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1. P3pt Triple point pressure 8 858914E 02 psia T3pt Triple point temperature 32 018 F PCpt Critical point pressure 3208 2347600665 psia TCpt Critical point temperature 705 47 F TSat Saturation temperature F Function amp Inputs Result Units Example ANYPT2 P T D Density Lb Cuft To obtain the entropy H Enthalpy Btu Lb of an H20 substance at P Pressure 5 Entropy Btu Lb R 6000 psia and 200 F from P 3pt to 15500 psia C Specific Heat Cp Btu Lb F enter ANYPT2S R Ratio of Specific Cp Cv 6000 200 and the T Temperature aV Heats Cuft Lb result will be from T3p F to 1500 F K Specific Volume Btu Hr ft F 0 287028 Btu Lb R U Thermal Conductivity Lb Sec ft Viscosity ANYPQ2 P Q D Density Lb Cuft To obtain the thermal H Enthalpy Btu Lb conductivity of an H20 P Pressure S Entropy Btu Lb R substance at 2600 Psia from P3pt to P cpt psia C Specific Heat Cp Btu Lb F and 80 quality enter R Ratio of Specific Cp Cv ANY P Q2K 2600 8 Q Quality V Heats Cuft Lb and your answer will be from 0 to 100 T Specific Volume oF 0 112809 Btu Hr ft F enter as 0 to 1 K Temperature Btu Hr ft F U Thermal Conductivity Lb Sec ft Viscosity ANYPH2 P H D Density Lb Cuft To obtain the density of S Entropy Btu Lb R an H20 substance at P Pressure Q Quality Percent 3000 psia and 500 from P3pt to 15500 psia C Specif
2. ecsseeeeeeeeeeeeeeeeeeeees 2 Metric Functions Begin With X cccccceceeeeeessseseeeeeeeeeeeeeeseeeeseaeees 3 Attaching the EndResult Hardware Key ccsscceeeseeeeeseeeeeeees 4 Installing the EndResult Add ins cccccccceeeseeeeeeeeeesteeeeseeeeeeees 5 Identifying the Cause Of an Error cecceeeceeeeeeeeeeeeeeeeeeeeeeeeteeeeeeees 5 Using Warnings dersinin aa A etd aaa aa a a okt Lenin ert neesacr ls 6 Add in Functions foto fab ee Beochedheame rect banctebrbehhelib each beboaderetenl EREXCEL 7 Mixed Gas Thermo Physical Property Add in ccceceeeeeeeeeeeeeeeteees 7 Computing Psychrometric Properties Using Relative Humidity nc eccocti ste tieerparener oan nretpanessesnnepes epearepaeseaaniee 15 Using Wet Bulb Temperature ccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeaaees 16 Steam and Water Property Add in cccceeeceeeeeeeeeeeeeeeeeeeeeeeeeeeeeee 17 Universal Functions so gs ae c13yccavenes sateen cca ytieyecpeheveenedunv ees vOensecevines 19 Region Specific PUNCHONS wis cesses ceticaiedes Seis ess etacetecelaceniuebacndeents 20 Saturation Pressure amp Temperature Functions ccccceeeeeeeees 21 Steam and Water Property Examples Worksheet cccecee 21 Boiler Efficiency Add in i 25 stool chaos sete pasasted caneciegpanessesonncpaenenepieasaacds 22 Moisture per Lb of Dry Ambient Air eeeeeeeeeeeeeeeeeeeee
3. function By entering your current units and desired units from the list below you can convert between any of the units shown in each category Examples appear on the following page Please note 1 If you enter pounds or Ib ERUNITS will assume you mean pounds mass Ibom 2 To enter pounds force you must specify either pounds force or Ibf and 3 The ERUNITS function converts all pounds and ounces according to the avoirdupois system of measure Area Square centimeters square feet square inches square kilometers square meters square miles Square yards Density mass density grams cubic cm grams cubic meter grams liter grams milliliter kg cubic meter lbm cubic foot lom cubic in lbm gallon milligrams liter Slugs cubic foot Energy Work ee of Heat calories foot lbf joules kW hr MetricHP hr USHP hr watt hr watt sec Enthalpy BTU lbm calories gram joules gram joules kilogram kilojoules kg megajoules kg Entropy Specific heat BTU lom F BTU lbm R cal gram C joules gram C kilojoules kg K Force dynes longtons or Iton newtons poundsforce or lbf Shorttons or ston Heating Value BTU cubic foot joules cubic meter cal cubic meter cal liter kilojoules cubic meter Length centimeters feet inches kilometers meters miles statute millimeters yards Mass Weight centigrams grams kilograms milligrams o
4. Copyright 1991 2003 by Sega Inc All rights reserved EndResult is a registered trademark of Sega Inc Add ins for Microsoft Excel English Unit Edition All rights reserved No part of this publication may be reproduced or distributed in any form or by any means without prior written permission of Sega Incorporated oSA Sega Inc 16041 Foster Stillwell Kansas 66085 913 681 2881 Fax 913 681 8475 www endresult com Software License Agreement The Sega Inc 16041 Foster Stilwell Kansas SEGA software and documentation Licensed Software is provided to you on the express condition that you agree to abide by the terms of this Software License Agreement The use of the Licensed Software by you constitutes acceptance of this License The Licensed Software that resides on diskette hard disk drive magnetic tape or any other device or media is licensed to you on a non exclusive basis for use ona SINGLE SYSTEM WITH A SINGLE USER AT A TIME The title copyright and proprietary rights to the Licensed Software are retained by SEGA You may not transfer sublicense rent lease convey copy other than a single working copy or modify the Licensed Software for any reason nor allow any other person to do so The Licensed Software is protected under copyright trade secret and other laws Unauthorized duplication transfer or modification of the Licensed Software is prohibited The term of this License
5. gt KJ Sulfur Dioxide SO9 in Wet Flue Gas WETSO2 K Likewise Carbon Dioxide in Wet Flue Gas in cell B43 could also be computed by entering each argument directly as in WETCO2 Dry Before 498 035 085 007 006 304 0 0576 48 7 6 65979E 04 N A N A 035 0005 N A 04 41 Hint To quickly enter the cell formulas in cells B37 to B40 enter the entire DRYCO2 function in cell B36 then copy it to cells B37 to B40 and then change each cell to the correct function Correct use of absolute references e g B 2 and relative references e g B2 will ensure that copied formulas have the desired references Cad EREXCEL 28 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Heat Loss Due to Radiation The RADLOSS and RADLOSS2 functions described in this section provide two separate methods for computing ABMA radiation loss in percent as fired fuel AFF for a boiler 69 Heat Loss Due To Radiation is the percent of heat energy in the fuel lost to surface radiation and convection off the outside skin of the boiler Heat Loss Due to Radiation increases as 1 the Number of Water Walls i e water cooled furnace walls decreases 2 the Air Velocity Around Boiler increases and 3 the Air to Boiler Temperature Delta i e difference increases The RADLOSS XLS worksheet from your Examples disk is shown below The inputs appear in the first 12 rows and the result appears in row 14 Cell B14 contain
6. 43 Fora discussion of the potential problems of trying to obtain a perfect fit see page Curve 17 and Curve 18 Sega EREXCEL 41 EndResult 2003 Sega Inc November 1 2002 English 2 Dimensional Data Modeling via Polynomials The POLY2DVAL function is used to model the data in a 2 dimensional table POLY2DVAL uses polynomial curve fits to interpolate between table values When modeling non linear data POLY2DVAL can estimate in between values more accurately than INTERP2D The POLY2D XLS worksheet from your EndResult Examples disk is shown below Cells C8 to G11 contain enthalpy values for pressures from 2000 to 2400 psia and temperatures from 800 F to 875 F For example the table shows us that the enthalpy of 850 F 2200 psia steam is 1363 3 Btu Lb The POLY2DVAL function requires five arguments POLY2DVAL table_range horiz_deg vert_deg horiz_val vert_val Argument 1 The first argument is the table range In the example below the table range is from cell B7 to G11 Your table must include from 3 to 101 columns and from 3 to 101 rows Arguments 2 5 The name of argument 2 3 4 and 5 appears in cells B2 through B5 and an example value for each argument appears in cells D2 through D5 A B Cc D E F G Pe Maximum horizontal degree Maximum vertical degree Horizontal value from 2000 to 2400 in table below Vertical value from 800 to 875 in table below Os o
7. From Two Points Square Curve Modeling Between Two Points Square Root Curve Modeling Between Two Points Sega Two Point Functions The following functions are helpful in situations when you have only two data points INTERP uses linear interpolation to determine the value of a line which passes through the x y7 and X2 y2 coordinates for the given value of x For example to obtain the value of a line which passes through the 0 10 and 100 3300 coordinates at the point x 72 enter INTERP 0 10 100 3300 72 and your answer will be 2378 8 if x lt x lt x then y INTERP x y 5X Y x EXTRAP uses linear extrapolation to determine the value of a line which passes through the x y and Xs 2 coordinates for the given value of x For example to obtain value of a line which passes through the 0 10 and 100 3300 coordinates at the point x 250 enter EXTRAP 0 10 100 3300 250 and your result will be 8235 if x SX or X2x then y EXTRAP x VY X Y X SQRXYXY returns the value of the square curve which passes through the x y and Xo Y2 coordinates for the given value of x For example to obtain the value of the square curve which passes through the 0 10 and 100 3300 coordinates at the point x 72 enter SQRXYXY 0 10 100 3300 72 and your answer will be 1715 536 y M x B y SQRXYXY x Y X Y 5X SQRTXYXY returns the value of the square root curve which passes thro
8. P T D Density Lb C uft To obtain the enthalpy Liquid H Enthalpy Btu Lb of liquid at 2000 psia and P ressure 5 Entropy Btu Lb R 400 F enter LIQ from P3pt to 15500 psia C Specific Heat Cp Btu Lb F LIQPTH 2000 400 R Ratio of Specific Heats Cp Cv and your answer will be T Temperature V Specific Volume Cuft Lb 377 1851 Btu Lb from T3pt F to Tsat F K Thermal Conductivity Btu Hr ft F U Viscosity Lb Sec ft WETP Q2 P Q D Density Lb C uft To obtain the entropy of H Enthalpy Btu Lb saturated steam at 1800 Saturated P Pressure S Entropy Btu Lb R psia and 45 quality m from P 3ptto Pc pt psia T Temperature F enter Stea j f C Specific Heat Cp Btu Lb F WETPQ2S 1800 45 WE T Q Quality R Ratio of Specific Heats Cp Cv and your answer will be from 0 to 100 V Specific Volume Cuft Lb 1 051466 Btu Lb R enter as 0 to 1 K Thermal Conductivity Btu Hr ft F U _ Viscosity Lb Sec ft Note The ratio of WETTQ2 T Q D Density Lb C uft To obtain the specific specific heats isnot remperat S Enmon ptubeR st200 F and 70 ually Temperature a ntropy u Lb a F an quality available under the from T3pt F to TCpt F P Pressure Psia enter conditions described in C Specific Heat Cp Btu Lb F WETTQ2V 200 7 and the appendix of the Q Quality aR Ratio of Specific Heats Cp Cv the result will be 23 55216 Flow Measureme
9. Po B x C x D x E x x F eliptic or hyperbolic Large Polynomial Po B x C x D x E x F x G x x H X X3 I x x3 In the polynomial equations above the highest power of an independent variable e g X1 X2 X3 etc in the equation is the Polynomial Degree shown in the rightmost column eoq EREXCEL 35 a D GOlo _ EndResult 2003 Sega Inc November 1 2002 English You should probably experiment with many different degrees of polynomial fits before deciding which polynomial model is the best Typically there is an optimum degree of fit for the polynomial Computing for degrees which are higher or lower than the optimum degree may decrease the desirability or accuracy of the fit The example graph below illustrates how a curve fit with a lower degree and a lower correlation coefficient may be a more suitable model for the data than a curve fit with a higher degree and a higher correlation coefficient This curve fit has a has a higher correlation coefficient but does not provide a suitable model of the data This curve fit has a lower correlation coefficient but provides a more suitable model of the data Taking the nth Derivative of a Model The table below demonstrates how you can take the nth derivative of a model by adding one or more d instructions to your model type type is discussed on page 32 If you have multiple indep
10. or per for division for multiplication a for power o1 wa The ERUNITS function analyzes each unit as a mathematical formula For example all of the following are equivalent and can be interconverted using ERUNITS kg m s 2 newton joule m watt s m Newton kg m s 2 watt s m Moreover all of the following units would be read as being equal m m m 2 m m m m m m m 2 m 2 1 m 2 1 m 2 0 etc If you want to know the conversion factor which ERUNITS is using to perform a particular conversion simply convert the value 1 For example ERUNITS 1 Lbm kg returns the conversion factor 45359237 If you enter an ERUNITS function and the cell returns N A you can move the cell pointer to the cell and select EndResult from the Microsoft Excel Help menu to display a brief explanation for why the error occurred e gd EREXCEL 46 a D GOlo _ EndResult 2003 Sega Inc November 1 2002 English
