Coupled Liquid TanksSamir Khan simulationconsultant@gmail.com

Parameters

Area of Tank 1 1

Area of Tank 2 0.5Pipe Diameter 0.3 mPipe Length 100 mPipe Roughness 0.0001 m

Liquid Density 1000Liquid Viscosity 0.0001 Pa s

Gravity 9.81Time Step 0.1 s

Time Flowrate Reynolds Friction0 1.5 1.2 0 0 0

0.1 1.5 1.2 0.000208 8829 0.0323360.2 1.4999791972 1.2000416057 0.000416 17657.86 0.0271190.3 1.4999375918 1.2001248164 0.000624 26484.55 0.0247220.4 1.499875189 1.2002496219 0.000832 35307.08 0.0232620.5 1.4997919987 1.2004160026 0.00104 44123.45 0.0222530.6 1.4996880353 1.2006239295 0.001247 52931.68 0.0215030.7 1.4995633179 1.2008733641 0.001454 61729.79 0.0209170.8 1.4994178706 1.2011642589 0.001661 70515.81 0.0204440.9 1.4992517216 1.2014965568 0.001868 79287.76 0.0200531 1.4990649042 1.2018701916 0.002074 88043.69 0.019723

1.1 1.4988574562 1.2022850877 0.00228 96781.64 0.019441.2 1.4986294198 1.2027411604 0.002486 105499.6 0.0191951.3 1.4983808421 1.2032383158 0.002691 114195.8 0.0189791.4 1.4981117747 1.2037764507 0.002895 122868.1 0.0187881.5 1.4978222736 1.2043554528 0.003099 131514.6 0.0186181.6 1.4975123996 1.2049752007 0.003302 140133.4 0.0184651.7 1.497182218 1.205635564 0.003504 148722.7 0.0183261.8 1.4968317985 1.206336403 0.003706 157280.4 0.01821.9 1.4964612154 1.2070775692 0.003907 165804.6 0.0180862 1.4960705474 1.2078589051 0.004107 174293.6 0.01798

2.1 1.4956598779 1.2086802442 0.004306 182745.3 0.0178842.2 1.4952292945 1.2095414111 0.004504 191157.9 0.0177942.3 1.4947788892 1.2104422215 0.004701 199529.6 0.0177112.4 1.4943087587 1.2113824826 0.004898 207858.4 0.0176352.5 1.4938190038 1.2123619924 0.005093 216142.6 0.0175632.6 1.4933097297 1.2133805406 0.005287 224380.3 0.0174962.7 1.492781046 1.214437908 0.00548 232569.7 0.0174342.8 1.4922330665 1.2155338669 0.005672 240709 0.0173752.9 1.4916659094 1.2166681812 0.005862 248796.3 0.01732

http://excelcalculations.blogspot.com

m2

m2

kg m-3

m s-2

Liquid Height in Tank 1

Liquid Height in Tank 2

0 20 40 60 80 100 1201.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65Liquid Height in Tank 1

Liquid Height in Tank 2

Time (s)

Heig

ht (m

)

This spreadsheet models the transient flow of liquid between two tanks connected by a pipe.The liquid momentum causes the liquid height in each tank tank to oscillate to an equilibrium.The spreadsheet solves the governing differential equations that describe the flowrate in the pipeand the height of liquid in each tank with a simple Euler routine

3 1.491079697 1.2178406061 0.006051 256829.9 0.0172693.1 1.4904745557 1.2190508885 0.006239 264808.1 0.017223.2 1.4898506165 1.2202987671 0.006426 272729 0.0171743.3 1.489208014 1.2215839721 0.006611 280590.9 0.017133.4 1.4885468872 1.2229062256 0.006795 288392.2 0.0170893.5 1.4878673792 1.2242652417 0.006977 296131 0.017053.6 1.4871696369 1.2256607261 0.007158 303805.8 0.0170133.7 1.4864538115 1.227092377 0.007338 311414.7 0.0169783.8 1.4857200578 1.2285598843 0.007515 318956.3 0.0169453.9 1.4849685349 1.2300629302 0.007691 326428.7 0.0169134 1.4841994054 1.2316011893 0.007866 333830.5 0.016883

4.1 1.4834128359 1.2331743283 0.008038 341159.9 0.0168544.2 1.4826089968 1.2347820064 0.008209 348415.4 0.0168274.3 1.4817880623 1.2364238755 0.008379 355595.5 0.01684.4 1.4809502101 1.2380995798 0.008546 362698.6 0.0167754.5 1.4800956218 1.2398087565 0.008711 369723 0.0167514.6 1.4792244823 1.2415510353 0.008875 376667.5 0.0167284.7 1.4783369805 1.243326039 0.009037 383530.4 0.0167064.8 1.4774333084 1.2451333832 0.009196 390310.2 0.0166854.9 1.4765136616 1.2469726767 0.009354 397005.6 0.0166655 1.4755782393 1.2488435214 0.00951 403615 0.016646

