamic Quality
The Very-Near Critical Region
Range, Physical Accuracy, and Consistency
REFERENCES
Appendix A SERVICE AND WARRANTIES
PRODUCT SERVICE
LIMITED WARRANTY
Figures
1.A Properties Screen Layout and Function
1.B Additional Transports Screen Layout and Function
2.A General Help Screen
2.B Input Help Screen
Tables
1 Thermodynamic and Transport Properties
2 Range and Accuracy
3 Units Conventions
INTRODUCTION
About STEAM93/PC
STEAM93/PC was written to provide the highest accuracy and
highest consistency reference for the properties of steam and
water available anywhere in a fast and easy to use form.
Much concern and time was spent to make sure that annoying
problems such as data overflow, format overflow, system lock-
ups during difficult calculations,... will not occur, and
protection against them is automatic. Also, knowledge of the
state range is not required. Our goal is to make the process
of using the program as comfortable, natural and
unsophisticated as possible without burdening you with quirks
of the solution techniques, system, machine, or programming
languages.
STEAM93/PC provides the state and transport properties shown
in Table 1 to the accuracy estimated in Table 2. The
exceptional accuracy is due to the following:
-- Each and every property calculation is evaluated from the
fundamental formulations. No approximations are introduced
by using tables, interpolations, splines, curve fits, or other
approximations.
-- The fundamental state property solvers are the most accurate
and most consistent formulation currently available anywhere.
These are applicable over a much wider range than any other
correlation [1, 3]. These solvers are based on the most recent
internationally approved material from the International
Association for the Properties of Steam. The formulations,
approved as the "IAPS Formulation 1984", were developed by the
US National Bureau of Standards and the National Research
Council of Canada and have also been approved by the American
Society of Mechanical Engineers through their Research
Committee on the Properties of Steam (as members of the
IAPS).
In addition, the STEAM93/PC implementation has been written to
take advantage of this correlation in some special ways:
STEAM93/PC is verified to source data and independent
parallel correlations
to the greatest number of significant digits published
in all available reference works, and
throughout the entire range of applicability.
The Gibbs condition for phase equilibrium is used for
the calculation of saturation conditions and coexisting
phases.
In the very-near critical region, where even mainframe
implementations have great difficulty, an optional
correlation is available to accurately resolve property
data.
The range of applicability is extended to 100,000 Bars
and 100,000░K.
Full data precision is available to SAVE and spreadsheet files
for accurate post-processing with the property data, or
for data logging.
STEAM93/PC includes transport and indirect properties from approved
standards commonly used in engineering applications.
To make STEAM93 more useful the general format is like a
spread sheet for systems and component studies, with data
copying, printable files for data logging, and other
features.
The development of STEAM93 for the PC began with the basic
formulations and embedded them in a fault-tolerant
environment for greater accuracy and transportability. This
environment was then improved by use of the FORTRAN Addenda
(also available from IMPULSE Engineering) which provides the
screen, keyboard, and file management utilities.
STEAM93 has been used in a variety of applications areas,
ranging from power systems studies, meteorology, aerospace,
component design, and pre-processing for fluid systems
simulation programs. Please let us know of your application,
and especially if you have questions or problems in using the
program.
Related Products
IMPULSE Engineering has a number of products that can help you
develop programs for science and engineering applications. You
can receive more information by writing, calling, or e-mailing
us at the locations shown on the cover sheet.
Verification Package for STEAM93
This documentation describes the extensive verification and
benchmarking for STEAM93. The document includes the plan,
results, and output files used.
STEAM93.DLL
STEAM93.DLL allows MS-Windows developers and users of
applications such as MS-Access, Win-Basic, MS-Word and Excel
to access the NBS/NRC steam tables from within their
application. Using MS-Windows Clipboard, OLE, and other
resource, the steam tables can now be imbedded in any Windows
application.
STEAM93/Win
This is a windows application that provides the same range of
services as STEAM93/PC for DOS. Written specifically for the MS-
Windows environment, STEAM93/Win allows Clipboard and real-time
OLE connections to other applications and documents.
STEAM93/PGM
The STEAM93 correlations are available as FORTRAN subroutine
source code for custom applications on non-IBM compatible
platforms. The package comes complete with a Programmer's
Reference manual, example source code, and structure charts and
diagrams. A FORTRAN application front-end and benchmark data set
are also included.
FORTRAN Toolkits
The FORTRAN Toolkits are libraries of routines for developing
user friendly programs in the DOS & FORTRAN environment. The
routines range from windowed graphics to string searches, from
on-screen editing control to file management.
Engineering Libraries
IMPULSE Engineering distributes libraries of engineering data.
These can be called from Windows programs or applications that
access Windows dynamic Link Libraries (.DLLs). These libraries
include
Geometry, properties, and schedules of pipes and tubes
Pressure drops in piping and components
Valve and damper characteristics
Psychometric calculations for water and steam
Steam tables (see STEAM93.DLL above)
Each comes complete with documentation and sample programs.
About IMPULSE Engineering
IMPULSE Engineering provides specialized consulting and software
services in thermodynamics and mechanical engineering to the
aerospace, environmental, and energy industries. Our mission
is to provide or create the highest quality state-of-the-art
technology to make our world a better place to live.
