Flow with Losses 3 | HP 50g Graphing, 48gII Graphing instruction

Equations:

Δ----P--

+ v----2----2---–----v----1---2-

+ g ⋅ Δy = 0

⋅



 A2



2

Δ----P--

1 – --

A------1--



+ -------------------

---2-----

---+ g ⋅ Δy = 0

⋅



A2



------

– 1

Δ----P--

+ --------------

------

A-----1-----------------

--- + g ⋅ Δy = 0

ΔP = P2 – P1 Δy = y2 – y1

M = ρ ⋅ Q

Q = A2 – v2

Q = A1 – v1

π ⋅

D12

A2 =

π ⋅

D22

A1 = -----------------

-------

-4---------

Example:

Given: P2=25_psi, P1=75_psi, y2=35_ft, y1=0_fr, D1=18_in, ρ=64_lb/ft^3, v1=100_ft/s.

Solution: Q=10602.8752_ft^3/min, M=678584.0132_lb/min, v2=122.4213_ft/s, A2=207.8633_in^2, D2=16.2684_in, A1=254.4690_in^2, P = 50_psi, y =35_ft.

Flow with Losses (3, 3)

These equations extend Bernoulli’s equation to include power input (or output) and head loss.

Equations:

M ⋅

 ΔP

v22 – v12



 --ρ----

---------

--2----------

-- + g

⋅ Δy + hL = W





⋅



 A2

 2





Δ----P--

1 – --

A-------1--

 