11. EA Rated Btu 400 from 1 to 10E 06 Mbtu Hr Number of Water Walls from 0 to 4 Air Velocity Around Boiler from 0 to 1800 Fpm Ea Air to Boiler Temperature Delta 50 from 0 F to 2000 F 69 Heat Loss Due to Radiation RADLOSS2 0 61718 AFF of gross heat input Likewise Heat Loss Due to Radiation in cell B7 can also be computed by entering each argument directly as in RADLOSS2 200 400 4 100 50 The HTWUNIT XLS worksheet provided on your EndResult Pre defined Spreadsheet Solutions disk demonstrates how the radiation loss RADLOSS2 add in function can be combined with other functions to compute boiler efficiency EREXCEL 30 EndResult 2003 Sega Inc November 1 2002 English Curve Fitting Add in General Model Types If you want to develop a square model ora square root model using only two points see the SQRXYXY and SQRTXYXY functions described on page 47 Sega The following table summarizes the general types of models which can be computed using the curve fitting add in functions and the minimum number of points for each model Where n the number of independent variables from 1 to 9 General Equation Minimum y Dependent Variable Number X X X tc Each Independent Variable of Points A A A etc Each Coefficient y A X A x const x 82 x 2 X See Modeling Using Polynomials on page 36 Unless you expect that your data points are d
12. INTERP and EXTRAP functions described on page 46 e gd EREXCEL 38 a D GOlo _ EndResult 2003 Sega Inc November 1 2002 English Computing Equations Longer than 255 Characters The longest equation which can be returned by the FITEQ function is 255 characters To obtain an equation which is longer than 255 characters you must use multiple EQAFRAGMENT functions If the equation is too long for FITEQ to display it will return an EQFRAGMENT line like that shown below Notice that this EQFRAGMEMT line indicates thatthe equation is composed of three fragments To return the entire function you must enter each EQFRAGMENT function into a separate cell as shown in cells B53 through B55 below Remember to replace point_range with the A B Cc D E F where your points example the point range on page 33 is A 1 B 19 To convert each EQFRAGMENT function to a live equation 1 Select the cells containing the EQFRAGMENT functions 2 Select EditCopy from the Excel menu 3 Move the pointer to an empty area in the worksheet and EditPaste Special and 4 Click the Values option button and then click OK A B Cc D E F The long equation to the gt 57 17 8371375215022 53 0912733397568 X 59 5706026033222 X 2 26 9864238073324 right was computed by fitting a 6 degree polynomial to gt 58 1 37678894596316 X 2 Y 0 770994294857225 Y 44 3 55348562565369 X Y3 the 100 po
13. T max 1500 Specific Heat Cp 7382281 Btu Lb F ANYPT2C P T Ratio of Specific Heats 1 349910 Cp Cv ANYPT2R P T coq EREXCEL 21 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Boiler Efficiency Add in The boiler efficiency add in contains functions which perform many of the calculations necessary for computing boiler efficiency and gas turbine performance including Moisture per Lb of Dry Ambient Air Specific Heat of Air Specific Heat of Flue Gas Combustion Calculations The boiler efficiency add in provides added flexibility by allowing you to either enter or compute many important quantities such as CO Oo H2O SOz Excess Air dry and wet gas constituents and air heater leakage Many of the calculations performed by the boiler efficiency add in are based on equations found in Steam Generating Units31 Power Test Code PTC 4 1 and formulations found in Steam Ilts Generation and Uses2 Individuals who are familiar with PTC 4 1 will find several of the example worksheets to be self explanatory Inputs and results which are the same as those on the PTC 4 7 short form test such as ENTHALPY OF WATER ENTERING are preceded by a number followed by an equal s sign e g 17 Enthalpy of Water Entering in both the EndResult example worksheets and the EndResult Reference Manual The COMBCYC XLS COGEN3 XLS GASTURB XLS GASTURBI XLS HTWUNIT XLS PKGBLR XLS and UTIL
14. accuracy of each type of fit to the points The best fitting model has the smallest maximum and average deviations and the argest correlation coefficient However since even curves with a good fit can include unexpected or undesirable changes in direction you should always graph your data along with each computed model to determine which curve fit is most appropriate applicable and realistic for your particular situation Developing Accurate Models You want to have as many data points as possible when developing an accurate model You should experiment with several different types of models to determine which model fits your data most appropriately The best way to do this kind of experimentation is by plotting each model ona graph For example if you are using a mathematical model for forecasting i e to predict values beyond the points which you currently know then you should test how different types of models react in the forecasted range by plotting each one ona graph The example graph on page 34 demonstrates how your computed results depend greatly on which type of model you choose G gd EREXCEL 37 a D GOlo _ EndResult 2003 Sega Inc November 1 2002 English Improving Accuracy by Modeling Small Regions Separately If your data points are scattered you may not be able to obtain a single equation which will fit all of the points with the desired accuracy In this case greater accuracy can be obtained by dividing your
15. each independent variable enclosed in quotes e g press 6 31 temp 7 31 Each independent variable name must appear in the top row of the point_range in all but the rightmost column fragment the nth part of an equation The beginning of the equation is always fragment 1 FITEQ returns the equation of the type model which fits the data in the spreadsheet FITEQ uses the independent and dependent variable names which you specified in the first row of your point_range Cell C23 on the following page contains the formula F ITEQ A 1 B 19 Poly2 which returns the equation of the 2nd order polynomial which fits the data points in the point range To obtain a live function 1 Select Edit Copy 2 Move the pointer to a different cell an EndResult 2003 Sega Inc FITEQ cont select Edit Paste Special 3 Click the Values option button and then click OK and 4 Insert an equals sign at the beginning of the equation FITVAL returns the value of the type model for the given values of the independent variables Cell E35 on page 34 contains the formula FITVAL A 1 B 19 exp x 72 which returns the value of the exponential model at x 72 The FITVAL function should only be used for spot checking Once your model is finished be sure to use the FITEQ function to convert the model to a live equation FITR2 returns the correlation coefficient r2 of the type m
16. it is greater than 1 24 The compressibility factor may be unrealistic if it is greater than 1 24 The density reference value may be unrealistic if it is greater than 100 The density value may be unrealistic if it is greater than 100 Sega EndResult 2003 Sega Inc EREXCEL 13 November 1 2002 English PCTBYVOL PCTBYWT GAS2PP GAS2TSAT and GAS2ZRA Function Computes an Individual Gas PCTBYVOL Percent by volume of the total gas mixture Percent by weight of the total gas mixture Partial pressure GAS2TSAT Temperature of saturation State at zero enthalpy reference and actual temp All five functions above require the same five arguments Arguments The first four arguments are the same as those listed on pages 1to 4 EREXCEL 8 and EREXCEL 9 Argument 5 The fifth argument must be one of the following gas names Acetylene Air Ammonia Argon Benzene Carbon Dioxide Carbon Monoxide Ethane Ethyl Alcohol Ethylene Hydrogen Gas Hydrogen Sulfide i Butane 1 Butene i Pentane Methane Methyl Alcohol n Butane cis 2 Butene n Heptane n Hexane n Nonane n Octane n Pentane 1 Pentene Neopentane Nitrogen Atmospheric Nitrogen Oxygen Propane Propylene Sulfur Dioxide Toluene o Xylene m Xylene p Xylene Water Vapor For example to compute the percent by volume of carbon dioxide of the total gas mixture cell B74 below contains the formula PCTBYVOL B 1 B 2 A 4 A 13 B 4 B 13 Carbon Dio
17. page 41 EREXCEL 32 November 1 2002 English Note To sort your points in either ascending or descending order select the entire table of points and use the Data Sort command gt Part of the FITXLS worksheet from your EndResult Examples disk is shown below A B E o e E EE EE 7 34 12 17 32 D E X 72 8 34 35 17 58 c Ty ee ee 7 16 68 08 56 89 17 68 19 57 69 18 70 88 60 49 19 74 73 65 05 27 Model Type Polynomial 1st Equation returned by FITEQ 17 7142520110828 1 04489704024574 X F 1 48114956107175 0 006 767229521 31612 X 0 0115013843515338 X 2 2 00069041435995 EXP 0 0507535135189556 X P 56 7239732569892 13 164884868393 X40 5 116 206639541582 39 3830687552381 LN X 0 00825314588685043 X42 10208656290306 Exponential Square Root Logarithmic Power Ga Co ka E Polynomial 2nd Z Ea Y 28 Inverse Y 63 2729139063545 1 195 43012344389 X e gd EREXCEL 33 aD GOlo _ EndResult 2003 Sega Inc November 1 2002 English The data points and equations from the previous page are shown on the graph below 100 yo Exponential Fit 50 Average Correlation Value at Power Fit 2nd Degree Polynomial Fit M 1st Degree Polynomial Fit M Square Root Fit Logarithmic Fit Inverse Fit Deviation FITMAXDEV FITAVGDEV Polynomial 1 11 2101 3 2109
18. perfect fit see page Curve 17 and Curve 18 Sega EREXCEL 40 EndResult 2003 Sega Inc November 1 2002 English Note To sort your x y points so that the x values are in either ascending or descending order select the table of x y points and use the Data Sort gt command DERIVSTR gt DERIWAL gt DERIVINDEX gt 1 Dimensional Data Modeling via Derivatives The chart below describes the functions for computing the first derivative of a least squares polynomial which is fit to a set of data points Where y an 1X 14 aox2 a1X AQ DERIVSTR x3 x99 ya y99 n X DERIVVAL x1 x99 y1 y99 1 x DERIVINDEX X1X99 V1 yoo Independent and dependent data point ranges which specify from 2 to 99 data points x1 y1 x2 y2 X3 Y3 Xm Ym Each range can be either a single row or single column of numbers In the spreadsheet below the independent x range is from cell A1 to A5 and the dependent y range is from cell B1 to B5 n the degree of the computed polynomial from which the derivative is taken from 1 to 8 However if m is the number of x y points and n gt m the function will compute a polynomial of degree m 1 x the value of the independent variable x the cell address enclosed in quotes of Re such as DERIVSTR returns the equation of the derivative of the nth degree polynomial which fits the data in the spreadsheet Cell B7 below contai
19. points into two or more groups and then modeling each group separately After you have divided your points you can make the transition between adjacent models smoother by forcing the models to overlap You can overlap adjacent models by putting points on both sides of the model border into each model s point_range The point_range is discussed on page 32 You can use the following procedure to determine when and where you should use multiple models Step 1 Select a model type e g Poly3 Poly4 etc which will provide the best fit for a of the data points Step 2 Use this model to compute the dependent variable for each of your known points Step 3 Compute the difference between the actual and computed values of the dependent variable for each of your known points Step 4 If the model deviates significantly from some of the points you may need to take these points out of the main group and model them separately Performing Linear Interpolation and Extrapolation To perform linear interpolation or extrapolation simply use the FITEQ point_range Poly1 function on page 32 to solve for a first degree polynomial After using the FITEQ function to compute the equation of the line you can compute points 1 between your known points i e interpolation or 2 beyond your known points i e extrapolation If you want to perform interpolation or extrapolation using only two points see the
20. pressure 3208 2347600665 psia Tcp Critical point temperature 705 47 F Tsat Saturation temperature F Function Result Example T2P T Saturation To obtain the saturation pressure Pressure of 79 F steam enter T2P 79 T Temperature and the answer will be from T3pt to Tcpt F 0 49049 1psia P2T P Saturation To obtain the saturation Temperature temperature of 2000 psia steam P Pressure enter P 2T 2000 and your answer from P 3nt to P cpt psia will be 635 8028 F Steam and Water Property Examples Worksheet Part of the STEAM XLS worksheet from your EndResult Examples disk is shown below The STEAM XLS worksheet provides a working example of all 79 steam and water property functions You can experiment with each function by entering numbers into the highlighted unprotected user input cells The minimum and maximum value for each input is displayed just beneath each input cell To compute steam density for example cell E16 contains the formula ANYPT2D B 16 B 20 The remaining results in column E are computed in a similar manner Density 5 8210023 Lb Cuft ANYPT2D P T A c omin 0 08859 aa Enthalpy 1529 1494 Btu Lb ANYPT2H P T pmax 15500 ae Entropy 1 5060786 Btu Lb R ANYPT2S P T 17 Spec Vol 0 1717917 Cuft Lb ANYPT2V P T a a Viscosity 2 529E 05 Lb Sec ft ANYPT2U P T min 32 018 Ther Cond 0 0681597 Btu Hr ft F ANYPT2K P