Table 1 Thermodynamic and Transport Properties
# Property Abbreviation Description
(many of the standard symbols are unprintable)
1 Pressure p, Press p = T(s/v)u
2 Temperature T, Temp T = 1/(s/u)v
3 Specific Enthalpy h, Enthal h = u + pv
4 Quality x, Qualty (See Technical Notes)
5 Specific Volume v, SpcVol v = 1/r
6 Availability go, Avail go = h - Tos
7 Specific Entropy s, Entrop s = -(A/T)v
8 Specific Internal
Energy u, IntEng u = A + Ts
9 Nozzle p/v p/v
10 Specific Heat Capacity
at Constant Pressure Cp Cp = (u/T)v
11 Specific Heat Capacity
at Constant Volume Cv Cv = (h/T)p
12 Dynamic Viscosity ╡ IAPS'75
13 Conduction Heat
Transfer Coefficient K, HtTran IAPS'85
14 Speed of Sound Cs, w,SndSpd
15 Isothermal Bulk
Modulus B|T, BulkM|T BT = 1/k
16 Hemholtz Function A, Hemhlz A = u - Ts
17 Gibbs Function g, Gibbs g = h - Ts
18 Prandtl No. Pr, Prandtl Pr = Cp╡/K
19 Critical Mass Flux W*/A* W*/A*
20 Isentropic Exponent -, Gamma - = -v/p(p/v)s
- = 1/a p
21 Kinematic Viscosity u ,KinVisc u =v╡
22 Isobaric
Compressibility ▀ , Comp|p ▀ = (1/v)(v/T)p
23 Isentropic
Compressibility _ , Comp|s _ = -(1/v)(v/p)s
24 Isentropic
Bulk Modulus B|s, BulkM|s Bs = 1/a
25 Free Convection
Coefficient ▀nc, NatCon ▀nc = gb/u2
26 Thermal Diffusivity a, ThrDif a = Kv/Cp
27 Surface Tension s, SurfTn IAPS'75
28 Static Dielectric
Constant _, Dielec IAPS'77
29 Isothermal
Compressibility k, Comp|T k = -(1/v)(/p)T
30 Compressibility Factor Z Z = pv/RT
(1) Calculated directly from the IAPS'84 Hemholtz function
and it's derivatives [1,3], not necessarily from the
equation shown. When an IAPS release date is shown, the
formulation is from that IAPS specification.
(2) In the 2-phase region the critical velocity V* is
substituted for Cs.
(3) Calculated assuming p, v, ... are TOTAL conditions.
Table 2 Range and Accuracy
PROPERTY RANGE ACCURACY (1) / NOTES
Pressure 0 < p < 10,000 Bars IAPS'84
p < 30,000 Bars IAPS Extrapolations / (3)
p < 100,000 Bars STEAM93 / (4)
Temperature 0.01 < T < 1,000░C IAPS'82 / (2)
T < 2,773░ IAPS Extrapolations / (3)
T < 100,000░C STEAM93 / (4)
Specific
Volume 0 < T < 600░C,
v(p,T) 0 < P < 500 Bars;
Liquid 1 part in 10,000 (0.01%)
Vapor 1 part in 1,000 (0.1%)
General:
T < 1,000░C,
p < 10,000 Bars 10 parts in 10,000 (0.1%)
Anomalous Region 2 parts in 100,000 0.002%)
Metastable States "... very good ..."
Vapor
Pressure 0.01 < T < Tcrit 12 parts in 100,000 (0.012%)
Specific Enthalpy of
Vaporization " 2 parts in 10,000 (0.02%)
Specific
Enthalpy 1 < p < 5,000 Bars h(p,T) = p_h(1,T)
5 < p 5,000 Bars h(p,T) = [5+2(p-5)]_h(1,T)
/ (5)
Specific Heat at Constant
Pressure p < 1,000 Bars Generally 1%
Dynamic Viscosity
[2] 0 < T < 800░C Generally 1% / (6)
0 < p < 1,000 Bars
Useful Range:
T < 100░C and p < 10,000 Bars
T < 560░C and p < 3,500 Bars
Thermal Conductivity
[2] 0 < T < 800░C / (6)
0 < p < 1,000 Bars
Notes:
(1) Accuracy is taken from References [1] and [2]:
conservative summary of high error estimates based on
comparisons with test measurements. Reference [1] has a
very complete review of accuracy and should be consulted if
range-specific accuracy information is required.
(2) International Practical Temperature Scale of 1968 (IPTS
'68)
(3) Extrapolation of fundamental equation as agreed upon by
the IAPS. [3]
(4) Convergent/Consistent/Reasonable upper limits of
calculation with no accuracy estimates proposed or
attempted.
(5) _h(1,T) is the uncertainty in dh at T and 1KBar.
(6) Within the uncertainty of the test measurements. [2]
STEAM93/PC USAGE OVERVIEW
The STEAM93 program is used like a spread-sheet program with
fixed form and functions of the data. The following sections
will present an overview of the program's functions and
usage. The easiest way to become familiar with the program is
to load the sample session and just play with the options and
capabilities. Remember to use a copy of the program for
this, and not the original diskette!
Starting The Program
Loading The Program
(1) "Boot" (start-up) your system (if not already on) and
insert the STEAM93/PC diskette into the drive you want
to use.
(2) Just as you normally would, use DOS to set the default
disk to the drive where you put the program diskette e.g.,
if the program diskette is in drive B and the prompt on the
display shows
A:>
then type in B: and hit the carriage return key (Enter key).
The DOS prompt should now show
B:>
(3) Type in STEAM and hit the Return key (Enter). After a
few seconds, the screen will fill and a pair of square
brackets, [ ], will appear to define a cell for input.
That's it. From here on you're in STEAM93/PC. For a Help
screen, reminder for what keys control the program, hit F10.
To print that page, turn on your printer and hit the PrtSc
key. Use this as your reference until you can
remember how the special keys work.
Practice Session
For practice, read in the data file found on the diskette.
To do this, hit the F6 key (this is the file read key) and
type in the file name, dummy.dat. Then hit *Enter and wait
until the data reprints on the screen. From here on, enter
or delete data or practice with the various functions.