5.1 1.4746272438 1.2507455125 0.009664 410137.2 0.0166275.2 1.4736608808 1.2526782385 0.009815 416570.6 0.016615.3 1.4726793593 1.2546412814 0.009965 422914 0.0165935.4 1.4716828916 1.2566342168 0.010112 429166 0.0165765.5 1.470671693 1.2586566141 0.010257 435325.3 0.0165615.6 1.4696459819 1.2607080362 0.0104 441390.5 0.0165465.7 1.46860598 1.2627880401 0.010541 447360.5 0.0165315.8 1.4675519116 1.2648961768 0.010679 453233.9 0.0165175.9 1.4664840043 1.2670319914 0.010815 459009.6 0.0165046 1.4654024885 1.2691950231 0.010949 464686.3 0.016491

6.1 1.4643075972 1.2713848056 0.01108 470262.8 0.0164786.2 1.4631995665 1.273600867 0.011209 475738.1 0.0164676.3 1.462078635 1.27584273 0.011336 481110.9 0.0164556.4 1.460945044 1.278109912 0.01146 486380.3 0.0164446.5 1.4597990375 1.280401925 0.011582 491545 0.0164346.6 1.4586408619 1.2827182762 0.011701 496604.1 0.0164236.7 1.4574707662 1.2850584676 0.011818 501556.4 0.0164146.8 1.4562890016 1.2874219967 0.011932 506401.1 0.0164046.9 1.4550958221 1.2898083559 0.012043 511137.2 0.0163957 1.4538914834 1.2922170332 0.012152 515763.6 0.016387

7.1 1.452676244 1.2946475121 0.012259 520279.6 0.0163787.2 1.4514503641 1.2970992717 0.012363 524684 0.016377.3 1.4502141065 1.299571787 0.012464 528976.2 0.0163627.4 1.4489677357 1.3020645287 0.012562 533155.3 0.0163557.5 1.4477115182 1.3045769637 0.012658 537220.3 0.0163487.6 1.4464457225 1.3071085549 0.012751 541170.7 0.0163417.7 1.4451706192 1.3096587617 0.012841 545005.5 0.016335

7.8 1.4438864802 1.3122270396 0.012929 548724.1 0.0163297.9 1.4425935796 1.3148128408 0.013014 552325.7 0.0163238 1.4412921929 1.3174156141 0.013096 555809.6 0.016317

8.1 1.4399825974 1.3200348052 0.013175 559175.3 0.0163118.2 1.4386650717 1.3226698565 0.013252 562422 0.0163068.3 1.4373398962 1.3253202077 0.013325 565549.2 0.0163018.4 1.4360073523 1.3279852953 0.013396 568556.2 0.0162978.5 1.4346677232 1.3306645535 0.013464 571442.7 0.0162928.6 1.4333212932 1.3333574136 0.013529 574207.9 0.0162888.7 1.4319683476 1.3360633047 0.013592 576851.5 0.0162848.8 1.4306091733 1.3387816534 0.013651 579373 0.016288.9 1.4292440579 1.3415118842 0.013708 581771.8 0.0162769 1.4278732903 1.3442534194 0.013761 584047.8 0.016273

9.1 1.4264971602 1.3470056796 0.013812 586200.3 0.016279.2 1.4251159582 1.3497680835 0.01386 588229.1 0.0162679.3 1.423729976 1.3525400481 0.013905 590133.9 0.0162649.4 1.4223395056 1.3553209887 0.013947 591914.4 0.0162619.5 1.4209448402 1.3581103196 0.013986 593570.2 0.0162599.6 1.4195462733 1.3609074533 0.014022 595101.2 0.0162579.7 1.4181440992 1.3637118016 0.014055 596507.1 0.0162559.8 1.4167386125 1.3665227751 0.014085 597787.7 0.0162539.9 1.4153301084 1.3693397833 0.014112 598942.9 0.01625110 1.4139188824 1.3721622352 0.014137 599972.5 0.01625

10.1 1.4125052305 1.374989539 0.014158 600876.4 0.01624910.2 1.4110894488 1.3778211025 0.014176 601654.6 0.01624710.3 1.4096718335 1.380656333 0.014192 602306.9 0.01624710.4 1.4082526812 1.3834946377 0.014204 602833.4 0.01624610.5 1.4068322883 1.3863354233 0.014213 603234.1 0.01624510.6 1.4054109515 1.3891780969 0.01422 603508.9 0.01624510.7 1.4039889672 1.3920220656 0.014223 603657.9 0.01624510.8 1.4025666318 1.3948667364 0.014224 603681.2 0.01624510.9 1.4011442414 1.3977115172 0.014221 603578.9 0.01624511 1.399722092 1.400555816 0.014216 603351.2 0.016245