M ⋅ 

+ --------------------------- -------------

+ g

⋅ Δy + hL = W











⋅



A1





-

--------



– 1



Δ----P--

A-----2--



M ⋅ 

+ ------------------ ----------------

+ g

⋅ Δy + hL = W









ΔP = P2 – P1

Δy = y2 – y1

M = ρ ⋅ Q

Q = A2 ⋅ v2

Q = A1 ⋅ v1

A1 =

π ⋅

D12

A2 =

π ⋅ D22

-----------------

--------4---------

520 Equation Reference

Page 456

Image 456

HP 50g Graphing, 48gII Graphing manual Flow with Losses 3

Contents

HP 50g / 49g+ / 48gII graphing calculator Advanced user’s reference manualPage Acknowledgements Printing HistoryPage Contents Names AlgbAlog Amort 317 Delalarm Delay→COL COL→ 359 Findalarm EXP2POWExpan Expand Halt IBPIDIV2 Iferr List MAX MaxrMIN Not PA2B2 ParametricParity Parsurface 3183 RND RnrmRoll Rolld 3226 Tabvar →TAGTail TAN Wireframe UpdirUtpc Utpf Contents 514 →ALG Apeek ARM→ ASM ASM→ 610 Alrmdat CST Exited Expr Iopar MASD.INIToff Tpar Vpar Contents of a Program Understanding Programming Calculations in a Program Examples of Program ActionsProgram Results To enter commands and other objects in a program Entering and Executing ProgramsTo enter a program To store or name a program To stop an executing program 3Q!Ì*4`3/*@Ï3Q!Ì*4#3/* @Ë@Ï @% @Ér # O4 /3 *!Ì Q3 @Ë@Ï Level Program Keys CommentsOsph K To switch between entry modes Viewing and Editing ProgramsTo view or edit a program @%SPH% ˜ Using Local Variables Creating Programs on a ComputerCreating Local Variables `J!%SPH% @%SPH% ˜ Program Comments `OSPHLV K Evaluating Local Names Defining the Scope of Local Variables Compiled Local Variables Creating UserDefined Functions as Programs Using Tests and Conditional Structures Testing ConditionsKey Programmable Description Command To include a test in a program Using Logical Functions Keys Programmable Description CommandLogical Functions TEST% L Using Conditional Structures and Commands To enter if then END in a programPress !%BRCH% !%IF% To enter IFT in a program To enter if then Else END in a program Press !%BRCH% @%#IF#%To enter Ifte in a program or in an algebraic Press !%BRCH% L!%IFTE% To enter Case END in a program Conditional Examples Otst K 26 `52 J %TST% Using Loop Structures Using Definite Loop StructuresWhile … Repeat … END Start Next Structure « … start finish Start loopclause Next … »To enter Start Next in a program Press !%BRCH% !%START% Start Step Structure « … start finish Start loopclause increment Step … »To enter Start Step in a program Press ! %BRCH% … %START% For Next Structure « … start finish for counter loopclause Next … »To enter for Next in a program Press !%BRCH% ! %FOR% For Step Structure « … start finish for counter loopclause increment Step … »To enter for Step in a program Press ! %BRCH% … %FOR% Using Indefinite Loop Structures Do Until END Structure« … do loopclause Until testclause END … » To enter do Until END in a program Duplicates n, stores the value into n While Repeat END Structure « … While testclause Repeat loopclause END … »To enter While Repeat END in a program Press !%BRCH% ! %WHILE% Using Loop Counters To enter Incr or Decr in a programPress ! #MEM# %ARITH% %INCR% or %DECR% Using Summations Instead of Loops ∑ j Using Flags Setting, Clearing, and Testing FlagsTypes of Flags To set, clear, or test a flag Recalling and Storing the Flag States ExampleMonth/day/year format Day.month.year format Using Subroutines To recall the current flag statesExecute Rclf !L %MODES% %FLAG% L%RCLF% To change the current flag states Torsa K Torsv K` 8 J %TORSV% To singlestep from the start of a program To turn off the Halt annunciator at any timePress !LL %RUN% %KILL% @·J6 `8 `O%TORSV% !LL%RUN% %DBUG% To singlestep when the next step is a subroutine To singlestep from the middle of a program@·J10 `12 O%TORSV% !LL%RUN% %DBUG% Trapping Errors Causing and Analyzing ErrorsTo cause a userdefined error to occur in a program SingleStep Operations To artificially cause a builtin error to occur in a program To analyze an error in a programError Trapping Commands %ERROR% Making an Error Trap « … Iferr trapclause then errorclause END … »Press !LL %ERROR% !