EXIT'ng Ending The Session
To exit back to DOS, just hit Ctrl+Home (hold down the Ctrl
key and hit the Home key at the same time). (It's a good
idea to save your session first.) If the data currently used
by the program is not the same as the SAVE file, the program
will ask you to verify if you want to exit without saving the
current data. This will give you an extra chance to SAVE
your data.
Screen Layout And Use
The STEAM93/PC program uses four screens to express itself -
two screens of data (shown in Figures 1.A and 1.B) and two
Help screens (Figures 2.A and 2.B). Use of the two data
screens is similar for all of STEAM93/PC's capabilities as
discussed in the following sections.
Properties Screen
When you start-up a session you'll see the screen shown on
Figure 1.A. This is the main screen for all water properties
operations. There are eight columns, labeled "Pt n",
referring to State Points, for process studies. To the right
of the screen there are two columns for property names and
units labels: these labels apply to each column and cell in
the row. The rows of properties for each of the 8 different
State Points are totally independent "calculators".
Each of these spaces are called "cells", just like a spread
sheet. The cell you are working on is identified by the
blinking (red) brackets. Movement for data entry and such is
done using the cursor controls on the keypad (to the right of
the keyboard).
A second screen, shown in Figure 1.B contains additional
transport data. This is accessed as discussed in a following
section.
Some of the units have coefficients, or exponents with the units
name. This is intended to be read as a literal suffix to the
number showing in the cell: don't invert the sign, just assume
that it is a multiplier to the number showing.
Additional Transports Screen
In addition to the main screen of property and transport
data, there is an additional page of data shown in Figure
1.B. You can access this page by hitting PgDn on the keypad.
The data layout for this screen is the same as the properties
screen discussed above. You can use the cursor to move
around this screen, and access most other program functions
except number input and calculate. When you are ready to
return to state operations, just hit PgUp.
Messages and Indicators
While you are working with the screen, take special note of
the top line. You will see four words which indicate where
you are and what to do (see the General Help screen or Figure
2.A). Mostly, keep track of the "Wait" indicator when it
appears: the program is working on something until "Inactive
Any Key" appears on the top line. As you work more with the
system you'll find these helpful in assuring that the program
has done what you want. Except for file I/O, you shouldn't
have to wait long.
On the top line you'll also see an indicator for the cell
location, as (n,y) where n is the state point number and y is
an abbreviation for the state property. When data for the
property and state point is available, the number will also
appear here. (If the number to 8 places doesn't immediately
appear, move the cursor away from the cell and back to the
cell. It should then appear.)
The time of day and the date are shown to the right of the
screen on the top and bottom lines. These are for your
reference as you use the program and are also written to the
print and save files for data logging or checking for the
right file.
During the use of the program you will also notices changes
in the intensity or the color in screen items. More about
these later.
Figure 1.A Properties Screen Layout and Function
STEAM`93(6,h)= .27245044E+04 Properties Operations Inactive any Key 15:37:24
----------------------S T A T E P O I N T S ( Water )---------------------
PROPERTY UNITS\ Pt 1 Pt 2 Pt 3 Pt 4 Pt 5 Pt 6 Pt 7 Pt 8
Press: Bars 100.000 100.000 100.000
Temp: C 311.031 311.031 311.031
Enthal:KJ/Kg 1407.28 2724.50[2724.50]
Qualty: .0E+00 1.00000 1.00000
SpcVol:m^3/Kg .001452 .018025 .018025
Avail: KJ/Kg 489.733 1191.05 1191.05
Entrop:KJ/Kg C 3.35912 5.61395 5.61395
IntEng:KJ/Kg 1392.75 2544.25 2544.25
Nozzle: p/v 68862.8 5547.71 5547.71
PROPERTY UNITS\ Pt 1 Pt 2 Pt 3 Pt 4 Pt 5 Pt 6 Pt 7 Pt 8
Cp: KJ/Kg C 6.12439 6.89730 6.89730
Cv: KJ/Kg C 3.05600 2.99751 2.99751
DynVis:e-6Pa-s 81.8295 20.2664 20.2664
HtTran:mW/m C 526.976 76.3337 76.3337
SndSpd:m/sec 843.401 474.303 474.303
Bulk|T:Bars 2444.25 54.2385 54.2385
Hemhlz:KJ/Kg -569.58 -735.31 -735.31
Gibbs: KJ/Kg -555.06 -555.06 -555.06
PROPERTY UNITS\ Pt 1 Pt 2 Pt 3 Pt 4 Pt 5 Pt 6 Pt 7 Pt 8
KEYS Soln: Analy. Analy. Analy.
AT Regn: SatLq SatVp SatVp
F10=Help!, F1/F2=Copy, F3=Calc, ^F4=Calc.all, F5=Save, ^Home=Quit 11/ 6/1992
Figure 1.B Additional Transports Screen Layout and Function
STEAM`93(6,P)= .18312173E+01 Transports Reference any Key 15:41:49
PROPERTY UNITS\ Pt 1 Pt 2 Pt 3 Pt 4 Pt 5 Pt 6 Pt 7 Pt 8
Prandl: .95100 1.83122[1.83122]
Wc/A: kg/m^2s 108640. 15491.1 15491.1
Exp|s: 48.9840 1.24803 1.24803
KinVis:mm^2/s .118830 .365312 .365312
Comp|P:1/ C .003847 .008263 .008263
Comp|S:1/Bars .000204 .008013 .008013
Bulk|S:Bars 4898.40 124.803 124.803
NatCon:1/mm^3C 2671.60 607.217 607.217
ThrDif:mm^2/s .124952 .199491 .199491
SurfTn:N/m .011863 .011863 .011863
Dielec: 18.7849 1.33296 1.33296
Comp|T:1/Bars .000409 .018437 .018437
Z: .053861 .668573 .668573
PROPERTY UNITS\ Pt 1 Pt 2 Pt 3 Pt 4 Pt 5 Pt 6 Pt 7 Pt 8
--------------------------------------------------------------------------------
----------------------------- IMPULSE Engineering ------------------------------
----------------- STEAM`93/PC v3.1 (C) 1992 B.R.Strong,Jr.,PE. -----------------
--------------------------------------------------------------------------------
PgUp to return to properties.