21. shall commence upon your initial use of the Licensed Software howe4ver this License may be terminated by SEGA in the event you are in breach of any provision of this License The License Agreement is the complete agreement and understanding of the parties with respect to the Licensed Software and supersedes all prior oral written or other representations or agreements The Licensed Software may not be exported outside the United States without the prior written permission of SEGA and if such permission is granted by SEGA the exportation of the Licensed Software shall be subject to the Export Administration Regulations of the United States Department of Commerce Cad EREXCEL A Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English EndResult E Limited Warranty Software License Agreement Continued SEGA WARRANTS THE MEDIA WHICH CONTAINS THE LICENSED SOFTWARE TO BE FREE OF DEFECTS IN MATERIALS AND WORKMANSHIP FOR A PERIOD OF 60 SIXTY DAYS FROM THE DATE OF YOUR RECEIPT OF THE LICENSED SOFTWARE IN THE EVENT OF NOTIFICATION WITHIN THE WARRANTY PERIOD OF DEFECTS IN MATERIALS OR WORKMANSHIP AND RETURN OF THE MEDIA TO SEGA AT ITS PLACE OF BUSINESS SEGA WILL REPLACE THE MEDIA YOUR REMEDY FOR BREACH OF THIS WARRANTY IS LIMITED TO REPLACEMENT AND SHALL NOT INCLUDE ANY OTHER DAMAGES INCLUDING BUT NOT LIMITED TO LOSS OF PROFIT SPECIAL INDIRECT INCIDENTAL CONSEQUENTIAL OR OTHER DAMAGES OR CLAIMS EXCEPT AS EX
22. sheen eon ree na hoe tee 44 Performing Unit Conversions v 25 occa csvocerein aie loca Aai eee alee ae eee 45 Overview The EndResult Steam Plant Engineering Tools add ins contain 169 functions which you can use just like built in Microsoft Excel functions You can use the EndResult add in to extend the capabilities of Microsoft Excel Versions 5 7 97 2000 and 2002 XP After the EndResult Steam Plant Engineering Tools add ins are loaded the EndResult functions work exactly like Microsoft Excel s built in functions EndResult functions can be used in any number of cells worksheets and macros and can even be combined with functions from other add ins An equals sign should be the first character in any cell containing an EndResult function In the example below two EndResult functions and an Excel F Function are used to determine a maximum value for enthalpy F B 55 gt 3208 235 CRTPT2H B 55 1500 S TMP T2H B 55 1500 Each EndResult function is described in this chapter and will appear in capital letters Arguments to each EndResult function appear in italics but actual arguments used in examples are not italicized For your convenience EndResult functions are provided for both English engineering units and metric engineering units English Functions Do not begin with X EndResult functions which use Quantity English units Metric units English engineering units DO Conductivity Bt
23. the ASHRAE Psychrometric Chart No 1 Normal Temperature and ASHRAE Psychrometric Chart No 2 Low Temperature in the appendix of the Boiler Efficiency chapter The wet bulb temperature cannot be greater than the dry bulb temperature To obtain the minimum wet bulb temperature use the function WETTEMP dry_bulb_temp 0 air_pressure For example if the dry bulb temperature is 65 F and the air pressure is 14 696 psia then the minimum wet bulb temperature is 40 977 F Cad EREXCEL 23 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English Specific Heat of Air The specific heat of air can be computed by the following two methods Method 1 The fast approximate and simplest method to compute specific heat of air at 14 696 psia is to use the function AIRT2C air_temperature In the AIR CP XLS worksheet from you Examples disk shown below cell B3 contains the formula AIRT2C B 1 The AIRT2C function reproduces the values given in Steam Generating Units35 Power Test Code PTC 4 1 Figure 3 The AIRT2C function is convenient and provides adequate accuracy in many situations A B Cc 1 Air temperature 400 from 0 F to 1000 F 2 3 Specific Heat of Air AIRT2C 0 24498 Btu Lb F Method 2 The slow but more rigorous method to compute the specific heat of air at any pressure is to use the mixed gas GAS2C function as described on pages EREXCEL 15 and EREXCEL 16 Specif
24. the Format Number list box to get Microsoft Excel to display the number as a percent or use the quick key combination lt CTRL gt Remember that Microsoft Excel allows you to adjust the number of displayed digits by 1 Adjusting the cell width of cells which have been formatted using the Format Number General command 2 Specifying the number of decimal places when formatting a range of cells using a fixed 0 00 scientific O 0O0E 00 or percent 0 00 format Several EndResult functions allow you to enter Not Applicable for one or more arguments in a function As shown by the examples below this can be accomplished by entering either NA N A or by leaving the argument blank XRADLOSS 1 5E 84 101000 30 5 10 1706 3396 1209 10200000 3023 3536 9250000 NA NA NA XRADLOSS 1 5E 84 101000 30 5 10 1706 3396 1029 10200000 3023 3536 9250000 N A N A N A XRADLOSS 1 5E 84 101000 30 5 10 1706 3396 1029 10200000 3023 3536 9250000 Cad EREXCEL 3 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English Attaching the EndResult Hardware Key Male End of the hardware key plugs into the computer parallel port EndResult hardware key Style One EndResult hardware key Style Two The EndResult hardware key sent with your EndResult software should support the Steam Plant Engineering Tools Add in in addition to all other EndResult add ins which
25. you have purchased The hardware key should be attached to the parallel printer port either LPT1 LPT2 or LPT3 of your IBM PC XT AT PS 2 or fully compatible computer f you are running EndResult under Microsoft Windows NT be sure to follow the instructions which start on page Installation 10 If the hardware key is incorrect or missing the following differences will be apparent 1 When the EndResult add ins are loaded a pop up window will notify you that the hardware key is missing 2 All EndResult functions within the Excel worksheet will return Key If you have purchased the EndResult Steam Plant Engineering Tools Add in and you are still having problems with your hardware key please contact Sega Inc immediately If the hardware key is incorrect or missing for more than 15 seconds any subsequent attempt to recalculate an EndResult function will return KEY After the hardware key is attached you can eliminate key errors in the worksheet by either 1 pressing F9 to recalculate the worksheet 2 moving the pointer to each Key cell and pressing F2 followed by lt ENTER gt to recalculate the cell 3 moving the pointer to inputs in the calculation chain and pressing F2 followed by lt ENTER gt to recalculate all cells which are dependent on the input If any EndResult function is displaying an error message e g N A KEY etc you
26. you want to enter each flue gas constituent s volumetric percent of a wet or dry flue gas sample 38 Arg If Flue Gas Measurement Selection If the Flue Gas Measurement Selection No is Dry enter the following is Wet enter the following 13 32 Carbon Dioxide in Dry Flue gas Before AH Carbon Dioxide in Wet Flue Gas before AH 14 33 Oxygen in Dry Flue Gas before air heater Oxygen in Wet Flue Gas before air heater 15 34 Carbon Monoxide in Dry Flue Gas before AH Carbon Monoxide in Wet Flue Gas before AH 16 Diluted Dry Gas CO3 after air heater Diluted Wet Gas CO3 after air heater 17 Diluted Dry Gas Oxygen after air heater Diluted Wet Gas Oxygen after air heater Note The higher the percent H and H20 in the fuel analysis the more difference there will be between a wet basis measurement and a dry basis measurement Generally analyzers classified as insitu in the gas stream provide wet basis moisture not condensed out of sample measurements However you will need to consult your analyzer manual to be sure Set the Air Heater Selection to None if you want to compute flue gas properties for a boiler without an air heater you want to compute flue gas properties for a boiler with an air heater and are not interested in the performance i e leakage etc of the air heater Set the Air Heater Selection to Before to compute flue gas properties before an existing air heater Set the Air Heater Selection to After
27. 000 4 46000 100 50 733 5924 1460 3950 442 5746 4640000 1299 7101 1520 2431 4200000 CQd EREXCEL 29 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English The Actual Btu cannot be greater than the rated Btu For standard radiation loss enter an air velocity around boiler for 100 FPM and an Air to Boiler Temperature Delta of 50 F Sega Although RADLOSS is not compensated for superheat or reheat spray flow because of the nature of radiation loss on large boilers the error is considered negligible However if you prefer you can calculate the maximum boiler heat output and the actual heat output and use RADLOSS2 The PKGBLR XLS and UTILBLR XLS worksheets provided on your EndResult Pre defined Spreadsheet Solutions disk demonstrate how the radiation loss RADLOSS add in function can be combined with other functions to compute boiler efficiency The PKGBLR XLS worksheet computes the efficiency of a boiler without a reheater and the UTILBLR XLS worksheet provides a demonstration of an efficiency calculation for a boiler with a reheater The RADLOSS2 XLS worksheet from your EndResult Examples disk is shown below The inputs appear in the first 5 rows and the result appears in row 7 Cell B7 contains the formula RADLOSS2 B 1 B 2 B 3 B 4 B 5 ASME numbers where applicable appear in column A and valid ranges for each input are listed in column C EA Actual Btu w from 1 to 10E 06 Mbtu Hr
28. 02 English Standard Conditions Actual Conditions Standard Conditions gt Actual Conditions To compute the ultimate analysis carbon cell B15 contains the formula GAS2CAR B 1 B 2 A 4 A 13 B 4 B 13 The GAS2CAR function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The results in cells B16 through B20 are computed in a similar manner using the same arguments and the function indicated in column A A B Ultimate Analysis Carbon GAS2CAR 4 683946 Ultimate Analysis Hydrogen GAS2HYD 540460 Ultimate Analysis Oxygen GAS20XY 23 859626 Ultimate Analysis Nitrogen GAS2NIT 70 772360 Ultimate Analysis Sulfur GAS2SUL 0 143609 Ultimate Analysis Total GAS2TOT 100 000000 To compute the higher heating value cell B22 contains the formula GAS2HHVSCF B 1 B 2 A 4 A 13 B 4 B 13 The GAS2HHVVSCF function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The results in cells B23 through B28 are computed in a similar manner using the same arguments and the function indicated in column A Higher Heating Value Reference SCF GAS2HHVSCF Btu Cuft Higher Heating Value ACF GAS2HHVACF Btu Cuft EE Higher Heating Value GAS2HHV o Btu Lb ea Lower Heating Value Reference SCF GAS2LHVSCF a Btu Cuft Lower Heating Value ACF GAS2LHVACF Btu Cuft Lower Heating Value GAS2LHV Btu Lb Theoretical Air per Lb As Fired Fuel GAS2A
29. 2 Low Temperature in the appendix of the Boiler Efficiency chapter 29 The wet bulb temperature cannot be greater than the dry bulb temperature To obtain the minimum wet bulb temperature use the function WETTEMP dry_bulb_temp 0 air_pressure For example if the dry bulb temperature is 110 F and the air pressure is 14 696 psia then the minimum wet bulb temperature is 60 419 F Sega EREXCEL 16 November 1 2002 English EndResult 2003 Sega Inc Steam and Water Property Add in The steam and water property add in includes functions for computing a variety of steam and water properties including density entropy enthalpy viscosity pressure temperature quality specific heat ratio of specific heats thermal conductivity specific volume saturation pressure and saturation temperature EndResult s steam and water property calculations are based on formulations found in ASME Steam Tables 0 and are similar to those described in the Steam Tables Properties chapter Each function has been tested to ensure that it produces the same values as the ASME Steam Tables All of the EndResult steam and water property functions use a similar format to the example shown below A cell formula should only have one equals sign at the beginning No others are required 1st 2nd ist 2nd input input Result Argument Argument to o v v Se RIN E LRA SEN Symbol Legend C Specific heat D Density H Entha