%IFERR% Iferr then END Structure Press !LL %ERROR% @%IFERR% Iferr then Else END StructureTo enter Iferr then Else END in a program Data Input Commands Using PROMPT, Cont for InputKey Command Description Input `OTPROMPT ‰ @·J %TPROM% Using Disp Freeze HALT, Cont for Input To enter Disp Freeze Halt in a programTo respond to Halt while running a program Using INPUT, Enter for Input « … promptstring commandline Input OBJ→ … »To enter Input in a program To respond to Input while running a program %VSPH% Commandline cursorposition operatingoptions To design the commandline string for InputTo include Input options Cursorposition To process the result string from Input Press @ Õ ! Ê a @`O Tinput ‰ %TINPU% Using Inform and Choose for Input To set up an input form To set up a choose box `OPHONES ‰ Using Wait for Keystroke Input Beeping to Get AttentionTo enter Beep in a program To enter Wait in a program Using KEY for Keystroke Input Data Output CommandsOutput OUT% Labeling Output with Tags Labeling and Displaying Output as StringsTo label a result with a tag %TTAG% 1.5 ˜1.85 ` Pausing to Display Output Using Msgbox to Display OutputTo set up a message box `OTSTRING ‰ Using Menus with Programs Using Menus for Input Using Menus to Run Programs To create a menubased applicationOlst ‰ SI% @·J%EIZ% Turning Off the Calculator from a Program %% !Ü.37~@6 68 %%I%% !%%Z%%@%%I%% 2*%%I%% !%%E%% To turn off the calculator in a programPage Fibonacci Numbers FIB1 Fibonacci Numbers, Recursive VersionRPL Programming Examples FIB2 Fibonacci Numbers, Loop Version %FIB1%FIB1% !Ü10 N FIB2 program listing %FIB2%10 %FIB2% Fibt Comparing ProgramExecution Time Techniques used in FibtStructured programming. Fibt calls both FIB1 and FIB2 Required Programs Displaying a Binary Integer PAD Pad with Leading Spaces13 %FIBT% Techniques used in PAD Preserve Save and Restore Previous Status PAD program listing`OPAD K Techniques used in Preserve Bdisp Binary Display Preserve program listing`OPRESERVE K Techniques used in Bdisp PAD Bdisp program listing `OBDISP K Median of Statistics Data Tile Percentile of a list144 %BDISP% Median Median of Statistics Data Techniques used in %TILETile program listing `O%TILE K Techniques used in Median Required Program Expanding and Collecting Completely `OMEDIAN K18 `12 `˜šš 11 `1 ` Multi Multiple Execution Techniques used in MultiMulti program listing `OMULTI K Exco Expand and Collect Completely Techniques used in ExcoExco program listing `OEXCO K Minimum and Maximum Array Elements MNX Minimum or Maximum Element-VersionÜ4 *Y+Z + User and system flags for logic control MNX program listing `OMNX K MNX2 Minimum or Maximum Element-Version 12 `56 `˜šš 45 `1 `Techniques used in MNX2 MNX2 program listing Applying a Program to an Array %MNX2%Techniques used in Aply Aply program listing Make sure the flag 1 is clear to begin Converting Between Number Bases `OAPLY KÔ3†2W†4` ‚Å 3 QA *7 `J %APLY% H#DISP ˜˜ Techniques used in nBASE NBASE program listing Verifying Program Arguments 1000 `23 J %NBASE% Names Check List for Exactly Two Names Techniques used in NamesNames program listing `ONAMES K VFY Verify Program Argument Techniques used in VFYVFY program listing Converting Procedures from Algebraic to RPN Oben `Ojeff ` Osarah ` %LIST% %²LIST% Techniques used in →RPN →RPN program listing Bessel Functions XQ3 `%²RPN%Techniques used in BER BER program listing `OBER K%BER% %BER% !Ü2 Animation of Successive Taylor’s Polynomials Sintp Converting a Plot to a Graphics ObjectTechniques used in Sintp Sintp program listing Setts Superimposing Taylor’s polynomials Techniques used in SettsSetts program listing `OSETTS K TSA Animating Taylor’s Polynomials Techniques used in TSATSA program listing `OTSA K Programmatic use of matrices and statistics commands Programmatic Use of Statistics and PlottingTechniques used in PIE Temporary menu for data input Angle `OPIE K 983 %SLICE% 416 %SLICE% 85 %SLICE% Trace Mode Techniques used in αENTER and ßENTERΑENTER program listing ßENTER program listing InverseFunction Solver Techniques used in RootrRootr program listing `OROOTR K Animating a Graphical Image @Å@É x †O3.7%X²FX% ` 599.5 ` 1 %ROOTR% Techniques used in Walk `OWALK K Introduction AcosType Input/Output How Commands Are Alphabetized Other Provided DetailsParallel Processing with Lists Computer Algebra System Commands and Functions Classification of Operations Backup identifier Realnumber time or angle in hoursminutessecond s formatLibrary identifier Binary integer Abcuv ABSACK Ackall Type Description ACOS2S ASIN, ATAN, COS, Isol Acosh ASIN2C, ASIN2T, ATAN2SAcosh z Symb ACOSHsymb ADD Addtmod Addtoreal AlgbAlog 10z Amort Principal Interest BalanceTVM, TVMBEG, TVMEND, Tvmroot Animate ANS Access …µAPPLY Input/Output ApplyARC Archive ARG Access …µARRY→ Input/Output AritARRY→ →ARRY Access !