_
On-Line Helps
By hitting the F10 key, the program will switch to one of the
Help screens. During non-input operations, a Help screen
that has memory "joggers" for the keys and special functions
of the program will appear. During input, a different Help
is available which describes special input and editing keys.
If you need more information than is on the two Help screens,
please refer to this manual.
To return from Help to your prior operation, just hit any
key.
Also note the bottom line during normal operation which has
the most common keys, and is used for messages and prompts
for file information.
Figure 2.A General Help Screen
STEAM`93/PC v3.1 Help Reference Inactive any Key (time)
Mode of Operation---+ ª ª
Operations Status--+ ª
User Prompt---+
STEAM9X NBS/NRC-IAPS`84 Steam Tables
KEY RESULT / Function ª KEY RESULT / Function
ª
F1 Copy cell into Xtemp. ª Esc Abort Process.
F2 Copy Xtemp into cell. ª
F3 Find St.Pt. Properties. ª Del Delete data at this cell.
F4 Find Props at ALL St.Pts ª Alt+D Delete ALL data for Pt.
F5 Open File. ª
F6 Save File. ª PgDn Transports Screen 2.
F7 Save File as ... ª PgUp Retn To States Screen 1
F8 Print to 1-2-3. ª Alt+T Toggle Transport Calc.s
F9 Change Units. ª Alt+C Toggle Critical Region.
F10 Help!. ª Ctl+Home Return to DOS
Notes: [ ] denotes current cursor (cell) location; move it using the keypad.
To input data, just type in the number and enter it with a return <CR>.
When 2 properties are input, hit the F3 key to calculate the others.
Use F1 and F2 (Xtemp I/O) for copying an entire cell.
Note the UNITS and POWER (e▒n) are a LITERAL SUFFIX to the cell value.
Next key is processed on return. Indicates data is different from SAVE file. ->
Figure 2.B Input Help Screen
STEAM`93/PC v3.1 Help Reference Inactive any Key 15:47:26
-------- INPUT HELP --------
STEAM`92 input is similar to a line editor and DOS. You enter data by
just typing the data and hitting the <CR>. Like DOS, the prior data is
stored in a buffer from which you can copy using F1 and/or F3. If you
wish to edit the prior data, hit F3 and a line editing mode is active.
This mode is also active when a syntax error is found. To exit without
any modifications, the `opps` functions are provided. STEAM`92 will
check your inputs STROKE by STROKE for context and syntax !
KEY FUNCTION
Esc Start over. If on col. 1, Esc an `opps`
<CR> Enter data. On a syntax error, the cursor ID`s the problem and
editing is turned on. <CR> on col. 1, is `opps`.
F1 Copy 1 char. from prior data (buffer).
F3 Copy remaining data from prior data (buffer). Editing turned on.
Del Delete the character to the right. (Buffer moves to left.)
BkSp Delete the character to the left. (Buffer moves to left.)
Ins Insert a keystroke at the cursor location. (Buffer moves to right.)
Ctrl+End Universal `opps`, available at any time.
Notes
`opps` Exit without any change of data or action.
Edit Editing is turned ON by F3 or a syntax error.
Editing is turned OFF by Esc.
NumLock Toggle to allow number input from the keypad. Cursor is turned OFF.
Any key to continue input.
_
Inputting and Deleting Data
Inputting Property Data
The input and editing is quite natural and follows DOS,
EDLIN, and word processors. Unlike those, STEAM93 will check
the context of the data.
To enter a number at the cell you're at (denoted by the
brackets), just start to type a number. A small cursor (_)
will appear at the left of the bracketed space indicating to
go ahead and type in your data. (There will also be a prompt
on the top line which indicates what type of input is being
requested.) Just type in the number in any real (with or
without a decimal point) or exponential (e, d, g) format and
enter it with a carriage return, *Enter. Unlike most
interactive programs, STEAM93 "buffers" your input data,
checking the inputs character -by- character. Almost
anything will work and the usual rigid forms are relaxed
here.
Data is entered with the usual carriage return key, *Enter.
If the number is unacceptable for some reason, the editing
mode is automatically turned on and the cursor is re-located
to the offending digit as discussed in the following section.
After successful entry, the program will modify the
appearance of your input to provide the maximum number of
digits of accuracy. This automatic formatting is for "looks"
only - all of the information you input is stored in the
computer, and will be echoed on the top line to 8 significant
digits.
You can also use Sidekick to input data by moving to the
location where you wish to enter the number stored by
Sidekick and hitting the key programmed to hold it. Refer to
your Sidekick manual for such operations.
All successful inputs are identified on the screen by an
inverse color or intensity. If you find you cannot input
data in a cell, it's because this property is not allowed as
one of the two acceptable inputs available for finding
property values.
The following sections describes the individual key
protocols. It's not as confusing as it appears, and follows
DOS or standard word processing protocols.
Normal Input
The standard input is as discussed above - just type in the
numbers and hit *Enter. Additional keys, similar to DOS and
EDLIN, are available to help you with this:
Esc
'Opps'. When on data column 1: Esc
is an 'opps', returning without
change of any kind. When anywhere
else, Esc restarts the input
process.
F1
Character Copy. Like DOS and Edlin,
this copies a single digit from the
data shown prior to starting input.
F3
Dump Buffer Copy. Like DOS and
Edlin, this copies the remaining
digits from the prior data and
turns on the editing mode (see
following section).