30. 52E 2 Lb Lb Absolute Humidity GAS2HMA 1 828890E 3 Lb Cuft Specific Heat Cp 7 GAS2C 24681362 Btu Lb F Volume Weight owo srorevwr 94 8311 96 7211 To compute the Relative Humidity28 cell C136 contains the formula GAS2RH C 130 C 131 A 133 A 134 C 133 C 1 34 GAS2RH air_pressure dry_bulb_temp Ident_Range Value_Range The same arguments as shown in the GAS2RH function above can be used to perform the calculations shown in cells rows 137 through 146 The first two arguments must be the pressure and dry bulb temperature of the atmospheric air and the last two arguments must be the Identifier and Value Ranges in which you have specified the Wet Bulb Temperature29 The only other item which you are allowed to specify in you Identifier and Value Ranges is the Zero Enthalpy Temperature A Zero Enthalpy Temperature of 32 018 F will be used if not otherwise Specified For more detailed instructions on specifying the Identifier and Value Ranges see pages EREXCEL 8 and EREXCEL 9 If you need a faster method for computing the specific heat of air the AIRT2C function on page EREXCEL 24 provides a fast and simple way to obtain an approximate value for the specific heat of air at 14 696 psia 28 Fora chart of relative humidity versus dry bulb temperature and wet bulb temperature see the ASHRAE Psychrometric Chart No 1 Normal Temperature and ASHRAE Psychrometric Chart No
31. A and valid ranges for each input are listed in column C The Flue gas Measurement Selection pertains to the flue A gas measurements shown on rows 13 through 17 below gt 1 Flue Gas Measurement Selection Dry either Wet or Dry The Air Heater Selectioh determines whethereach gt 2 Air Heater Selection Before either Before After or None result described on pages 27 and 28 applies to conditions 3 43 Ultimate Analysis Carbon 49 8 from 0 to 100 by Weight before the air heater after the air heater or to a boiler without an air heater None 4 44 Ultimate Analysis Hydrogen 3 5 from 0 to 100 by Weight Argument 3 must be the 5 45 Ultimate Analysis Oxygen from 0 to 100 by Weight Ultimate Analysis Range In gt this example the ultimate 6 46 Ultimate Analysis Nitrogen from 0 to 100 by Weight analysis is the shaded region to the right 7 47 Ultimate Analysis Sulfur from 0 to 100 by Weight Your fuel ultimate analysis gt ash is assumed by the add in 8 37 Ultimate Analysis Moisture 30 4 from 0 to 100 by Weight to be 100 minus the total of the specified ultimate 9 22 Dry Refuse per Lb As Fired Fuel 0 0576 from 0 to 1 Lb Lb analysis constituents 10 23 Btu per Lb in Refuse Wtd Avg 48 7 from 0 to 14500 Btu Lb 11 Moisture per Lb of Dry Ambient Air 6 6598E from 0 to 081 Lb Lb 4 12 36 Percent Excess Air from 100 to 15000 or N A Before air he
32. BLR XLS worksheets provided on your EndResult Pre defined Spreadsheet Solutions disk demonstrate how you can use the calculations for combustion moisture per pound of air specific heat of air and specific heat of flue gas to compute boiler efficiency The COMBCYC XLS COGEN3 XLS GASTURB XLS GASTURBI XLS HTWUNIT XLS PKGBLR XLS worksheets compute the combustion products of boilers and gas turbines without an air heater and the UTILBLR XLS worksheet computes the efficiency of a boiler with an air heater 31 Steam Generating Units Power Test Code PTC 4 1 New York American Society of Mechanical Engineers 1974 32 Babcock amp Wilcox Steam Its Generation and Use 40th Edition New York Babcock amp Wilcox Company 1992 Section 6 Sega EREXCEL 22 EndResult 2003 Sega Inc November 1 2002 English Method 1 Default is 14 696 psia if gt pressure is omitted 34 Method 2 Method 3 Default is 14 696 psia if pressure is omitted gt Method 4 Moisture per Lb of Dry Ambient Air33 The moisture per pound of dry ambient air can be computed by the following four methods using either relative humidity Methods 1 amp 2 or wet bulb temperature Methods 3 amp 4 The fast approximate and simplest method to compute moisture per pound of dry ambient air for a given relative humidity and pressure is to use the function H2ONAIR dry_bulb_temp rel_humidity air_pressure In the MOISTURE XLS worksh
33. IR Lb Lb 11 Hint To quickly enter the cell formulas in cells B15 to B20 enter the GAS2CAR function in cell B15 then copy it to cells B16 to B20 and then change each cell to the correct function Correct use of absolute references e g B 2 and relative references e g B2 will ensure that copied formulas have the desired references Sega EREXCEL 10 EndResult 2003 Sega Inc November 1 2002 English To compute the reduced temperature cell B30 contains the formula GAS2RT B 1 B 2 A 4 A 13 B 4 B 13 The GAS2RT function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The remaining results in cells B31 through B35 are computed in a similar manner using the same arguments and the function indicated in column A 12 A B Cc 30 Reduced Temperature GAS2RT 2 4090887 31 Reduced Pressure GAS2RP 1 863681E 2 32 Critical Temperature GAS2TC amasa oR 33 Critical Pressure GAS2PC 788 54691 Psia 34 Critical Volume GAS2VC 4 821743E 02 Cuft Lb 35 Critical Compressibility GAS2ZC 0 2846665 eel The following 6 items are only results if water vapor is present otherwise these items will return N A To compute the water vapor partial pressure cell B37 contains the formula GAS2H2OPP B 1 B 2 A 4 A 13 B 4 B 13 The GAS2H2OPP function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The remaining results in cells B38 through B42 are computed in a sim
34. PRESSLY PROVIDED IN THIS SOFTWARE LICENSE AGREEMENT THE LICENSED SOFTWARE IS PROVIDED ON AN AS IS BASIS SEGA SPECIFICALLY DISCLAIMS ALL OTHER WARRANTIES EXPRESS OR IMPLIED INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE SEGA SHALL IN NO EVENT BE LIABLE FOR ANY LOSS OF PROFIT OR ANY OTHER COMMERCIAL DAMAGE INCLUDING BUT NOT LIMITED TO SPECIAL INDICREC INCIDENTAL CONSEQUENTIAL OR OTHER DAMAGES EVEN IF SEGA HAS BEEN ADVISED AS TO THE POSSIBILITY OF SUCH DAMAGES IN NO EVENT SHALL SEGA S LIABILITY HEREUNDER IF ANY EXCEED THE PURCHASE PRICE PAID FOR THE LICENSED SOFTWARE SOME STATES MAY NOT RECOGNIZE THE FOREGOING LIMITED WARRANTY LIMITATION OF REMEDIES OR LIMITATION OF LIABILITY AND IF YOU QUALIFY YOU MAY HAVE DIFFERENT OR ADDITIONAL RIGHTS AND REMEDIES YOU SHOULD CONSULT THE APPLICABLE LAW IN YOUR STATE IN THIS REGARD THIS AGREEMENT SHALL BE GOVERENED BY KANSAS LAW coq EREXCEL B GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Add ins for Microsoft Excel Fy dResylt Vi Ver 5 7 97 2000 amp 2002 XP for Windows Table of Contents Software License AQre Ment ccccccceeeeeeseeeeeeeeeeeeeeeeeeeeeeeneeeeeees EREXCEL A Limited ales id ea Saeererer ener eRe en teeth eee ere a entre Pten eet een were ener ees EREXCEL B COVE TWIG W di eile ates feces trees ce uss a a a rE EE EREXCEL 2 English Functions Do not begin with X
35. Polynomial 7 5943 2 0504 2 Exponential 23 7425 5 2464 Square Root 12 7402 4 7785 Logarithmic 13 8673 Coefficient FITR2 0 959092 0 984010 0 923115 0 925357 0 875620 X 72 FITVAL 57 5183 61 5916 77 3040 54 9838 52 2216 Power 8 1316 0 976033 66 2054 Inverse 17 7737 ap SEQGAe_ EndResult 2003 Sega Inc 0 739488 46 6697 EREXCEL 34 November 1 2002 English Modeling Using Polynomials The following table lists the minimum number of points which you must enter to compute polynomial equations of various degrees with various numbers of independent variables Number of Inde pendent Variables oOANOO POND o oANOO PWN GSRBNGTSOw I l I I l l l NNN NO BO O ok So I l I I I l l l Additionally the rightmost column of the table above shows the maximum degree polynomial which can be computed by the curve fitting add in functions due to the number of independent variables The following table contains several commonly used polynomial models which can be computed using the curve fitting add in functions Numberof Minimum Polynomial Equations Model Independent Number y Dependent Variable Polynomial Types Variables of Points x x x etc Each Independent Variable Degree 1 to 9 A B C etc Each Coefficient 1 to 9 Po PO B x C Po 3 B x 2 C x D Po Jt B x C x D x E Po B x C Paraboloid
36. The MIXGAS XLS worksheet from your EndResult Examples download file is shown below and on the following pages The name of each argument appears in cells A1 to A13 and an example value for each argument appears in cells B1 to B13 Valid ranges for each input are listed in column C The second argument can A 2 c Be either Temperature Enthalpy or Entropy 1 Pressure 14 696 from 2 25E 14 to 3208 235 Psia See the following page For more information gt 2 Temperature 364 0922 from 425 F to 4000 F 3 4 Babcock amp Wilcox Steam Its Generation and Use 40th Edition New York Babcock amp Wilcox Company 1992 Section 6 5 Richard W Miller Flow Measurement Engineering Handbook New York McGraw Hill Book Company 1983 6 International Formulation Committee The 1967 Formulation for Industrial Use ASME Steam Tables Fifth Edition New York American Society of Mechanical Engineers 1873 Appendix 1 pages 11 29 7 T E Daubert and R P Danner ed Physical and Thermodynamic Properties of Pure Chemicals Data Compilation New O York Hemisphere Publishing Corporation 1991 Faires Thermodynamics New York The MacMillan Company 1957 Fan Engineering New York Buffalo Forge Company 1983 ASHRAE Psychrometric Chart No 1 amp No 2 American Society of Heating Refrigerating and Air Conditioning Engineers Inc 1963 coq EREXCEL 7 GD GOlo _ EndResult 2003 Sega Inc No
37. ach argument directly as in placement of the DRYCO2 Dry Before 498 035 085 007 006 304 0 0576 48 7 braces 6 65979E 04 N A N A 035 0005 N A 04 The dry flue gas constituents in cells B36 through B40 are computed by the Total Gas method which assumes that SOo is not condensed out with H2O To compute the carbon dioxide in dry flue gas by the Total Gas method cell B36 contains the formula DRYCO2 B 1 B 2 B 3 B 8 B 9 B 10 B 1 1 B 12 B 13 B 14 B 15 B 16 B 1 7 The remaining dry flue gas constitutents in cells B37 through B40 are also computed by the Total Gas method using the same arguments 41 a B sremooniconnorrcos vent fase ova 2 eeno vee eas Sova 39 Note The addin 35 Nitrogen No in Dry Flue Gas DRYN2 80 83483 by Vol assumes that 100 of the sulfuris 40 Sulfur Dioxide SO in Dry Flue Gas DRYSO2 0 07041 by Vol burned to yield only SO 41 Total 100 00000 by Vol To compute the carbon dioxide in wet flue gas cell B43 contains the formula WETCO2 B 1 B 2 B 3 B 8 B 9 B 10 B 11 B 12 B 13 B 14 B 15 B 16 B 17 The remaining wet flue gas constituents in cells B44 through B48 are computed in a similar manner using the same arguments A B c ae E Carbon Monoxide CO in Wet Flue Gas WETCO 46 Nitrogen N9 in Wet Flue Gas WETN2 71 54016 by Vol Water Vapor H90 in Wet Flue Gas WETH20 11 49835 by Vol See note above
38. ars in rows 19 through 48 of the spreadsheet on the following pages Each function uses the inputs from rows 1 through 17 on page EREXCEL 25 38 For instructions on Converting a Wet Basis Sample to a Dry Basis Sample using the Mixed Gas Thermo Physical Properties application see page MixGas 12 39 ASME number applicable only if Flue Gas Measurement Selection is Dry Sega EREXCEL 26 November 1 2002 English EndResult 2003 Sega Inc To compute the Carbon burned per Lb As Fired Fuel cell B19 contains the formula CARBURNED B 1 B 2 B 3 B 8 B 9 B 10 B 11 B 12 B 13 B 14 B 15 B 16 B 17 The results in cells B20 through B28 are computed in a similar manner using the same arguments 40 A B c 19 24 Carbon burned per Lb As Fired Fuel CARBURNED 20 Dry Air per Lb As Fired Fuel AFF DRYAIR 21 36 Percent Excess Air EXCESSAIR 19 3790 Percent 22 25 Dry Gas per Lb As Fired Fuel ASME DRYGAS 23 Wet Air per Lb As Fired Fuel AFF WETAIR 24 Dry Gas Including Fly Ash Wt Basis BALDRY 8 1885761 25 Dry Gas Excluding Fly Ash Wt Basis MOLEDRY 8 1811761 26 Wet Flue Gas Including Fly Ash Wt Basis WETGAS 8 8106093 27 Wet Flue Gas Excluding Fly Ash Wt Basis MOLEWET 8 8032093 Lb Lb 28 Air Heater Leakage Actual LEAKAGE 2 57876 by Wt Likewise Carbon Burned per Lb As Fired Fuel in cell B19 could also be computed by entering each argument directly as in Notice the Oe brace
39. ater gt 13 32 Carbon Dioxide in Flue Gas Before AH from 0 to 20 9 by Vol or N A Before air heater gt 14 33 Oxygen in Flue Gas Before AH from 0 to 20 9 by Vol or N A a Before air heater gt 15 34 Carbon Monoxide in Flue Gas Before AH from 0 to 20 9 by Vol After air heater gt 16 Diluted Carbon Dioxide after Air Heater from 0 to 20 9 by Vol or N A 17 Diluted Oxygen after Air Heater from 0 to 20 9 by Vol or N A t a E 19 24 Carbon burned per Lb As Fired Fuel 4978065 Lb Lb Each combustion calculation add in function requires the same arguments as the CARBURNED function in cell B19 To compute the Carbon burned Notice that argument per Lb as Fired Fuel cell B19 contains the formula CARBURNED B 1 a Sen ee ape ee a r ewer tne B 17 After air heater gt 36 See table on page EREXCEL 26 for explanation 37 ASME number applicable only if Flue Gas Measurement Selection is Dry Cad EREXCEL 25 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English Argument 1 A Wet flue gas sample contains water vapor whereas a dry flue gas sample is water vapor free Argument 2 Argument 3 Arguments 7 12 Before air heater gt Before air heater gt Before air heater gt After air heater gt After air heater gt As shown in the table below set the Flue Gas Measurement Selection according to whether