¼ ¼is the leftshift of the Skey ASIN2C ASIN2TAsinh ASN Asinh zSymb ASINHsymb ACOSH, ATANH, ISOL, Sinh Access … ÃL BIT ASR ASRAssume Skey Atan ADDTOREAL, Unassume ATAN2S Atan zSymb ATANsymb ACOS, ASIN, ISOL, TAN Access …µATICK AtanhAtick Atanh z Access …µATTACH Input/Output AttachAugment #n #m Access …µAUTO Input/Output None AutoAxes BAR Access …µAXES Input/Output AXLAXM Atick xaxis label yaxis label AXQ BARAXL, AXQ AXL, AXM, GAUSS, QXA Access …µBAR Input/Output None BarplotBasis Baud Access …µBESTFIT Input/Output None Access … Ã BINBeep Bestfit Access !L Pict BOX Is the leftshift of the Nkey BinsBlank BOX Access …µBUFLEN Input/Output BuflenBytes #n1 #m1 #n2 #m2 X1, y1 X2, y2 Access … Ã B → R C2PCascfg Cascmd CaseHelp Ceil CentrXunit Nunit Symb CEILsymb FLOOR, IP, RND, Trnc Chinrem Cholesky Command Result ChooseCHR Circ CksmNUM, POS REPL, SIZE, SUB Clear ClkadjCllcd Closeio CLΣ ClusrClvar Cmplx →COL COL→COL COL+ ColctCollect Symb1 Symb2 Colσ CombCON Symb COMBsymb ,m COMBn, symb COMBsymb ,symb Cond Rarray constantCarray constant Name IDN Access …µCONIC Input/Output None ConicConj Conlib ConstConstants Rarray Carray Symb CONJsymb Cont ConvertCorr X1unitssource X2unitstarget X3unitstarget Access Flags COSCosh COV Crdir CrossCswp …µCR Curl CyclotomicCylin COL+, COL-, Rswp →PX DarcyDate #n, #m →DATE DATE+Dbug →date Ddays DECDecr « program » or program name Dedicace DEFDefine Result See also Delalarm DEGDegree Name=exp Namename Name =expname Delay RCLALARM, StoalarmDelkeys CR, OLDPRT, PRLCD, PRST, PRSTC, PRVAR, PR1 Access …µDEPND Input/Output DepndDepth Xkey1, ... ,xkey n Deriv DervxDesolve Access …µDETACH Input/Output DETDetach Attach DIAG→ →DIAGDiagmap Diff Diffeq Access …µDIFFEQ Input/Output DIRDisp Dispxy DistribObj List FREEZE, HALT, INPUT, Prompt DIV DIV2DIV2MOD CURL, Hess Divis DivmodDivpc DIV2 TAYLOR0, TAYLR, Series DERIV, DERVX, DESOLVE, ∂Until testclause END END Error DoerrDolist List List n « program » Results Command Name List n+1 DomainDosubs SIGNTAB, Tabvar List « program » Command Name DOTDOLIST, ENDSUB, NSUB, Stream CNRM, CROSS, DET, Rnrm Access …µDRAW Access …µDRAX Input/Output NoneDraw DRAW3DMATRIX Droite DropDROP2 Lagrange Dropn DtagDUP DUP2 Dupdup Dupn Edit EditbEgcd EGV EgvlElse END Endsub ENGEPSX0 Sign mantissa E sign exponent Eqnlib EQWEQ→ Erase ERR0 ErrmErrn Euler Eval ExlrObj See above →NUM EXP&LN EXPEx,y = excosy + iexsiny EXP2HYP EXP2POWExpan Expand ExpandmodCOLCT, EXPAND, ISOL, QUAD, Show Result X2+X Expfit ExplnExpm Eyept F0λ FactFactor …µF0λ Factormod FactorsModsto Access …µFANNING FanningFAST3D Access …µFAST3D Input/Output None Access ! Test LL FC ? CFcoef FC? Fdistrib FFTCF, FC?, FS? FS?C, SF Distrib Findalarm Access …µFINISHFiler Finish Flasheval FloorFONT6 Xunit Nunit Symb FLOORsymb FONT7 FONT8FONT→ →FONT For Fourier FreeFreeze Xunit Yunit Symb FPsymb Froots FS?Display Area Value Code CLLCD, DISP, Halt FS?C FunctionCF, FC?, FC?C, FS?C, SF Access …µFUNCTION FxndExlr Gamma GaussGbasis AXQ, QXA GCD GcdmodGET GCDMOD, EGCD, IEGCD, LCM Geti ObjgetGETI, PUT, Puti GOR GradGET, PUT, Puti #n #m Grob1 Gramschmidt GraphGreduce DEG, RAD Access …µGRIDMAP Input/Output None Access …µ→GROBGridmap →GROB Grob GrobaddGxor →LCD, LCD→ Hadamard HalftanHalt GOR, REPL, SUB Head HEADER→→HEADER Help Hermite HessHEX CURL, DIV Hilbert Histogram Access …µHISTPLOT Input/Output None HistplotHMS HMS+ HMS→ →HMS… & 9L HMS + … &9L HMS → Home HornerIabcuv Ibasis IbernoulliIBP ABCUV, Iegcd Ichinrem IDNResults See also Chinrem IDIV2 IegcdDIV2, Iquot Ax+by=c Iferr CaseELSE, END, IFERR, then ∑ Y k e Ifft IFT IfteIlap Obj It depends Image LAP, Lapl…ßIM Rarray Carray Symb IMsymb Incr IndepInform Global Global xstart xend Resets Title Format Resets Init → valsInput Init Stack prompt Commandline prompt Result INTPROMPT, STR→ Integer IntvxINV INTVX, Risch Command INVMOD2 Result InvmodIquot Iremainder IsolIsom Symb1 Global Symb2 ISPRIME? JordanMkisom NEXTPRIME, Prevprime KER KerrmKEY BASIS, Image Access …µKEYEVAL Input/Output Keyeval→KEYTIME KEYTIME→ KgetKill Label Access …µ→LANGUAGE Input/Output LagrangeLANGUAGE→ →LANGUAGE LAP LaplLast Objn Obj1 Lastarg LCD→→LCD LCM Lcxm Ldec Lgcd LibevalLibs HERMITE, Tchebycheff Lim LimitLIN Title, nlib, nport, ...,title, nlib, nport Line ΣlineLinfit Model Form of Expression Linin LinsolveLIST→ →LIST List ΠlistΣlist Access …¹ ¹is the rightshift of the Qkey Lname LncollectLNP1 Local LOGLn x + Symb LNP1symb Access !