Bksp
Delete Character. Deletes the digit
to the left of the cursor
Ins
Insert On/Off. Toggles on/off the
insert function. If Ins is ON, the
next input digit is entered and the
buffer (prior data) is shifted
right.
Del
Delete Buffer Item. Shifts the
buffer (prior data) left (like DOS)
F10
Help. The input Help screen. Any
key is used to return from this
screen.
*Enter
Enter Data. If there is an error,
the cursor will move to the source
of the error and editing is turned
on.
Editing Mode (F3 During Input or Input Error)
If F3 is hit (or if the *<─┘Enter would not allow the data),
the full editing is turned on and additional editing
capabilities are available:
Esc
Restart. Restarts input and returns
to non-editing (normal) input mode.
A second Esc is an 'opps', restoring
the screen and data.
Bksp
Delete Single Item. Deletes the
digit to the left of the cursor (_)
and closes up the data to the right.
Del
Delete Single Item. Deletes the
digit over the cursor (_) and closes
up the data to the right.
Ins
Insert On/Off. Toggles On/Off the
Ins mode. If Ins is on, the next key
struck is inserted above the cursor
and the data is moved right to make
room for it.
*
Right. Just moves the cursor (_)
right. Ins mode is turned off.
*
Left. Just moves the cursor (_)
left. Ins mode is turned off.
Home
Flush Left. Cursor is moved to
column 1. Ins mode turned off.
End
Flush Right. Cursor is moved to the
last significant (non-blank) digit.
Ins mode turned off.
Editing After an Error
If the bell sounds after hitting *Enter to enter data, the
number is unacceptable and the editing mode is automatically
turned on. The cursor moves to the location of the offending
digit or symbol, and you can edit just like a data string as
discussed in the prior (F3) section.
Editing the Previous Data
To edit data showing on the screen, first hit a number to get
into the input mode and then hit Esc once to get you back to
column 1. Then hit F3 to re-print the previous data and turn
on the editing mode. Once the editing mode is on, edit the
data using the cursor and keys as discussed in the prior (F3)
sections.
Input Property Combinations
You need not overly concern yourself too much with the valid
input combinations allowed; STEAM93 checks them
automatically. For your reference, they are:
p and T
Pressure and temperature
p and h
Pressure and enthalpy
p and x
Pressure and quality
p and v
Pressure and specific volume
p and s
Pressure and entropy
T and x
Temperature and quality
T and v
Temperature and specific volume
Don't bother to memorize these, as the program allows only
the acceptable combinations.
Copying Data
The F1 and F2 keys are used to copy data. Hitting F1 will
store the number at the current cell (within the brackets) to
internal storage. Hitting the F2 key will copy the number
currently stored to the current cell. So, for repeating a
number, enter the number in a cell, hit F1, move the cursor
to the new locations, and hit F2.
The number stored is the full 64-bit accuracy allowed by the
machine, even though all of the significant digits may not
appear. Output values provided from the program are to the
full machine accuracy, so for consistency it is always better
to reproduce a number using the F1 F2 sequence than to re-
input it by hand. Full state consistency can be assured this
way without being limited to the accuracy of your inputs
digits.
Note that the copying process is units dependent, so that
copying vertically to another data type will likely yield a
different magnitude. So copying data is best for horizontal
copying between state points.
Deleting Data
Just hit the "Del" key on the keypad to delete the data shown
at the cursor. If additional data is deleted it's because
you may have deleted data which was one of your previous
inputs. This is intentional for consistency.
To delete an entire column (State Point) of data use Alt+D
(hold down the "Alt" key and hit the "D" key).
F3 Key, Finding State Values
When any two primary state variables (i.e., p and T or others
identified in Section 3.5.2) are available for a state point,
just hit the F3 key. The inputs will be checked in context
and the search for the other consistent state and transport
properties. You need not concern yourself with the range or
state region of your inputs,
STEAM93 is smart enough to manage it alone and tell you what
region your input / output is in. If the inputs are out of
range, a message will appear on the lowest line echoing the
property at fault. (This checking includes some pre-
calculation in certain regions so it may take a second.)
Simply reinput the number and use F3 again.
While calculation is proceeding the messages on the top line
will often change and the clock will continue to run.
Calculation continues until the screen has reprinted the data
for the state point and the "Inactive" message appears on the
top line.
Some calculations, notably p-s and p-h calls, take quite a
bit time. As long as the clock changes time every few
seconds or so, the program is still trying to find the
consistent state values. If you do not have an 80i87
installed in your machine, please be patient, and wait for
the "Inactive" message to appear on the top line.
If you wish to abort calculation before completion, hit the
Esc key.
OPPS! = ESC and Recovery
The Esc key is used to end the current operation of the
program. During input of a number or filename, hitting Esc
will end input, and restore the original data.
During calculation of a state point, hitting the Esc key will
abort the calculation and return you to normal operation.
Calculation Options
There are two toggles you can use to reset calculation
options of STEAM93 and control the handling of the very-near
critical region and the calculation of transport properties:
Critical Region Toggle
In the very-near critical region, STEAM93 has an optional
calculation method to evaluate properties and transports.
When you start the program, this toggle is "off" as denoted
by the letter "A" (for Analytic) appearing under the "Keys"
note near the bottom-left of the screen. In this default mode,
the canonical fundamental equation (IAPS'84) is used throughout
the calculations.
To access the alternative critical region method, hit Alt+C
(hold down the Alt key and hit the C key). This toggle is
noted on the screen as a "C" (for Critical) instead of the
"A". This critical region formulation and correlations will
be substituted for the IAPS'84 formulation whenever the state
point is found to be in the very-near critical region. (More
about the this region and how it is defined and handled in a
later section.) To turn off this critical region detail, just
hit the Alt+C key combination again.