40. can display a brief explanation for the error by moving the cell pointer to the cell containing the error message and selecting EndResult from the Microsoft Excel Help menu Note The absence of the hardware key only affects EndResult functions Microsoft Excel as well as add ins sold by other vendors will still function normally with or without the EndResult hardware key Since the Steam Plant Engineering Tools Add in is not copy protected you may make the number of backup copies of the add in stipulated in the preceding Software License Agreement However since only one key is provided with each original copy only one copy of the add ins can be run at any one time Cad EREXCEL 4 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Installing the Add in Files on Your Hard Disk Please reference the latest readme file for installation instructions This can be found at www endresult com Also available for download are the Examples Spreadsheets and the Pre Defined Spreadsheet Solutions Identifying the Cause of an Error If a cell containing an EndResult Steam Plant Engineering Tools function displays an error message e g N A HKEY etc you can move the cell pointer to the cell and select EndResult from the Microsoft Excel Help menu to display a brief explanation for why the error occurred Remember that you can select EndResult from the Help menu by using the mouse
41. cell F78 contains the formula GAS2ZRA B 1 B 2 A 4 A 13 B 4 B 13 Water Vapor For most common combustion air and flue gas applications if you ask the GAS2ZRA function for the state of H O the letters returned by the GAS2ZRA function will include Z and R indicating that H O is a liquid at both the zero enthalpy conditions and reference conditions Since the mixed gas add in is linked to the ASME steam tables the enthalpy and entropy contribution from H O should still be correct even if H O is a liquid at these conditions However if one of the letters returned by the GAS2ZRA function is a letter A i e actual conditions the results computed by the add in may not be valid Notice to users of previous versions of the EndResult add ins The GAS2H20O function for computing Ultimate Analysis Moisture is obsolete and should not be used To insure compatibility with worksheets developed using previous versions of EndResult the GAS2H2O function will ALWAYS return zero and will not return an error Additionally the Analysis Compensated or Uncompensated option is obsolete and should not be used To insure compatibility with worksheets developed using previous versions of EndResult any appearance of Analysis Compensated or Uncompensated within a mixed gas calculation will be ignored and the analysis will ALWAYS be uncompensated coq EREXCEL 9 GD GOlo _ EndResult 2003 Sega Inc November 1 20
42. computation method the molecular weights and the energy conversion constants used by this add in are based on data and equations found in Steam Its Generation and Use 4 m The gas compressibility is computed using the Redlich Kwong method Viscosity is computed using Arnolds Correlation and the square root rule m Critical properties computed by this add in are based on formulations found in the Flow Measurement Engineering Handbook Enthalpy and entropy of water vapor are from the ASME Steam Tables m Additional gas properties are computed from formulations found in the Physical and Thermodynamic Properties of Pure Chemicals Thermodynamics8 Fan Engineering9 and the ASHRAE10 Psychrometric Charts Both the COMBCYC XLS and GASTURB XLS worksheets provided in the www endresult com Pre defined Spreadsheet Solutions download file demonstrate how the mixed gas thermo physical property add in functions can be combined with other functions to compute boiler efficiency gas turbine heat rate and properties of the combustion air and flue gas For a working example of all of the mixed gas thermo physical property functions shown below load the MIXGAS XLS worksheet provided in the www endresult com Examples download file The MIXGAS XLS worksheet provides an easy way to familiarize yourself with each EndResult function You can experiment with each function by entering numbers into the highlighted unprotected user input cells
43. ct EndResult from the Microsoft Excel Help menu and a pop up window does not appear the EndResult add in is not properly installed m You cannot access Help EndResult messages if your document is protected AND your cell pointer is on a locked cell You must either unprotect the document or unlock the cell before selecting EndResult from the Microsoft Excel Help menu Using Warnings EndResult functions can also provide information in the form of Warnings Whereas an error causes an EndResult function to return an error message e g N A KEY etc a warning still allows the function to compute a result To determine if an EndResult function is causing a warning move the cell pointer to the cell and select EndResult from the Help menu This will cause either a list of warnings or the message No error or warning in this cell to appear Remember that you can select EndResult from the Help menu by using the mouse or by pressing lt ALT gt H R on the keyboard Lastly if an EndResult function evokes one or more errors and one or more warnings the errors will always be listed first Cad EREXCEL 6 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Add in Functions Mixed Gas Thermo Physical Property Add in The results computed by the Mixed Gas Thermo Physical Properties add in are based on formulations from the following sources m The ultimate analysis
44. ctions on specifying the Identifier and Value Ranges see pages EREXCEL 8 and EREXCEL 9 an Absolute Humidity 25 If you need a faster method for computing the specific heat of air the AIRT2C function on page EREXCEL 24 provides a fast and simple way to obtain an approximate value for the specific heat of air at 14 696 psia 26 Fora chart of relative humidity versus dry bulb temperature and wet bulb temperature see the ASHRAE Psychrometric Chart No 1 Normal Temperature and ASHRAE Psychrometric Chart No 2 Low Temperature in the appendix of the Boiler Efficiency chapter EREXCEL 15 November 1 2002 English EndResult 2003 Sega Inc Sega Computing Psychrometric Properties Using Wet Bulb Temperature applies to enthalpy and entropy default is 32 018 F gt Water Vapor in Dry Air gt Water Vapor in Moist Air Water Vapor in Moist Air gt Ideal Gas gt 27 The worksheet below demonstrates how to compute the properties of atmospheric air with a given wet bulb temperature A B c D E F Dry Bulb Temperature 110 from 80 F to 200 F Wet Bulb Temperature 90 from 56 7658 F to 110 F from 425 F to 4000 F Zero Enthalpy Temperature Relative Humidity GAS2RH 48 65026 Percent Reference Pressure GAS2REFP 14 696 Pia Reference Temperature GAS2REFT 60 Humidity Ratio GAS2HMR_ 3 386498E 2 Lb Lb Specific Humidity GAS2HMS 3 2788
45. d 2 columns of numerical data Arguments An example value for arguments 2 and 3 i e horizontal and vertical 2 amp 3 value appears in cells D2 and D3 respectively A B G Note INTERP2D will 1 even work with an incomplete table For 2 Horizontal value 2250 from 2000 to 2400 in table below example if cell G6 is blank INTERP2D will 3 Vertical value 865 from 800 to 875 in table below still interpolate between the remaining 4 gt pong 5 blank 2300 2400 6 l 800 1316 7 1310 1 7 Temp 825 1338 0 1332 1 8 l 850 1358 1 1352 8 9 875 1391 3 1386 7 1382 0 1377 2 1372 4 10 11 Estimated enthalpy 1372 058 The example worksheet uses the INTERP2D function to estimate the enthalpy of 2250 psia 865 F steam Cell D11 above contains the formula INTERP2D B 5 G 9 D 2 D 3 As shown above the enthalpy computed by INTERP2D is 1372 058 Btu Lb which is only slightly different from the actual enthalpy of 1372 16265 Btu Lb Although INTERP2D is not as accurate as POLY2DVAL for in between points INTERP2D is exactly correct for the points included in the table and it executes faster than POLY2DVAL The OILVISC XLS worksheet provided in your EndResult Pre defined Spreadsheet Solutions disk demonstrates a use of the INTERP2D function e qd EREXCEL 43 aD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Simple Interpolation Between Two Points Simple Extrapolation
46. eeeeeeees 23 Specific Meal Ol Milas een hath ane ier olka eis 5 rors clei 24 Specific Heat of Flue Gas ath Aee eee et eee 24 Combustion Calculations ccccccccceceeeeeeeeeeeeeeeeeeeeeenneeeeeeeeeeeeee 25 Heat Loss Due to Radiation ccccccccccceeeeeeeeeeeeeneeeeeeeeeeeeeeeeeneees 29 C me Fitting Add M a aa aeoea ea Ea ce Ea DEENA E EAE SEENE 31 Curve Fitting Add in Functions ise ce ac cavgsevesescee es caverevecavgusseqsgctveense ees 32 Modeling Using Polynomials cicr side cts ciscelaceuevesaccteceis ciateinucbanize 35 Taking the nth Derivative of a Model eccceeeeeeeeeeeeeeteeeeeees 36 Determining the Accuracy of the Fit eeeeeeeeeeeeeeeeeeeeeeeeeeeeeees 37 Developing Accurate Models ccccccceeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeneees 37 Improving Accuracy by Modeling Small Regions Separately 38 Performing Linear Interpolation and Extrapolation 0000 38 Computing Equations Longer than 255 Characters cccccee 39 1 Dimensional Data Modeling via Polynomials 00ceeee 40 1 Dimensional Data Modeling via Derivatives seeeeees 41 Cad EREXCEL 1 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English 2 Dimensional Data Modeling via Polynomials eeeeeeeees 42 2 Dimensional Data Modeling via Interpolation eeeeeees 43 Two Point FUNGOS 24 intr tes cis a ta
47. eet from your Examples disk shown below cell B4 contains the formula H2ONAIR B 1 B 2 B 3 Ambient air relative humidity 65 from 0 to 100 0 to 1 Ambient air pressure 14 696 from 2 25e 14 to 15 472 psia 4 Moisture per Lb of Dry Ambient Air 5 3115E 03 Lb Lb A Cc Ambient air dry bulb temperature from 80 F to 200 F The slower but more rigorous method to compute moisture per pound of dry ambient air i e Humidity Ratio for a given relative humidity and pressure is to use the GAS2HMR function as described on page EREXCEL 15 The fast approximate and simplest method to compute moisture per pound of dry ambient air for a given wet bulb temperature34 and pressure is to use the function HEONAIRW dry_bulb_temp wet_bulb_temp air_pressure In the MOISTURE XLS worksheet from your Examples disk a below cell B9 contains the formula H2ZONAIRW B 6 B 7 B 8 A c Ambient air dry bulb temperature from 80 F to 200 F Ambient air wet bulb temperature from 40 977 F to 65 F e Ambient air pressure from 2 25e 14 to 15 472 psia 9 Moisture per Lb of Dry Ambient Air 8 6698E 03 Lb Lb The slower but more rigorous method to compute moisture per pound of dry ambient air i e Humidity Ratio for a given wet bulb temperature34 and pressure is to use the GAS2HMR function as described on page EREXCEL 16 33 Fora graph of moisture per pound of dry ambient air see
48. endent variables in your model then you can obtain the nth partial derivative with respect to one or more independent variable s Example Formulas Examples Explained FITEQ A 1 B 19 Poly4 d X 2 Computes the equation of the 2nd derivative with respect to X of the 4th degree polynomial FITVAL A 1 B 19 Poly5 d A 2 Computes the value of the 2nd d B A 3 B 5 derivative with respect to A and the 1st derivative with respect to B of the 5th degree polynomial at the value A 3 and B 5 FITEQ A 1 B 19 Poly4 d X d X Computes the equation of the 2nd derivative with respect to X of the 4th degree polynomial Since there is no reason to compare your original points to a derivative of your model the FITR2 FITAVGDEV and FITMAXDEV functions will return N A if you have any d instructions in your model type eoq EREXCEL 36 a D GOlo _ EndResult 2003 Sega Inc November 1 2002 English Determining the Accuracy of the Fit Each model computed by the curve fitting add in functions is a best fitting curve which passes directly through or as close to the entered points as possible with a smooth transition between the points As you might expect if your data is scattered it may be difficult to find a curve which closely fits all of your points The maximum FITMAXDEV and average FITAVGDEV deviations as well as the correlation coefficient FITR2 provide a measure of
49. function from the State specific functions shown on page EREXCEL 20 If you are unconcerned about the state of the steam and simply want to know the properties of any steam or water select your function from the Universal functions shown on page EREXCEL 19 The pressure and temperature minimums and maximums shown by the bar graphs below provide a visual description of the differences between the universal functions and the state specific functions Pressur Critical Point Pressure 3208 2347600665 Psia Triple Point Pressure gt 8 858914E 02 Psia Any Steam Liquid Saturated Superheated Supercritical or Water ANY LIQ Steam WET Steam STM Steam CRT Universal State specific Functions Functions 1500 F Critical Point Temperature 705 47 F Any Given Saturation Temperature Triple Point Temperature 32 018 F Any Steam Liquid Saturated Superheated Supercritical or Water ANY LIQ Steam WET Steam STM Steam CRT Universal State specific Functions Functions Cad EREXCEL 18 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Steam and Water Property Universal Functions The chart below describes the universal functions for calculating steam and water properties Note The ratio of Specific heats is not available under the conditions described in the appendix of the Flow Measurement chapter on page Flow A4 Sega