Ø Input/Output Logfit Access …µLR Input/Output Full Command and Function Reference 3139LSQ Intercept x Slope x Lvar MADDET, INV Lname Access …µMAP Input/Output MainMant MAP Access …µ↓MATCH Input/Output Access …µ↑MATCH↑MATCH Symb Symb symb Maths MatrMAX Symb Symb , symb Maxr MaxσMcalc Input/Output See also Mean MEMMenu BINS, MAXΣ, MINΣ, SDEV, TOT, VAR Menuxy RCLMENU, Tmenu Merge MINMinehunt MENU, Tmenu MINIFONT→ →MINIFONTMinit Minr Minσ MitmMkisom 00000000000E-499 MOD ModstoModular Mod y Molwt MrootMsgbox Name Or xunit String Mslv Msolvr Multmod Muser→NDISP EQNLIB, MCALC, MINIT, MITM, MROOT, MSLV, Muser Access …ß NEG ßis the rightshift of the 1key NdistNdupn NEG Newob NextNextprime Access ! Test L not Is the leftshift of the Nkey NIPNot Noval Nsub →NUMNUM …µNΣ Numx NumyOBJ→ OCT OFFOldprt … &NL OBJ → Access …µOLDPRT Access …µOPENIOOpenio Order OverMemory Directory Lorder is the leftshift of the Nkey Global1 ... globaln P2C PA2B2Parametric Xmin, ymin, xmax, ymax, indep, res, axes, ptype, depend Access …µPARITY Input/Output Parity Parsurface Partfrac Path PcarPcoef Home directoryname 1 ... directoryname n Access …µPCONTOUR Input/Output None PcontourPcov Pdim PerinfoPerm Xmax, ymax Pertbl PevalPgdir Pick Pict Command Puts the name Pict on the stack PictPicture Pinit Access …µPKT PIX?Pixoff Pixon Plot PlotaddPmax Pmin Pmini PolarFinds the minimal polynomial of a matrix An nxn matrix a Access …µPOLAR PolynomialPOP Form of Current Plotting Action Equation Input An expression raised to a power POSPotential Powexpand Powmod PR1 Predv Predx…µPR1 Object Predy Preval Prevprime PrlcdPrompt Promptsto Proot PropfracGlobal→ Prompt STO Prst PrstcPrvar Name Name1 name2 Nport global Psdev PSIPsi MEAN, PCOV, PVAR, SDEV, TOT, VAR Ptayl PtpropPurge Symb String or x or xunit or name Push PUTGlobal Global1 ... globaln CLEAR, CLVAR, NEWOB, Pgdir This command sequence PutiObj put List Obj put List Name Pvar PvarsMEAN, PCOV, PSDEV, SDEV, VAR Access …µPVARS Input/Output Nport namebackup MemoryPview Pwrfit PX→C →Qπ+ c/d*i Quad ̟ + c/ d* ̟+ c/ d LQ, LSQ Quot QuoteArithmetic, !ÞPOLYNOMIAL !« Quotient of the Euclidean division QXA RADRand Rank Access …µRATIO RanmRatio LQ, LSQ, QR Rceq RCIRcij Steq Rclalarm RCL FINDALARM, Stoalarm RclfRclkeys Rclmenu Rclvx RclσRcws RDM RDZ COMB, PERM, Rand…ßL RE Recn RectRecv REsymb Remainder RenameQuot New name Old name Reorder RepeatRepl END, While Plot Type Default Interval RESString target String String result Restore Backup To restore aResultant Slopefield Revlist RewriteRisch RKF Rkferr Problem for a differential equation RkfstepIs the rightshift 3key RLB RNDRLB, RR, RRB RNDsymb Rnrm RollRolld Romupload Root ROTROW 3207 ROW+ ROW→→ROW Access … ÃL Byte RRB Is the rightshift of the 3key RPLRRB RL, RLB, RRB Rref Rref Rrefmod RRK − 2 t + t 2 Rrkstep Rsberr RSDRKF, RKFERR, RKFSTEP, RRK, Rsberr Access … Ã R → B RswpRules DET, IDN Same →R, IM, RE180/̟x →Dsymb Access …µSCALEH Input/Output SbrkScale Scaleh Scatrplot ScatterAUTO, SCALEH, Xrng Access …µSCATTER Input/Output None SchurSCI Sclσ Sconj ScrollSdev Send SEQ SeriesDOSUBS, Stream Server Seval Show SidensSigma X1/cm3 Access !ÖDERIV L Access !ÖDERIV LLSigmavx Sign Signtab SIMP2SIGNsymb ABS, MANT, Xpon Simplify SINSincos Sin z Sinh SinvSize Sinh z SLB SlopefieldString Integer List Vector Symb Grob Sneg SnrmNEG, SCONJ, Sinv Solve Solveqn Solver SolvevxSort Sphere SradSquare Analytic Function Returns the square of the argument SQsymb SRB SrecvCOND, SNRM, Trace ASR, SL, SLB, SR Access …µSRECV SreplSST SST↓ Start STDStep Access …µSTIME StepSteq Stime Stoalarm Access Input/OutputSTO Buflen Access …µSTOF StofStokeys Óis the rightshift of the 9 key Store StovxSTO+ STO/, + Stoσ STR→→STR DTAG, EQ→, LIST→, OBJ→, →STR Stream StrmSturm List Obj Result Sturmab StwsSUB Sturmab Subst SubtmodX1, y1 X2, y2 CHR, GOR, GXOR, NUM, POS, REPL, Size SVD SVLSwap DIAG→, MIN, SVL Syseval SylvesterSYST2MAT Tabval 100 yX, symb Symb 1, symb Tabvar →TAGTail →ARRY TAN TAN2CS2TAN2SC Tan z TAN2SC2 TanhTanh z TANHsymb TAYLOR0 TaylrTchebycheff HERMITE, Legendre Tcollect TdeltaTests TDELTAsymb1, symb2 Teval TexpandText Then Ticks Time→TIME Tinc Tlin TlineTINCsymb1, symb2 SIMPLIFY, TCOLLECT, Texpand Tmenu TOTTrace Tran Transio TrigEffect BAUD, CKSM, Parity Trigcos TrigoTrigsin Trigtan TRN TrncCONJ, Tran Trunc TruthTRNCz TRNCsymb Access …µTRUTH Input/Output None TsimpTstr Tvars TVMTvmbeg Tvmend Builtin Commands TypeUbase Object Type