Transport Calculation Toggle
If you have no need of the transport properties or specific
heats, you can turn off their calculation. When you start
the program, this toggle is "on" as denoted by the letter "T"
appearing under the "Keys" note near the bottom-left of the
screen. In this mode, the transport properties are
automatically calculated.
To turn off automatic transport property calculation, hit
Alt+T (hold down the Alt key and hit the T key). Calculation
of the transports will then be skipped, as denoted by a "N"
in place of the "T". To calculate the transports, you need
only to reset the toggle by repeating the Alt+T combination.
Note that if you have an 80i87 installed in you PC that the
transport calculations do not take much time compared to
state point calculations. Most of the time is spent printing
to the screen rather than in calculation.
Printing
You can print out the screen at any time by using the shift-
PrtSc key (upper case and PrtSc keys at the same time) as
provided by your operating system. The files written by
STEAM93 are also printable using the DOS "TYPE" command, but
the output will not be as readable.
The DOS PrtSc command takes precedence over any STEAM93
operation so the program will pause until the printing has
finished. Make sure your printer or spooler is on or DOS
will wait forever for the printer to be available.
Units
Units are summarized in Table 3 with the abbreviations
appearing on the screen. Common units and abbreviations are
used and should be self-explanatory.
For a few properties, notably the viscosity, there is an
exponent ( e-6 ) preceding the unit. This, and the unit, are
to be interpreted as a literal suffix to the number. As you
would expect, if the data itself has an exponent (i.e., e-9),
the exponents in the number and in the dimension are added
(in this example, summing to e-15).
To switch back and forth from SAI to English/Engineering
units, just hit F9. All conversions are automatic.
Conversion factors all use 8 significant digits and are
consistent with ANSI/NBS Standards.
USING THE STEAM TABLES
As well as an accurate reference for properties and
transports at state points, STEAM93/PC offers a variety of
convenient calculations capabilities. A few of these are
described in the following sections.
Finding Saturation Values
As you might expect, data right on the saturation lines is
found using pressure and quality (p and x) or temperature and
quality (T and x) as inputs. Quality is input as either 0
for saturated liquid or 1 for saturated steam. (Also see
Sections 8.1 and 8.3 for additional information.)
Isentropic Searches and Efficiencies
One of the most common uses of the steam tables is for
observing isentropic processes and using efficiencies. Using
STEAM93/PC, this process takes just a few seconds.
For example, take an isentropic expansion process from
StPt's (state points) (1) to (2) resulting from a nozzle or
turbine. In this example p1 and T1 are known. First, p1 and
T1 are input, and the F3 key is struck to calculate the
remaining data for StPt (1). Then s1 is copied to s2 at StPt
(2) (using the F1 key at s1 and F2 key at s2). The new
pressure is entered at p2 and the F3 key is struck to
calculate the remaining data at StPt (2). The resulting data
at StPt (2) are the properties and transports at (2) from the
isentropic expansion. This process can be rep-resented by:
s1(p1,T1)
s2=s1
y2(p2,s1)
where y2(p2,s1) is any property at StPt (2).
For an imperfect expansion process as for a turbine, an
efficiency et, may be available for the process to discover
data at p2 using StPt (3). For the expansion, this
efficiency may be described as:
et = (h1 - h3) / (h1 - h2)
To find data for the inefficient expansion process (1) to (3),
StPt's 1 and 2 are created as in the above. Then h3 is
calculated using Sidekick or another calculator from:
h3 = h1 - et( h1 - h2 )
and h3 is entered at StPt (3). p3 is copied from p2 (again
using F1 and F2), and F3 used to calculate data at the StPt
(3) for the inefficient process.
Note that critical mass flux (assuming pn and vn are at total
conditions) and critical velocity (assuming pn and vn are at
local static conditions) are available to assist in sizing
and flow calculations. Using the F1 and F2 copy sequence is
recommended because the full 15 significant digits are copied
and used for the calculation at the new state point -
manually input will yield only 5 places or so of input
accuracy and inconsistencies may appear.
For a compression process like a pump, the sequence of
solution is similar. The isentropic process (1) to (2) is
resolved as for the compression process. h3 is then found
from the pump efficiency:
ep = (h2 - h1) / (h3 - h1)
h3 = h1 + (h2 - h1) / ep
and entered for StPt (3). p3 is copied from p2 and the new
StPt (3) is found using the F3 key for the imperfect
compression process.
Of course, the analogous process can be used for any constant
property process: isobaric, isochoric (constant density),
isothermal,...
Availability
The (steady-flow) availability function is provided for the
evaluation of equipment and processes. The availability
function is defined as:
go = h - Tos
where:
go = steady-flow availability function
h = enthalpy
To = environment absolute temperature (heat sink)
= 273.15░C, is chosen for evaluation.
s = entropy
To evaluate the maximum work output for a reversible process
between two states the difference in availability is used as:
Specific Power = Power out / Mass Flow Rate
Specific Power <= go1 - go2
The difference between the maximum possible useful work
output and the actual work output is sometimes called the
irreversibility of the process. By evaluating the
availability and irreversibility, the primary sources of
expensive energy waste can be identified and corrected. The
irreversibility can be used as a measure of the gains
achieved in improving performance.
SAVING AND RETRIEVING YOUR SESSION DATA ON DISK
The protocol for file names in DOS is so flexible as to give
most programs problems. The protocol includes the disk drive
(d:), the file name (filename), and an optional extension
(.ext) put together as d:filename.ext. If the file you want
is on your default disk (identified by the d>_ or d: prompt
before you executed the program), then the disk drive need
not be entered, resulting in filename.ext.