50. ic Heat Cp Btu Lb F Btu Lb enter R Ratio of Specific Cp Cv ANY PH2D 3000 500 H Enthalpy of liquid atT3ptto V Heats Cuft Lb and your result will be enthalpy of superheated T Specific Volume F 49 5627 Lb C uft steam at 1500 F in Btu Lb K Temperature Btu Hr ft F U Thermal Conductivity Lb Sec ft Viscosity ANYPS2 P S D Density Lb C uft To obtain the specific H Enthalpy Btu Lb heat of an H20 P Pressure Q Quality Percent substance ata from P3ptto 15500 psia C_ Specific Heat Cp Btu Lb F pressure of 2600 Psia R Ratio of Specific Cp Cv and an entropy of S Entropy of liquid atT3ptto V Heats Cuft Lb 1 2 Btu Lb R enter entropy of superheated T Specific Volume F ANY PS2C 2600 1 2 steam at 1500 F in K Temperature Btu Hr ft F and your answer will be Btu Lb R U Thermal Conductivity Lb Sec ft 4 887736 Btu Lb F Viscosity EREXCEL 19 EndResult 2003 Sega Inc November 1 2002 English Steam and Water Property Region Specific Functions The chart below describes the region specific functions for calculating steam and water properties P3pt Triple point pressure 8 858914E 02 psia Tsat Saturation temperature F P cot Critical point pressure 3208 2347600665 psia T3pt Triple pointtemp 32 018 F Tcpt Critical pointtemp 705 47 F Function amp Inputs Result Units Example LIQPT2
51. ic Heat of Flue Gas The specific heat of flue gas can be computed by the following two methods Method 1 The fast approximate and simplest method to compute specific heat of flue gas at 14 696 psia is to use the function GASTR2C gas_temp carbon_to_hydrogen_ratio In the GAS CP XLS worksheet from you Examples disk shown below cell B4 contains the formula GASTR2C B 1 B 2 The GASTR2C function reproduces the values given in Steam Generating Units85 Power Test Code PTC 4 1 Figure 7 The GASTR2C function is convenient and provides adequate accuracy in many situations 1 Flue gas temperature 500 from 0 F to 1000 F 2 Carbon to Hydrogen Ratio from 0 to 100 3 4 Specific Heat of Flue Gas GASTR2C 0 249725 Btu Lb F Method 2 The slower but more rigorous method to compute the specific heat of flue gas at any pressure is to use the mixed gas GAS2C function described on page EREXCEL 12 35 Steam Generating Units Power Test Code PTC 4 1 New York American Society of Mechanical Engineers 1974 Cad EREXCEL 24 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Combustion Calculations The COMBUST XLS worksheet from your Examples disk is shown below Each molar combustion function requires 12 input arguments The name of each argument appears in cells A1 to A17 and an example value for each argument appears in cells B1 to B17 ASME numbers where applicable appear in column
52. ifier may be left center or right justified Although capitalization is not significant hyphens should be included where shown An dentifier can be followed by a comment as long as a non alphanumeric character e g comma semicolon parenthesis colon precedes the comment The dentifierand Value Ranges can include blank rows Argument 4 The fourth argument is the Value Range In the example spreadsheet above the Value Range extends from cell B4 to B13 and includes five gases The Value Range must be a single column wide If your identifier is a gas its percent by volume or weight should be entered into the worksheet as a number from 0 to 1 If desired you can select 0 00 from the Format Number list box to get Microsoft Excel to display the number as a percent or use the quick key combination lt CTRL gt Omitted gases are automatically assigned zero percent Under conditions of very low temperature and or high pressure one or more of the gas constituents may become liquid Under marginal conditions you should use the GAS2ZRA function described on page EREXCEL 14 to insure that the answer returned by the add in is valid If the GAS2ZRA function tells you that a constituent in the gas mix is in the liquid state at the zero enthalpy reference and or actual conditions the results computed by the add in may not be valid The ZR exception for Water Vapor As shown in the example worksheet on page EREXCEL 14
53. ilar manner using the same arguments and the function indicated in column A 37 Water Vapor Partial Pressure GAS2H20PP Psia 38 Water Vapor ASME Enthalpy at Partial Pressure GAS2H2OHPP 1225 143 Btu Lb 39 Water Vapor ASME Entropy at Partial Pressure GAS2H2OSPP 22 1359245 Btu Lb R 40 Water Vapor Contribution to Specific Enthalpy GAS2H20H Btu Lb 41 Water Vapor Contribution to Specific Entropy GAS2H20S Btu Lb R Dew point gt 42 Water Vapor Dew Point Temperature GAS2DPT F temperature is only computable if the gas temperature is between 80 F and 705 47 F otherwise GAS2DPT will return AN A 12 Hint To quickly enter the cell formulas in cells B30 to B35 enter the entire GAS2RT function in cell B30 then copy it to cells B31 to B35 and then change each cell to the correct function Correct use of absolute references e g B 2 and relative references e g B2 will ensure that copied formulas have the desired references Cad EREXCEL 11 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English 15 16 17 18 To compute the water saturation vapor pressure cell B44 contains the formula GAS2SATP B 1 B 2 A 4 A 13 B 4 B 13 The GAS2SATP function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The remaining results in cells B45 through B50 are computed in a similar manner using the same arguments and the function indicated in colum
54. ill clear the Move Selection after Enter check box If desired you can select from the Excel i menu to re enable this item g D P 55 0 Viscosity N A Lb Sec ft WETPQ2U P Q 0 0 Spoor ron TENIA Cuft Lb WETPQ2V P Q 100 0 Spec Heat _ N A Btu Lb F_ _ WETPQ2C P Q 4 E coq EREXCEL 5 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English If you enter a number which is below the minimum allowable the function will return a N A error If desired you can display the minimum on your screen by moving your pointer to the cell and selecting EndResult from the Microsoft Excel Help menu m If the hardware key is incorrect or missing the function will return a KEY error You can determine if the hardware key is causing the problem by moving your pointer to the cell and selecting EndResult from the Microsoft Excel Help menu a f you select EndResult from the Microsoft Excel Help menu while your pointer is on a cell which does not contain an error or warning the EndResult pop up window wil tell you that there is No Error or Warning in this Cell f you select EndResult from the Microsoft Excel Help menu while your pointer is on a cell which does not contain an EndResult function the pop up window will tell you that there is No EndResult function in this cell m If cells with EndResult functions display REF or if you sele
55. ints shown on the graph on page 39 gt 59 0 00381625498017175 Y 6 0 00587521503621247 X Y 5 0 00655490897641504 X 2 60 SUM B57 B59 Lastly use a SUM function to add up each of the fragments to determine the value of the complete equation e e EREXCEL 39 aD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Note To sort your x y points so that the x values are in either ascending or descending order select the table of x y points and use the Data Sort gt command POLYSTR gt POLYVAL gt POLYINDEX 1 Dimensional Data Modeling via Polynomials The chart below describes the functions for computing a best fitting least squares polynomial curve to a set of data points Where y anX 4 Asx aX Ap P OLY STR x1 X99 1 y99 n x POLYSTR returns the equation of an nth degree P OLY VAL X1 Xa9 y1 y99 N X polynomia which fits the data in the spreadsheet POLYINDEX f Cell B7 below contains the formula 7 x1 xoo yy99 n POLYSTR A 1 A 5 B 1 B 5 2 E 1 which X1 X99 1 y99 Independent and dependent returns a string representation of the equation of the data point ranges which specify from 2 2nd order polynomial which best fits the data in the to 99 data points x1 y1 X2 y2 spreadsheet To obtain a live function 1 Select X3 Y3 Xm Ym Each range can be Edit Copy 2 Move the pointer to a different cell either a single
56. istributed in such a way that they can be modeled using a Power Logarithmic Inverse Exponential or Square Root equation you will probably obtain the greatest accuracy by using the Polynomial model The curve fitting add in functions use the least squares method to compute each mathematical model Each model is a function which means that for one or more independent variables there is one and only one dependent variable i e result The following table demonstrates how a point is defined by the number of independent variables Number of Independent Required format for each point Variables y Dependent Variable X X X etc Each Independent Variable X Y X1X2 X3 Y X1 X2X3 X4 Y X1X2X3X4X5 Y X1 X2X3 X4X5 X6 y X1 X2X3X4X5 XoX7Yy X1 X2X3 X4 X5 X6X7Xg y X1 X2X3 X4 X5 X6 X7Xg X9Y 1 2 3 4 5 6 7 8 9 EREXCEL 31 EndResult 2003 Sega Inc November 1 2002 English Since there is no reason to compare your original points to a derivative of your model the FITR2 FITAVGDEV and FITMAXDEV functions will return N A if you have gt any d instructions in your model type We recommend that you allocate a named cell in your worksheet to store the value of each independent variable You can assign a name to a cell by selecting Insert Name Define from the Microsoft Excel Versions 3 4 or 7 menus or Formula Define Name from the Microsoft Excel Ve
57. l SSF Seconds Saybolt F ural Volume barrels 42 gallons cubic centimeters cubic feet cubic inches cubic meters cubic millimeters cubic yards gallons US liquid kiloliters liters microliters milliliters pints US liquid quarts US liquid Volume flow cubic centimeters second cubic feet day cubic feet hour cubic feet minute cubic feet second cubic inches second cubic yards minute gallons hour gallons minute liters minute liters second EREXCEL 45 November 1 2002 English Example 1 To convert 300 cm3 second to liters second simply enter any of the following ERUNITS 300 cubic centimeters per second liters per minute ERUNITS 300 centimeter 3 second liter minute ERUNITS 300 cucm sec L min ERUNITS 300 cm 3 sec L min Example 2 To convert 50 BTU Ib F to kJ kg K simply enter either of the following ERUNITS 50 BTU poundmass F kilojoules kilogram K ERUNITS 50 BTU lbm F kJ kg K When entering your current units and desired unit 1 You MUST enter your units in quotes 2 Hyphens should be included as shown on page 49 3 Hyphens have higher precedence than division symbols For example you can enter units like kJ kg K by simply typing in kJ kg K Be sure to use parentheses where necessary to insure that ERUNITS will interpret your units correctly 4 Spaces are optional Legal operators include for grouping
58. lpy K Thermal Conductivity P Pressure Region pues State Legend ANY Any steam or water LIQ Saturated liquid WET Saturated steam STM Superheated steam CRT Supercritical steam Q Quality R Ratio of Specific Heats S Entropy T Temperature U Viscosity V Specific Volume From left to right each function must have 3 letters symbolizing the state 1 letter symbolizing the 1st input 1 letter symbolzing the 2nd input a number 2 symbolizing TO 1 letter symbolizing the result 2 arguments which you specify Like bult in Microsoft Excel functions each EndResult function can be pasted into the spreadsheet by selecting Paste Function from the Formula menu 30 International Formulation Committee The 1967 Formulation for Industrial Use ASME Steam Tables Fifth Edition New York American Society of Mechanical Engineers 1983 Appendix 1 pages 11 29 Cad EREXCEL 17 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English EndResult functions require that all pressures be entered as absolute pressures If however you have a value in gage pressure e g 1500 psig simply add the atmospheric pressure e g 14 7 psia to the gage pressure as shown by the liquid density calculation below LIQPT2D 1500 14 7 300 If you are interested in the properties of a particular steam or water state select your