Number User objects Ufact UFL1→MINIFUnassign Unassume Unbind →UNITUnpick Unrot UntilUpdir Utpc Utpf UtpnUTPF, UTPN, Utpt UTPC, UTPN, Utpt Utpt UvalUVALsymb Flag -16 clear Rectangular mode Flag -16 set Polar mode € y Coordinate System -16, Complex ModeX1, x2 X1, x2, ..., xn Xn-2 Vandermonde VAR Access …µVERSION Input/Output VarsVER Version Variable name Contents opened in the command line Editor Variable name Contents opened in the most suitable EditorVisit Visitb Access ! L in Wait Is the leftshift of the Nkey VtypeWait Wireframe WhileWhile testclause Repeat loopclause END While Repeat Wslog Access …µWSLOG Access …µΣX Input/OutputΣX2 Log4 ... log1 ΣX2 XcolXget Xmit Access …µXMIT XnumXOR Xpon XputXPONsymb MANT, Sign Command XQ.3658 Results 1829/5000 Command XQ.3658 Results √19/142Xrecv Xrng Access …µXSEND XsendXserv Input/Output RPN Xvol XxrngΣXY ΣX*Y ΣY2 ΣY2Ycol …µΣY Yrng YsliceAUTO, PDIM, PMAX, PMIN, Xrng Yvol YyrngZeros EYEPT, XVOL, XXRNG, YYRNG, Zvol Power Access QZfactor Zvol Where √ Square RootZsymb Symbz SQ, , Isol Access …Á Áis the rightshift of the Ukey Integrate? Undefined Lower limit, upper limit, integrand, name ∞ Infinity SummationSigma Plus Results -π/2 Access …µΣ+ Input/Output Access …µΣ Input/OutputSigma Minus X 2, …, x m 1, …, x 1 m x n 1, … , x n m ∂ Derivative Factorial14159265359… Symb Name Xunit Percent Unit attachmentXy/100 Symb,x « » Program delimiters Less thanType Object Description ≤ Less than or Equal #n1 #n2 Greater than ≥ Greater than or Equal ≠ Not equal Multiply ≠ symb + Add Subtract Divide = Equal Y1/unit == Logical Equality Store → Create LocalDEFINE, RCL, →, STO … É Semicolon CLEAR, DROP, DROPN, DROP2 CAS Settings Selecting CAS SettingsPoints to note when choosing settings CAS directory, Casdir Computer Algebra System Using the CAS Examples and HelpCompatibility with Other Calculators Extending the CAS Computer algebra command categories listed by menu Arithmetic commandsAlgebra commands, …× Arithmetic Integer commands, !ÞINTEGER Arithmetic Modulo commands, !Þ Modulo Arithmetic Permutation commands, !Þ PermutationOther Arithmetic commands, !Þ Calculus commands Exp and Lin commands, !Ð Matrixrelated commandsCreate, !Ø Create Operations, !Ø Operations Quadratic form, !Ø Quadratic Form Linear Systems, !Ø Linear SystemsLinear Applications, !Ø Linear Appl Eigenvectors, !Ø Eigenvectors Symbolic solve commands, !Î Trigonometry commandsOther Trigonometry commands, …Ñ Hyperbolic, …Ñ Hyperbolic Convert commands, !Ú Unit conversion tools, !Ú Units ToolsBase conversion tools, !Ú Base Trigonometric conversions, !Ú Trig Conv Other CAS operations, …µ Matrix convert, !Ú Matrix Convert CAS menu commands, …µ These commands display menus or lists of CAS operationsCAS utility operations Equation Reference Equation Reference FLUIDS, 24 *********************3 Columns and Beams Variable DescriptionΣcr Critical stress Σmax Maximum stress Internal bending moment at Elastic Buckling 1 Eccentric Columns 1Equations Example Simple Deflection 1 Simple Slope 1Equation Solution V=624.387lbf Simple Moment 1Simple Shear 1 Cantilever Deflection 1 Cantilever Slope 1Cantilever Moment 1 Solution V=200lbf Equation Reference Cantilever Shear 1 Electricity Relative permittivityRelative permeability Ohm’s Law and Power 2 Coulomb’s Law 2 Wire Resistance 2 Solution V1=80VSolution I1=5.6250A Voltage Divider 2 Solution R=0.175 Series and Parallel R 2Series and Parallel C 2 Solution V=50V Series and Parallel L 2Capacitive Energy 2 Inductive Energy 2 RLC Current Delay 2 Solution q=0.0020C Equation ReferenceDC Capacitor Current 2 Capacitor Charge 2 Solution V=3.2968V DC Inductor Voltage 2RC Transient 2 RL Transient 2 Solution I=0.0072A Resonant Frequency 2Plate Capacitor 2 Cylindrical Capacitor 2,19 Solenoid Inductance 2 Toroid Inductance 2 Fluids Sinusoidal Voltage 2Sinusoidal Current 2 Pressure at Depth 3 Bernoulli Equation 3Reynolds number Initial and final velocities Flow with Losses 3 Forces and Energy Flow in Full Pipes 3 Linear Mechanics 4 Angular Mechanics 4 Centripetal Force 4Hooke’s Law 4 1D Elastic Collisions 4 Drag Force 4Law of Gravitation 4 MassEnergy Relation 4 Gases Ideal Gas Law 5 Solution Vf=21 Ideal Gas State Change 5Isothermal Expansion 5 Polytropic Processes 5 Real Gas Law 5 Real Gas State Change 5 Heat Transfer Kinetic Theory 5 Heat Capacity 6 Thermal Expansion 6Conduction 6 Convection 6 Conduction + Convection 6 Magnetism Black Body Radiation 6Fba