As you may know from using other programs, DOS takes control
on file name errors (illegal characters) or requests to disk
drives which are unavailable (i.e., the door on the disk
drive is open). This usually disrupts program execution and
results in unrecoverable aborts.
STEAM93/PC uses a number of protection devices to avoid most
of these problems: filename inputs are checked for legal
characters, the disk directories or local drives are checked
to make sure the file is present (on reads), the drive name
input is checked for legality,... This is to make sure that
you can always save your session.
When you hit a key signaling for file I/O, a prompting
message will appear on the bottom line. For the entry, upper
or lower case does not matter.
Extensions (using a .ext at the end of the file name) are
recommended. For data (save) files use an extension of .DAT,
and the 1-2-3 output file uses .PRN (Lotus REQUIRES an
extension of .PRN).
Saving Your Session
To save your data, just hit F5. On the bottom line a message
and prompt will appear for you to type in the file name.
Type it in and hit return. If you hit the key accidentally,
use the Esc key to recover.
The "Prompt" message on the top line will change after the
read or write has been accomplished and reprinting of any new
data is finished.
Saving To Your Default File
If you're saving to the same data file more than once, use
the F8 key. If you've typed in a save file name once it is
stored in the buffer and can be used any time later for the
default.
Data in the save file is in the STEAM93 SAI units set in
printable ASCII form with time and date of creation suitable
for archiving.
Retrieving a Data File
To retrieve a session, use the F6 key. You will be prompted
for the file name as discussed above.
Merging Partial Data Sets
State points without data are not written to the SAVE file,
and will not be reproduced / reprinted to the screen and not
over-write data appearing for that state point. You can use
this to merge SAVE files from different data sets.
USING STEAM93 WITH Spreadsheets
To write the property data to a file compatible with 1-2-3,
just hit F7. The resulting file format is readable by Excel and
Quatro Pro and other spreadsheets. As in the other functions
to save and retrieve your session, a file name prompt appears on
the bottom line. Make sure that you use a file name extension of
.PRN for 1-2-3. When you are in 1-2-3, locate the cursor where
you want the upper left hand corner of the STEAM93 data set to
appear. Then use the /File Import Number (/FIN) selections from
the 1-2-3 menu to access and enter the data file. Make sure to
locate the 1-2-3 cursor at a new point so that it doesn't
overwrite existing data: 35 rows by 10 columns should be
anticipated.
The .PRN file written for 1-2-3 use includes headers and
dates as well as the complete number data set.
The full accuracy of the data is stored in 1-2-3 even if it's
not printed. If you wish to show more digits of data, use
the 1-2-3 display commands (/WG, etc.).
ENGINEERING NOTES
Critical Mass Flux
The critical mass flux is calculated by assuming the input
intensive state properties are providing TOTAL (stagnation)
conditions. This is the only property provided in this way:
all others assume input intensive properties are at local
static conditions.
Speed of Sound in the Two-Phase Region
In the two-phase region the speed of sound is undefined. In
this region the critical velocity V*, calculated for
isentropic process and equilibrium conditions, is substituted
for the speed of sound.
Thermodynamic Quality
The thermodynamic quality, or vapor mass fraction, is
generally calculated using specific volume. However, for p
- h or p - s inputs in the saturated region enthalpy and
entropy fractions are used instead as:
p - h
x = (h-hf) / (hg-hf)
p - s
x = (s-sf) / (sg-sf)
other
x = (v-vf) / (vg-vf)
When a state search results in subcooled values, x will be
retained at 0. Similarly, x for superheated vapor results
will be set to 1. In the supercritical region, x may be 0 or
1. The "Region" note for the state point near the bottom of
the screen will advise you of the region.
Natural Convection Heat Transfer Coefficient
This term is a portion of the nondimensional Grashof Number
used for free convection heat transfer studies. The full term is:
Gr = BETAnc * ( L**3 ) * ( T - Tinf )
where
BETAnc = the term provided by STEAM'92
L = the dimensional length
T = the local fluid or body surface temperature
Tinf = the ambient fluid temperature
These terms are dimensioned such that Gr is nondimensional.
Where T - Tinf is large, it is recommended that this term
(as well as the Nusselt number) be evaluated at (T+Tinf)/2.
Units Coefficient
Some of the units have coefficients, or exponents with the units
name. This is intended to be read as a literal suffix to the
number showing in the cell: don't invert the sign, just assume
that it is a multiplier to the number showing.
Cv and Alpha:
The current release has incorporated new solvers for Cv and alpha
(isentropic compressibility), in the 2-phase region. These solvers
circumnavigate the calculational problems as well as accurate results.
The Very-Near Critical Region
Accurate and unconditionally consistent resolution of
properties in the critical region is a major strength of the
STEAM93/PC and /PGM implementations and has previously been a
long standing problem even in main frame programs. For
research purposes in the very near critical region an
alternative, "Scaled Fundamental" formulation is provided.
The analytic (IAPS'84) formulations are recommended and the
default option.
The region very-near the critical point is very difficult to
evaluate by any general purpose formulation even on mainframe
computers. The difficulty of calculation in this region is
largely due to the flatness of Zq/ZT within a degree or so of
the critical temperature.
For the IAPS'84 analytic formulation,
"It should be noted that state of the art measurements
for this region are consistent only to within ...
p/p = (2x10-4)
g/g = (2x10-5)
... for the region ...
200 < p < 280 Bars
160 < q < 450 kg/m3 "
(liberally paraphrased from [1])
As an option to using the IAPS'84 Formulation in this
difficult to evaluate region, an alternative is available
which uses the scaled fundamental equation recently
recommended by members or the NBS and presented to the IAPS.