59. n A 13 These items are bleif the 2 Water Saturation Vapor Pressure GAS2SATP 161 0886 Psia iE IF b Degree of Water Saturation GAS2H20SAT 7 797244 Percent otherwise they will retum a 4NA gt Relative Humidity Water Vapor in Dry Gas GAS2RH 7208939 Percent Humidity Ratio Water Vapor in Dry Gas GAS2HMR 330768E 2 Lb Lb Specific Humidity Water Vapor in Moist Gas GAS2HMS 4 829916E 2 Lb Lb idi in Moi 2 367001E 3 Lb Cuf Wet bulb temperature is Absolute Humidity Water Vapor in Moist Gas GAS2HMA 367001E 3 b Cuft computable if only air and perhaps water vapor are gt present and if the gas temperature is between 80 F A i AE N To compute the Molecular Weight cell B52 contains the formula GAS2WB will return HWA GAS2MW B 1 j B 2 A 4 A 1 3 B 4 B 1 3 The GAS2MW function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The remaining results in cells B53 through B56 are computed in a similar manner using the same arguments and the function indicated in column A Thermodynamic Wet Bulb Temperature GAS2WB AN A oF Molecular Weight GAS2MW 29 47396 Specific Gravity Molecular Weight Ratio GAS2SGMW 1 017536 Specific Gravity Density Ratio Reference GAS2SGREF_ 1 0187097 Specific Gravity Density Ratio GAS2SG 6401903 G EJ Specific Heat Cp Ideal Gas GAS2C 2562904 Btu Lb F Hint To quickly enter the cell form
60. ns the formula DERIVSTR A 1 A 5 B 1 B 5 2 E 1 which returns a string representation of the equation of the derivative of the 2nd order polynomial which best fits the data in the spreadsheet To obtain a live function 1 Select Edit Copy 2 Move the pointer to a different cell and select Edit Paste Special 3 Click the Values option button and then click OK and 4 Insert an equals sign at the beginning of the equation DERIVVAL returns the value of the derivative of an nth degree polynomial which best fits the data in the spreadsheet for the given value of x Cell B8 below contains the formula DERIVVAL A 1 A 5 B 1 B 5 2 72 which returns the value of the derivative of the 2nd degree polynomial which fits the data in the spreadsheet where x 72 DERIVINDEX returns the index of an nth degree least squares polynomial of the specified degree Cell B9 below contains the formula DERIVINDEX A 1 A 5 B 1 B 5 2 which returns the index of the 2nd order polynomial equation which fits the ppints in the spreadsheet An index of 1 is a perfect fit The DERIV XLS worksheet from your EndResult Examples disk is shown below A B Cc D E F e oe oo a gat 7 y 6 6860714E 4 E 1 0 0790809 8 y 0 030941 BE ee o ee OOO eee eee eee The OPTLDALOXLS worksheet provided on your EndResult Predefined Spreadsheet Solutions disk demonstrates a use of the add in derivative functions
61. nt from 0 to 100 V Specific Volume Cuft Lb Cuft Lb chapter on page F low enter as 0 to 1 K Thermal Conductivity Btu Hr ft F A4 U Viscosity Lb Sec ft STMPT2 P T D Density Lb C uft To obtain the specific heat H Enthalpy Btu Lb of superheated steam at Superheated P Pressure S Entropy Btu Lb R 2000 psia and 950 F Steam STM from P 3pt to P Cpt psia C Specific Heat Cp Btu Lb F enter R Ratio of Specific Heat Cp Cv STMPT2C 2000 950 T Temperature V Specific Volume Cuft Lb and the result will be from Ts at F to 1500 F K Thermal Conductivity Btu Hr ft F 0 652954 Btu Lb F U Viscosity Lb Sec ft CRTPT2 P T D Density Lb C uft To obtain the thermal A cE Ey mea cosets P ressure n ntropy u Lb critical steam a psia Steam C RT from P Cpt psia to C Specific Heat Cp Btu Lb F and 1200 F enter 15500 psia R Ratio of Specific Heat Cp Cv CRTPT2K 6000 1200 V Specific Volume Cuft Lb to get 0 073924 T Temperature K Thermal Conductivity Btu Hr ft F Btu Hr ft F from Tcpt to 1500 F U Viscosity Lb Sec ft EREXCEL 20 EndResult 2003 Sega Inc ospa November 1 2002 English Saturation Pressure amp Temperature Functions The chart below describes two functions which compute saturation pressure and temperature Ps Triple point pressure 8 858914E 02 psia Tapt Triple point temperature 32 018 F Pep Critical point
62. ntropy Ea default is 32 018 gt 104 105 Zero Enthalpy Temperature from 425 F to 4000 F 106 Wet Bulb Temperature 93 701501 Reference Pressure Reference Temperature GAS2WB GAS2REFP GAS2REFT GAS2HMR Humidity Ratio 4 197367E 2 Specific Humidity GAS2HMS 4 032289E 2 Water Vapor in Dry Air gt GAS2HMA 2 279395E 03 Lb Cuft Water Vapor in Moist Air gt GAS2C 24830705 Specific Heat Cp PCTBYVOL Btu Lb F Part Psia Sat Temp F zra GAS2PP GAS2TSAT Water Vapor in Moist Air gt Weight Ideal Gas gt PCTBYWT 93 6718 95 9677 11 241 321 42 1e Water Vapor 6 3282 4 0323 0 759 92 70 E To compute the Wet Bulb Temperature26 cell C106 contains the formula GAS2WB C 100 C 101 A 103 A 104 C 103 C 104 GAS2WB air_pressure dry_bulb_temp Ident_Range Value_Range The same arguments as shown in the GAS2WB function above can be used to perform the calculations shown in rows 107 through 116 The first two arguments must be the pressure and dry bulb temperature of the atmospheric air and the last two arguments must be the Identifier and Value Ranges respectively in which you have specified the Relative Humidity The only other item which you are allowed to specify in your Identifier and Value Ranges is the Zero Enthalpy Temperature A Zero Enthalpy Temperature of 32 018 F will be used if not otherwise specified For more detailed instru
63. o of Specific Heats Ideal Gas 19 GAS2CR 1 357678 Cp Cv Temperature Dry Ideal Gas H2O ASME GAS2TEMP 364 0922 oF Specific Enthalpy Dry Ideal Gas HO ASME GAS2ENTH20 135 2667 Btu Lb Specific Entropy Dry Ideal Gas H 0 ASME GAS2ENTR20 2211987 Btu Lb R Compressibility Factor Reference 21 GAS2Z0 0 9982604 Z0 Compressibility Factor22 GAS2Z1 0 9997867 Z1 Super Compressibility GAS2SZ 1 000107 Fpv Density Reference 23 GAS2DR 7 798304E 2 Lb Cuft Density24 GAS2D 4 900708E 2 Lb Cuft Specific Volume Reference Specific Volume Viscosity Dry Ideal Gas Viscosity Dry Ideal Gas 60 61 62 63 64 Entering Gage Pressures GAS2RVOL GAS2VOL GAS2U GAS2UC 12 823300 20 405214 1 572015E 05 2 339416E 02 Cuft Lb Cuft Lb Lb Sec ft Centipoise EndResult functions require that all pressures to be entered as absolute pressures If however you have a value in gage pressure e g 1500 psig simply add the atmospheric pressure e g 14 696 psia to the gage pressure as shown by the gas density calculation below GAS2D 1500 14 696 300 A 4 A 13 B 4 B 1 3 The specific heat ratio may be unrealistic if it is less than 0 1 or greater than 4 Enthalpy and entropy calculations are based on a change in enthalpy or entropy from the zero enthalpy temperature which can be modified as shown on page EREXCEL 8 The compressibility factor reference may be unrealistic if
64. odel The value of r2 is from 0 to 1 and the closer r2 is to 1 the better the fit A correlation coefficient of 1 is a perfect fit Cell D36 on page 34 contains the formula F ITR 2 A 1 B 19 sqrt which returns the correlation coefficient of the square root curve which fits the data points in the point_range FITAVGDEV returns the average absolute deviation of the type model from the specified points The average absolute deviation is the average gap or average error between the model and the entered points If the computed model passes directly through all of the entered points the average absolute deviation will be zero Cell C37 on page 34 contains the formula F ITTAVGDEV A 1 B 19 log which returns the average absolute deviation of the logarithmic equation from the data points in the point_range FITMAXDEV returns the maximum absolute deviation i e maximum error of the type model from Specified points The maximum absolute deviation is the largest gap or greatest error between the model and any of the entered points If the computed model passes acy through all of the entered points the maximum absolute deviation will be zero Cell B38 on page 34 contains the formula F ITMAXDEV A 1 B 19 power which returns the maximum absolute deviation of the power equation from the data points in the point_range EQFRAGMENT is discussed in the section entitled Computing Equations Longer than 255 Characters on
65. or by pressing lt ALT gt H R on the keyboard As shown in the example below the error message displays the name of the EndResult Steam Plant Engineering Tools function which is evoking an error and a brief explanation for why the error occurred If the error is being caused by the value of one or more arguments being passed to the function the error message will identify the argument s which are responsible for the error f you enter a number which is above the maximum allowable the function will return a N A error As shown in the picture below you can display the maximum on your screen by moving your pointer to the cell and selection EndResult from the Microsoft Excel Help menu ee Move pointer Then select EndResult of Microsoft Excel to error cell to view explanation Version 3 0 EndResult will not appear in the Excel Help menu if you have selected Short Menus Microsoft Excel File Edit Formula Forma Format Data Options Macro Window Index Keyboard Lotus 1 2 3 E Multiplan Density 54 5467417 Lb Cuft Tutorial min 0 088589 Enthalpy 378 4749569 Btu Lb Fntropy poe Btu Lb R If desired you can select Full Menus from the Excel Options menu to re enable the Help EndResult menu Gea Excel __ ERROR WETPQ2V Arg 1 Maximum for Pressure is 3208 23476 Psia You entered 20000 Psia from the Excel Help menu w
66. row or single column of and select Edit Paste Special 3 Click the Values numbers In the spreadsheet below option button and then click OK and 4 Insert an the independent x range is from cell equals sign at the beginning of the equation a AS eee y range POLYVAL returns the value of an nth degree polynomial iS WO Ge BTID which best fits the data in the spreadsheet for the n the degree of the computed polynomial given value of x Cell B8 below contains the formula equation from 1 to 8 However if m P OLYVAL A 1 A 5 B 1 B 5 2 72 which is the number of x y points and n gt m returns the value of the 2nd degree polynomial which the function will compute a polynomial fits the data in the spreadsheet where x 72 of degree m 1 POLYINDEX returns the index of an nth degree least x the value of the independent variable Squares polynomial of the specified degree Cell B9 j below contains the formula x the cell address enclosed in quotes POLYINDEX A 1 A 5 B 1 B 5 2 which of the independent variable such as returns the index of the 2nd order polynomial equation E 1 which fits the ppints in the spreadsheet An index of 1 is a perfect fit The POLY XLS worksheet from your EndResult Examples disk is shown below a E E e elaz 84 6325 10 8o32 0302 3 3430357E 4 E 1 2 0 0790809 E 1 80 4586200 84 41942 999933 42 For a discussion of the potential problems of trying to obtain a
67. rsion 5 menu For example the independent variable X was defined as cell E 2 shown on page 33 Sega Curve Fitting Add in Functions The chart below summarizes the curve fitting add in functions F ITEQ point_range type FITVAL point_range type IV FITR2 point_range type FITAVGDEV point_range type F ITMAXDEV point_range type EQFRAGMENT point_range type fragment type the model type enclosed in quotes must be selected from the following list sqrt for a square root model log for a logarithmic model inv for an inverse model power for a power model exp for an exponential model or poly n for an nth degree polynomial where n is from 1 to 9 See Taking the nth Derivative of a Model on page 36 for additional options which you can include in your type point_range a range containing from 2 to 150 data points As shown in the example on the following page the first row of the point_range should contain the name of each independent variable and the name of the dependent variable You can specify from 1 to 9 independent variables You should provide a separate column for each independent variable However the rightmost column should always contain the dependent variable The data points in the example worksheet on the following page contain only one independent variable X and the dependent variable Y IV the value of
68. s S CARBURNED Dry Before 498 035 085 007 006 304 0 0576 48 7 6 65979E 04 4 N A N A 035 0005 N A 04 The dry flue gas constituents in cells B30 through B33 are computed by the ASME method which assumes that SO2 condenses out with H20 To compute the carbon dioxide in dry flue gas by the ASME method cell B30 contains the formula DRYCO2 B 1 B 2 B 3 B 8 B 9 B 10 B 11 B 12 B 13 B 14 B 15 B 16 B 17 The remaining dry flue gas constituents in cells B31 through B33 are also computed by the ASME method using the same arguments EJ 32 Carbon Dioxide CO2 in Dry Flue Gas ASME DRYCO2 15 54476 by Vol Ea 33 Oxygen O in Dry Flue Gas ASME DRYO2 3 50000 by Vol 32 34 Carbon Monoxide in Dry Flue Gas ASME DRYCO 0 05000 by Vol 35 Nitrogen N2 in Dry Flue Gas ASME DRYN2ASME 80 90524 by Vol Total 100 00000 by Vol 40 Hint To quickly enter the cell formulas in cells B20 to B28 enter the entire CARBURNED function in cell B19 then copy it to cells B20 to B28 and then change each cell to the correct function Correct use of absolute references e g B 2 and relative references e g B2 will ensure that copied formulas have the desired references Cad EREXCEL 27 Q _ GOlo _ EndResult 2003 Sega Inc November 1 2002 English Likewise Carbon Dioxide in Dry Flue Gas in cell B30 on the preceding page Notice the gt Could also be computed by entering e