Ia, Ib Straight Wire 7 Force between Wires 7 Solution B=0.0785T Magnetic B Field in Solenoid 7Magnetic B Field in Toroid 7 Motion Linear Motion 8 Object in Free Fall 8Projectile Motion 8 Angular Motion 8 Circular Motion 8Terminal Velocity 8 Escape Velocity 8 Optics Law of Refraction 9 Critical Angle 9 Brewster’s Law 9 Solution n2=1.5000 Spherical Reflection 9Spherical Refraction 9 Thin Lens 9 Oscillations MassSpring System 10 Simple Pendulum 10Example Given L=15cm Conical Pendulum 10 Torsional Pendulum 10Simple Harmonic 10 Plane Geometry Circle 11 Ellipse 11Equations Example Rectangle 11 Regular Polygon 11 Circular Ring 11 Triangle 11 Solid Geometry Cone 12 Cylinder 12 Parallelepiped 12 Sphere 12 Solid State Devices Saturation current density Drawn mask length PN Step Junctions, orDrawn gate length Nmos Transistors, or Channel length JFETs PN Step Junctions 13 Nmos Transistors 13 VDS Bipolar Transistors 13 JFETs 13 Xdmax = ⋅ Vbi VGS + VDS Stress Analysis Maximum principal normal stressMinimum principal normal stress Normal Stress 14 Shear Stress 14Stress on an Element 14 Mohr’s Circle 14 Example Waves Transverse Waves 15,1Longitudinal Waves 15 Sound Waves 15 References Page Development Library Development Library Command Reference Obj StringObj1 … objn Symb Obj1, ...,objn Development Library BetaTesting String Obj Debug string Error listString Obj Code String String Error list Edited string Library Object StringLibrary n LC~C Ey,z.Et →LST Obj … obj Obj 1, ...,obj n Pokearm Obj 1 … obj n Obj 1, ...,obj n →S2 String1 String2Returns String Global Crlib Create Library Command Xlib Extension program Masd The Machine Language and System RPL Compiler IntroductionStarting Masd Modes Errors Format of the error listError messages Message Description Links Labels Extable Constants Expressions Operator Priority Macros and includes Filename conventions Compilation directiveDirective Description !DBGINF directive Docstr Saturn ASM mode CPU architectureBit registers Other notes New instructionsSkips Skips instructions Equivalents These instructions Are equivalent to Tests Saturn instructions syntax Syntax Example Syntax Example DReg=hh See above. This is only valid in emulated Saturn Places the value of Exp in the code, on x nibbles CARRY0 003AA Autousertest ARM mode ARM architecture Instruction set Description Form Operation Assembler Action Flags Armsat instruction Offset ElementREG a REG B REG C REG D REG R0 REG R1 REG R2 REG R3 REG R4 System RPL mode InstructionsReals and system binary Unnamed local variables Defines TokensToken Description Code LC 001 Gosbvl Outcinrtn ?CBIT=1.6 Turnmenuoff LC 80100 Armsat Disassemblers Level Entry Point Library Extable LibraryNop String String 1, ...,string n Error and Status Messages A1 Messages Listed AlphabeticallyMessage Meaning # hex C0C A2 Error and Status Messages Error and Status Messages A3 A4 Error and Status Messages Σdat Error and Status Messages A5 A6 Error and Status Messages Error and Status Messages A7 C0EC0B C0D A8 Error and Status Messages Error and Status Messages A9 # hex Message General Messages A10 Error and Status Messages # hex Message Error and Status Messages A11 OutofMemory Prompts Stack Errors and Messages A12 Error and Status MessagesObject Editing Messages Equation Writer Application Messages # hex Message FloatingPoint Errors Error and Status Messages A13Array Messages Statistics Messages Mode and Plot Input Form Prompts A14 Error and Status Messages Error and Status Messages A15 # hex Message 70F A16 Error and Status Messages 73F Error and Status Messages A17 75F A18 Error and Status Messages 78F Error and Status Messages A19 A20 Error and Status Messages Advanced Statistics Messages Error and Status Messages A21 80F A22 Error and Status Messages 82F Error and Status Messages A23 85F A24 Error and Status Messages 87F Error and Status Messages A25 Statistics Help MessagesHP Solve Application Messages # hex Message Unit Management PrintingTime Messages Programmer’s Doerr Error and Status Messages A27 A28 Error and Status Messages System Flags Choose Box Prompts Error and Status Messages A29 A30 Error and Status Messages Error and Status Messages A31 A32 Error and Status Messages Prompts Error and Status Messages A33 A34 Error and Status Messages Error and Status Messages A35 Statistics Prompts Time and Alarm Prompts A36 Error and Status Messages Error and Status Messages A37 Symbolic Application Prompts A38 