"... the scaled fundamental equation is recommended in
cases where it is important that the surface, and in
particular its derivatives, display the physical
behavior predicted by the modern theory of critical
phenomena." [3]
This scaled fundamental formulation is valid in the region:
644 < T < 693 K
200 < q < 420 kg/m3
This formulation is quite fast and provides a level of
consistency difficult to achieve with the general fundamental
equation.
To remove potential inconsistencies in very-near critical
two-phase and vapor applications the range of application of
the scaled fundamental is adjusted upward slightly to:
645.37 < T < 693 K
When the toggle is on for use of the equation (Alt+C has been
hit and the "C" Key note is showing), the solution manager
will check to see if the analytic result is in the applicable
range for use. If it is within range, the scaled fundamental
equation will be used to calculate all state and property
values. When this formulation has been used, the Regn: note
(for the state point near the bottom of the screen) will show
"Criticl".
Be careful when you are working immediately on/near the
limits of the range of the scaled fundamental formulation.
There has been no attempt to remove the discontinuity in data
and derivatives at the boundary of the range. All values of
the data are, of course, within the specified physical
accuracy and consistency. However, the relative error change
across the border of applicability can appear large.
Range, Physical Accuracy, and Consistency
STEAM93/PC was designed to provide the most accurate and
consistent properties of steam available. STEAM93/PC has
been benchmarked to be identical in all significant digits
over the range of published data and tests or seven
significant digits, whichever is MORE accurate. NO
approximations have been introduced in the implementation of
the IAPS'84 formulations.
Table 2 is an overview of the stated accuracy and range of
the IAPS Formulation 1984 and transport formulations. It is
most significant that these are summaries of the comparisons
with the physical data and not calculational accuracy.
STEAM93 has been verified to all published significant digits
throughout the ranges of the published data for these
formulations.
The differences found in real applications occur with
comparisons with earlier less physically accurate
formulations. A detailed analysis of the physical accuracy
and comparison with other correlations can be found in
References [1] and [4].
STEAM93/PC and /PGM were written for process studies as well
as a standard properties reference. Therefore there is a
heavy emphasis on consistency as well as very high accuracy.
This consistency extends throughout the calculational range
of the program and the through the discontinuities. You can
test this consistency by inputting data for a state point
using output data from another point. You should find, as we
have, consistency to twelve significant digits.
As changes to the industry standards are published (including
the recent NBS publications), these will be incorporated if
necessary. You will be advised of the new release and if
changes have resulted which might change the accuracy or
reliably of the STEAM93/PC property data.
REFERENCES
1. L.Haar, J.S.Gallagher, & G.S.Kell, "NBS/NRC Steam
Tables", Hemisphere Publishing Co., N.Y., 1984.
2. C.A.Meyer, R.B.McClintock, G.J.Silvestri, R.C.Spencer,
"ASME Steam Tables", 5th Ed., ASME, N.Y., 1983.
3. J.Kestin, J.V.Sengers, B.Kamgar-Parsi, J.M.H.Levalt
Sengers, "Thermophysical Properties of Fluid H2O", Amer.
Chem. Soc., J. Phys. Chem. Ref. Data, Vol. 13, No. 1,
1984, (Reprint 242)
4. J.M.H.Levalt Sengers, B.Kamgar-Parsi, F.W.Balfours,
J.V.Sengers, "Thermodynamic Properties of Steam in the
Critical Region", Amer. Chem. Soc., J. Phys. Chem. Ref.
Data, Vol. 12, No. 1, 1983, (Reprint 214)
5. W.C.Reynolds, "Thermodynamics", 2nd Ed., McGraw-Hill,
N.Y., 1968. (Chpt. 8)
6. R.C.Reid, J.M.Prausnitz, T.K.Sherwood, "The Properties of
Gases & Liquids", 3rd Ed., McGraw-Hill, N.Y., 1977.
7. Hendricks, R.C., Peller, I.C., and Baron, A.K., "WASP - A
Flexible Fortran IV Computer Code for Calculating Water
and Steam Properties", NASA-TN-7391, 11/1973.
8. T.Baumeister, E.A.Avallone, T.Baumeister III, "Mark's
Standard Handbook for Mechanical Engineers", 8th Ed.,
McGraw-Hill, N.Y., 1978.
APPENDIX A SERVICE AND WARRANTIES
PRODUCT SERVICE
The program is supported by:
IMPULSE Engineering
B. R. Strong, Jr., P.E.
415 Arch Street
San Francisco, California 94132
(415) 239-0940 Office
(415) 229-2354 Fax
Internet: Thermo@hooked.net (daily)
Internet: ThermoRay@AOL.com (weekly)
Internet: 76260,1200@CIS.COM (weekly)
New versions of this program, incorporating new features and
capabilities, are regularly introduced as part of our new
product development program. We will notify registered users
whenever a new release is introduced. You have the option to
purchase the new release or upgrade the version at a discount.
This product has a limited warranty for 3 months from
purchase or receipt.
Please let us know if you have problems or wish a special
configuration of the program.
LIMITED WARRANTY
IMPULSE Engineering warrants that:
The program(s) and manual are complete and properly recorded;
The User's Manual is substantially complete and
contains all the information which is deemed
necessary for use of the program(s);
The program(s) functions substantially as described
in the Manual;
This limited warranty is for 3 months from purchaser's
receipt of the software and is extended only to the original
purchaser of the software.
IMPULSE Engineering excludes any and all implied warranties,
including warranties of merchantability and fitness for a
particular purpose and limits the end-user's remedy to return
of the software and User's Manual to the address above for
replacement.
IMPULSE Engineering specifically disclaims any other warranties, expressed or implied. In no event shall B.R.Strong,Jr. or
IMPULSE Engineering be liable for any loss of profit or any other commercial damage, including but not limited to special,
incidental, consequential, or other damages.
Governing Law
This warranty statement shall be interpreted, construed and
governed by the laws of the State of California.
(end)