69. s the formula RADLOSS B 1 B 2 B 3 B 4 B 5 B 6 B 7 B 8 B 9 B 10 B 1 1 38812 ASME numbers where applicable appear in column A and valid ranges for each input are listed in column C ES Boiler Capacity 4800000 from 500 to 10E 06 Lb Hr Number of Water Walls from 0 to 4 Drum Blowdown Water Flow from 0 to 10E 06 Lb Hr For standard radiation loss enter an air velocity around boiler of 100 FPM and an air to boiler temperature delta of 50 F Air Velocity Around Boiler from 0 to 1800 FPM Air to Boiler Temperature Delta from 0 F to 2000 F 15 Enthalpy of Saturated Liquid 733 5924 from 1E 7 to 906 96 Btu Lb 16 Enthalpy of Superheated Steam 1460 3950 from 715 86 to 1586 Btu Lb 26 Actual Water Evaporated 4640000 from 500 to 10E 06 Lb Hr If the boiler does not have a reheater enter N A for the last three arguments i e cells B10 to B12 18 Enthalpy of Steam at R H Inlet 1299 7101 from 715 86 to 1586 Btu Lb or N A 19 Enthalpy of Steam at R H Outlet 1520 2431 from 715 86 to 1586 Btu Lb or N A 27 Reheat Steam Flow 4200000 from 500 to 10E 06 Lb Hr or N A 69 Heat Loss Due to Radiation RADLOSS 0 172002 AFF of gross heat input 17 Enthalpy of Water Entering 442 5746 from 1E 7 to 906 96 Btu Lb You can also enter the formula values directly For example the radiation loss shown in cell B14 above could also be calculated by entering the formula RADLOSS 4800
70. sure of the gas mixture in Psia Argument 2 The Second Argument identifier shown above in row 4 specifies whether the second argument is temperature enthalpy or entropy If you specify Second Argument as Enter a value for the 2nd argument which is T MPCrature scscescscessessssessssessseseseesaeen from 425 F to 4000 F Enthalpy iscsi ved anita from 1300 to 3400 Btu Lb ENUODY wiissisiintiicnssancaniiiunidiiee from 1 27 to 2 21 Btu Lb R Argument 3 The third argument is the Identifier Range In the example spreadsheet wo Sega above the dentifier Range extends from cell A4 to A13 and includes five gases The dentifier Range must be a single column wide As a minimum the dentfier Range must include from 1 to 37 of the following gases Acetylene Air Ammonia Argon Benzene Carbon Dioxide Carbon Monoxide Ethane Ethyl Alcohol Ethylene Hydrogen Gas Hydrogen Sulfide i Butane 1 Butene i Pentane Methane Methyl Alcohol n Butane cis 2 Butene n Heptane n Hexane n Nonane n Octane n Pentane 1 Pentene Neopentane Nitrogen Atmospheric Nitrogen Oxygen Propane Propylene Sulfur Dioxide Toluene o Xylene m Xylene p Xylene Water Vapor Identifiers can be abbreviated to as few as 3 characters e g Ben for Benzine as long as enough characters of each identifier are entered to EREXCEL 8 November 1 2002 English EndResult 2003 Sega Inc distinguish it from other identifiers Each ident
71. to compute flue gas properties after an existing air heater Argument 3 must be a range which includes in exact order the fuel ultimate analysis carbon hydrogen oxygen nitrogen sulfur and moisture The range in the example on page EREXCEL 25 is from cell B3 to B8 The table below displays the different ways in which you can enter measured percentages shown as _ for arguments 12 to 17 Be sure to enter N A rather than zero for any not 1 2 measured value Specifying any combination of measured inputs not shown in the table below will cause the function to return an error message i e N A Be sure that any measurements taken for arguments 13 through 15 are taken before the air heater Arg If the Air Heater If the Air Heater Selection No Selection is None is Before or After 12 36 Percent Excess Air ANJA N A N A __ N A N A N A ANIA 13 3239 Carbon Dioxide in Flue Gas Before AH _ WIA ANIA AA 14 3339 Oxygen in Flue Gas Before AH __ __ ANIA ANIA ANIA _ __ 15 3439 Carbon Monoxide in Flue Gas Before AH 16 Diluted Carbon Dioxide after air heater ANJA N A N A N A _ N A _ N A 17 Diluted Oxygen after air heater AN A N A N A N A ANIA WIA __ An example of each of the 21 combustion calculation add in functions appe
72. u FtHr F W m K NOT begin with the letter x Density Lb Cuft kg m 3 For example to compute the Energy MBtu Hr MJ Hr enthalpy of steam at 2500 Psia Enthalpy Btu Lb kJ kg and 900 F and you would Entropy Btu Lb R kJ kg K enter STMPT2H 2500 900 Mass flow Lb Hr kg Hr and your result would be Pressure Psia ekPa 1386 688 Btu Lb Notice that Specific heat Btu Lb F kJ kg K both the inputs and the result Temperature F C are in English engineering Viscosity Lb Sec ft Pa sec units Throughout the EndResult software pressures in kPa are assumed to be absolute unless kPa gage is specified Microsoft is a registered trademark of Microsoft Corporation Cad EREXCEL 2 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Metric Functions Begin with X EndResult functions which use metric engineering units begin with the letter X For example to compute the enthalpy of steam at 13700 kPa and 510 C you would enter XSTMPT2H 13700 510 and your result would be 3355 246 kJ kg Notice that both the inputs and the result are in metric engineering units The EndResult ERUNITS function described on page EREXCEL 45 provides you with a convenient way to perform many unit conversions EndResult functions require any percentage e g percent quality relative humidity etc to be entered into the worksheet as a number between 0 and 1 If desired you can select 0 00 from
73. ugh the x y and X2 y2 coordinates for the given value of x For example to obtain the value of the square root curve which passes through the 0 10 and 100 3300 coordinates at the point x 72 enter SQRTXYXY 0 10 100 3300 72 and your result will be 2801 658 y My x B y SQRTXYXY x y X 4 5X EndResult 2003 Sega Inc EREXCEL 44 November 1 2002 English Any of the following units and abbreviations are equivalent calories calorie cal feet foot ft gallons gallon gal grams gram g horsepower hp hours hour hr inches inch ins in joules joule J liters liter L meters meter m miles mile mi minutes minute min newtons newton N ounces ounce 0z pascals pascal Pa poises poise p poundsmass pound Ibm Ib poundsforce poundf lbf seconds second sec S stokes stoke St watts watt W yards yard yds yd Prefix Symbol Value kil k 10 lo hector h 108 deca ca 1 deci d 101 centi c 101 milli m 102 micro u 103 nao n 106 me P 19 cubic cu 1012 squar sq e 3 2 OCapital C refers to degrees Celsius C Capital F refers to deg Fahrenheit F p K refers to Kelvin K Capital R refers to deg Rankine R May not be combined with other units Sega Performing Unit Conversions You can perform unit conversions by using the ERUNITS value current units desired units
74. ulas in cells B44 to B50 enter the entire GAS2SATP function in cell B44 then copy it to cells B45 to B50 and then change each cell to the correct function Correct use of absolute references e g B 2 and relative references e g B2 will ensure that copied formulas have the desired references When saturation vapor pressure is greater than the total gas pressure as occurs with high temperature flue gas and the relative humidity is greater than 0 00 the degree of saturation can be negative See reference 7 page 1 15 equation 1 24 The specific gravity value may be unrealistic if it is greater than 5 The specific gravity value may be unrealistic if it is greater than 5 The specific gravity value may be unrealistic if it is greater than 5 If you need a faster method for computing the specific heat of flue gas the GASTR2C function on page EREXCEL 24 provides a fast and simple way to obtain an approximate value for the specific heat of flue gas at 14 696 psia Cad EREXCEL 12 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English 19 20 21 22 23 24 To compute the ratio of specific heats cell B58 contains the formula GAS2CR B 1 B 2 A 4 A 13 B 4 B 13 The GAS2CR function uses the four arguments described on pages EREXCEL 8 and EREXCEL 9 The remaining results in cells B59 through B70 are computed in a similar manner using the same arguments and the function indicated in column A Rati
75. unces poundsmass or Ibm quarters quintals Slugs Mass flow Kilograms hour lbm hour Power BTU hour BTU minute BTU second dyne cm sec ft lbf hr ft lbf min ft lbf sec metric Horsepower or MHP US Horsepower or USHP joules second kiloBTU hour cal hour cal minute cal second kilowatts megaBTU hour megajoules hour megaW atts watts Pressure stress etc bars centimeters H20 at 60 F centimeters Hg at 32 F dynes sqcm feet H20 at 60 F feet Hg at 32 F inches H20 at 60 F inches Hg at 32 F kilopascals meter H20 at 60 F meter Hg at 32 F newtons sq meter pascals lof sqft lbf sqin or Psi ltons sqft ltons sqin stons sqft stons sqin Specific Volume cubic cm gram cubic meter gram liter gram milliliter gram cubic meter kg cubic foot lbm cubic in lbm gallon lbm cubic foot slug Speed linear centimeters second feet hour feet minute or FPM feet second or FPS kilometers hour kilometers minute kilometers second meters minute meters second miles hour or MPH miles minute Temperature CO F ke RO Time seconds minutes hours days Thermal Conductivity BTU hr ft F EndResult 2003 Sega Inc W m K Viscosity absolute centipoises dyne second sqcm grams sec cm lbf sec sqft Ibf sec sqin pascal seconds poises Viscosity kinematic stokes centistokes Redwood Redwood No 1 saft sec sqm sec SSU Second Saybolt Universa
76. vember 1 2002 English The items in rows 4 to 13 are optional If you omit any of these items the default value shown to the left of each row will be used A B c dfautis T BUG 4 Second Argument Temperature Temperature Enthalpy or Entropy default is 60 F gt 5 Reference Temperature 60 from 425 F to 4000 F eraut 51473 la 6 Reference Pressure 14 73 from 2 25E 14 to 3208 235 Psia applies to enthalpy and gt entropy default is 32 018 F 7 Zero Enthalpy Temperature 32 018 from 425 F to 4000 F default is Volume gt 8 Gas Mixture Percent by Volume Weight or Volume 9 Carbon Dioxide 11 4940 from 0 to 100 by Volume or Weight Use a formula like SUM B99 B 13 to 10 Atmospheric Nitrogen 74 0720 from 0 to 100 by Volume or Weight ensure that 100 of the gas constituents 11 Oxygen 6 4000 from 0 to 100 by Volume or Weight have been specified 12 Sulfur Dioxide 0 1320 from 0 to 100 by Volume or Weight 13 Water Vapor 7 9020 from 0 to 100 by Volume or Weight 14 15 Ultimate Analysis Carbon GAS2CAR 4 683946 by Wt Each mixed gas thermo physical property function requires the same four arguments as the GAS2CAR function in cell B15 To compute the Ultimate Analysis Carbon cell B15 contains the formula GAS2CAR B 1 B 2 A 4 A 13 B 4 B 13 Argument 1 The first argument is the pres
77. w a s a oer on of ree s f o oa roar eo T ran l 850 1373 5 1368 4 1363 3 1358 1 1352 8 875 1391 3 1386 7 1382 0 1377 2 1372 4 a Estimated enthalpy 1372 159 The example worksheet uses the POLY2DVAL function to estimate the enthalpy of 2250 psia 865 F steam Cell D13 above contains the formula POLY2DVAL B 7 G 1 1 D 2 D 3 D 4 D 5 As shown above the enthalpy computed by POLY2DVAL is 1372 159 Btu Lb which is only slightly different from the actual enthalpy of 1372 16265 Btu Lb 44 Fora discussion of the potential problems of trying to obtain a perfect fit see page Curve 17 and ap SEQGAe_ EndResult 2003 Sega Inc Curve 18 EREXCEL 42 November 1 2002 English Argument 1 2 Dimensional Data Modeling via Interpolation The INTERP2D function is used to model the data in a 2 dimensional table INTERP2D uses double interpolation to interpolate between table values The INTERP2D XLS worksheet from your EndResult Examples disk is shown below Cells C6 to G9 contain enthalpy values for pressures from 2000 to 2400 psia and temperatures from 800 F to 875 F For example the table shows us that the enthalpy of 850 F 2200 psia steam is 1363 3 Btu Lb The INTERP2D function requires three arguments INTERP2D table_range horiz_val vert_val The first argument is the table range In the example below the table range is from cell B5 to G9 Your table must include at least 2 rows an
78. xide Similar formulas are used to compute the values in cells B74 through F78 73 PCTBYVOL PCTBYWT GAS2PP GAS2TSAT 74 Carbon Dioxide 11 EA 17 1626 1 689 164 54 75 Atmospheric Nitrogen 74 0720 70 7724 10 886 324 35 76 Oxygen 64000 4000 6 9482 om sea 77 Sulfur Dioxide kaa 0 2869 oms aor oO Under conditions of very low temperature and or high pressure one or more of the gas constituents may become liquid If this happens for other than water vapor your mixed gas results will not be valid See warning on page EREXCEL 9 The GAS2ZRA function should be used if you are uncertain as to whether or not ALL of the constituents in the gas mixture will be a gas at the specified pressures and temperatures The GAS2ZRA function returns one or more of the following letters Z Ifthe constituent is not a gas at zero enthalpy conditions R Ifthe constituent is not a gas at reference conditions A Ifthe constituent is not a gas at actual conditions coq EREXCEL 14 GD GOlo _ EndResult 2003 Sega Inc November 1 2002 English Computing Psychrometric Properties Using Relative Humidity The worksheet below demonstrates how to compute the properties of atmospheric air with a given relative humidity Pressure from 9492356 to 15 472 Psia Dry Bulb Temperature Relative Humidity from 80 F to 200 F from 0 to 100 applies to enthalpy and e

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