Error and Status Messages Error and Status Messages A39 Plot Application Prompts A40 Error and Status Messages Error and Status Messages A41 A42 Error and Status Messages Solve Application Prompts Error and Status Messages A43 A44 Error and Status Messages Error and Status Messages A45 CAS Messages A46 Error and Status Messages Error and Status Messages A47 A48 Error and Status Messages Filer Application MessagesDF0A DF0B DF0C DF0D DF0E DF0F DF1A DF1B DF1C DF1D DF1E DF1F Error and Status Messages A49 Constants Library Messages A50 Error and Status Messages Equation Library MessagesMinehunt Game Prompts MultipleEquation Solver Messages Error and Status Messages A51 Periodic Table MessagesFinancial Solver Messages Development Library and Miscellaneous Messages A52 Error and Status Messages Units Tables of Units and Constants B1 B2 Tables of Units and Constants Tables of Units and Constants B3 B4 Tables of Units and Constants Tables of Units and Constants B5 Constant Full Name Value in SI Units Properties of Elements B6 Tables of Units and Constants System Flags Flag DescriptionNot used System Flags C1 C2 System Flags System Flags C3 C4 System Flags System Flags C5 C6 System Flags System Flags C7 Internal use only /0 occurred C8 System Flags User Flags System Flags C9Page Reserved Variables D1 Contents of the System Reserved Variables ΒENTER Reserved Variables D3 Exited D4 Reserved Variables Reserved Variables D5 MHpar MparN1, n2 Nmines BAR, etc Reserved Variables D7 Prtpar D8 Reserved Variables S1, s2 Reserved Variables D9 Parameter Description Default Value Command To use for input into the tableNUMX, Numy D10 Reserved Variables Var1 var2 … varm Statistical Matrix for Variables 1 to mReserved Variables D11 EXPFIT, PWRFIT, or Logfit D12 Reserved Variables Casdir Reserved Variables Modulo D14 Reserved Variables Object Size Object Type Size bytesTechnical Reference E1 Symbolic Integration Pattern AntiderivativeE2 Technical Reference Technical Reference E3 →DEF Expansions E4 Technical Reference Order Operation Technical Reference E5 International Standard publication No. ISO 31/l197 8 E E6 Technical Reference Group 1 Commands that cannot parallel process Group 2 Commands that must use Dolist to parallel processGeneral rules for parallel processing Parallel Processing with Lists F1 Group 5 Commands that set modes / states Group 6 Oneargument, oneresult commandsGroup 4 ADD and + F2 Parallel Processing with Lists Group 7 Two argument, one result commands Group 8 Multipleargument, oneresult commandsGroup 9 Multipleresult commands Group 10 Quirky commands Using Dolist for Parallel Processing F4 Parallel Processing with Lists $ & C $ & D$ & F $ & + Keycode Keystroke Definition ¥ ! &I@ & ³ @ & O ~@ & O ~@ & Í @ &† @%VARNAME% = varnameKeyboard Shortcuts G3 G4 Keyboard Shortcuts Menu Numbers Syntax ExampleMenuNumber Table H1 Menus 0 through H2 The MenuNumber Table MenuNumber Table H3 Menus 118 through H4 The MenuNumber Table Menus 178 through BuiltIn Library MenusMenuNumber Table H5 Page Command MenuPath Table Key ALPHARS2 MTH NXT Prob+ key Command Type Library Size Keys Menu First I2 The Command MenuPath Table MTH List Arith Modul«MODULAR» Addtoreal CAT Algb I4 The Command MenuPath Table LS&MODE Flag PRG Test NXT NXT PRG NXT Modes Flag ChinremPRG NXT CHR I6 The Command MenuPath Table CAT Delalarm PRG NXT NXT Time Alrm DelayRS&TIME NXT PRG NXT NXT Time NXT I8 The Command MenuPath Table PRG NXT NXT Error Iferr «POLYNOMIAL» EGVMTH Matrx NXT Else I10 The Command MenuPath Table I11 I12 The Command MenuPath Table Calc Deriv NXT «INTEGER»PRG Brch NXT «DIFF» NXT NXT I14 The Command MenuPath Table I15 I16 The Command MenuPath Table I17 I18 The Command MenuPath Table I19 I20 The Command MenuPath Table I21 I22 The Command MenuPath Table I23 I24 The Command MenuPath Table I25 I26 The Command MenuPath Table I27 I28 The Command MenuPath Table Matrices Creat NXT NXT MTH Matrx Make NXT NXT DUP Menuxy VersionCAT Vtype XLIB~ I30 The Command MenuPath Table SLV NXTAlphalse MTH NXT Const «CONSTANTS» Σline ΣlistPRG Test «TESTS» NXT →ALG I32 The Command MenuPath Table Code Description Character CodesAscii Character Codes and Translations J1 Code Trans. Description J2 Ascii Character Codes and Translations Index Alpha keyboard Calculator 59, 531 375 Preserving calculator status Flags 132 Last argument Memory Nested structures 545 Programs Range 3115 Serial communications 237, D3 Tagged objects UPs