11.1 1.3983004793 1.4033990415 0.014208 602998.1 0.01624611.2 1.3968796984 1.4062406031 0.014197 602519.9 0.01624611.3 1.3954600444 1.4090799112 0.014182 601916.7 0.01624711.4 1.3940418115 1.4119163771 0.014165 601188.9 0.01624811.5 1.3926252935 1.414749413 0.014145 600336.6 0.01624911.6 1.3912107838 1.4175784325 0.014122 599360.1 0.01625111.7 1.3897985747 1.4204028506 0.014096 598259.8 0.01625211.8 1.3883889583 1.4232220835 0.014067 597036 0.01625411.9 1.3869822254 1.4260355491 0.014036 595688.9 0.01625612 1.3855786664 1.4288426672 0.014001 594219.1 0.016258

12.1 1.3841785706 1.4316428589 0.013963 592627 0.0162612.2 1.3827822262 1.4344355476 0.013923 590912.8 0.01626312.3 1.3813899207 1.4372201587 0.01388 589077.2 0.01626612.4 1.3800019402 1.4399961195 0.013834 587120.5 0.01626812.5 1.3786185701 1.4427628598 0.013785 585043.3 0.016271

12.6 1.3772400942 1.4455198116 0.013733 582846.2 0.01627512.7 1.3758667952 1.4482664095 0.013678 580529.6 0.01627812.8 1.3744989547 1.4510020906 0.013621 578094.1 0.01628212.9 1.3731368527 1.4537262947 0.013561 575540.3 0.01628613 1.3717807678 1.4564384643 0.013498 572868.8 0.01629

13.1 1.3704309775 1.4591380451 0.013432 570080.4 0.01629413.2 1.3690877573 1.4618244854 0.013364 567175.5 0.01629913.3 1.3677513815 1.4644972371 0.013293 564155 0.01630313.4 1.3664221226 1.4671557548 0.013219 561019.5 0.01630813.5 1.3651002516 1.4697994968 0.013142 557769.7 0.01631413.6 1.3637860376 1.4724279247 0.013063 554406.5 0.01631913.7 1.3624797482 1.4750405037 0.012981 550930.5 0.01632513.8 1.3611816488 1.4776367024 0.012896 547342.5 0.01633113.9 1.3598920034 1.4802159933 0.012809 543643.5 0.01633714 1.3586110736 1.4827778527 0.01272 539834.1 0.016344

14.1 1.3573391196 1.4853217609 0.012627 535915.2 0.0163514.2 1.356076399 1.487847202 0.012532 531887.8 0.01635714.3 1.3548231678 1.4903536644 0.012435 527752.7 0.01636514.4 1.3535796797 1.4928406405 0.012335 523510.9 0.01637214.5 1.3523461863 1.4953076273 0.012232 519163.1 0.0163814.6 1.3511229371 1.4977541259 0.012128 514710.5 0.01638814.7 1.349910179 1.500179642 0.01202 510153.9 0.01639714.8 1.3487081571 1.5025836857 0.01191 505494.4 0.01640614.9 1.347517114 1.504965772 0.011798 500733 0.01641515 1.3463372897 1.5073254205 0.011684 495870.6 0.016425

15.1 1.3451689222 1.5096621556 0.011567 490908.3 0.01643515.2 1.3440122467 1.5119755067 0.011448 485847.3 0.01644515.3 1.342867496 1.514265008 0.011326 480688.5 0.01645615.4 1.3417349005 1.516530199 0.011202 475433 0.01646715.5 1.3406146879 1.5187706241 0.011076 470082 0.01647915.6 1.3395070834 1.5209858332 0.010948 464636.5 0.01649115.7 1.3384123094 1.5231753813 0.010817 459097.8 0.01650415.8 1.3373305856 1.5253388288 0.010685 453467 0.01651715.9 1.3362621291 1.5274757417 0.01055 447745.2 0.0165316 1.3352071543 1.5295856914 0.010413 441933.7 0.016544

16.1 1.3341658725 1.531668255 0.010274 436033.6 0.01655916.2 1.3331384924 1.5337230151 0.010133 430046.2 0.01657416.3 1.3321252198 1.5357495603 0.00999 423972.8 0.0165916.4 1.3311262576 1.5377474848 0.009845 417814.4 0.01660616.5 1.3301418056 1.5397163889 0.009697 411572.5 0.01662316.6 1.3291720607 1.5416558786 0.009548 405248.3 0.01664116.7 1.3282172169 1.5435655662 0.009398 398843.1 0.0166616.8 1.3272774651 1.5454450698 0.009245 392358.1 0.01667916.9 1.326352993 1.5472940139 0.00909 385794.8 0.01669917 1.3254439855 1.5491120291 0.008934 379154.4 0.01672

17.1 1.3245506239 1.5508987522 0.008775 372438.3 0.01674217.2 1.3236730867 1.5526538265 0.008615 365647.9 0.01676517.3 1.3228115492 1.5543769017 0.008454 358784.5 0.016789

17.4 1.3219661832 1.5560676336 0.00829 351849.4 0.01681417.5 1.3211371575 1.557725685 0.008125 344844.2 0.0168417.6 1.3203246375 1.559350725 0.007959 337770.1 0.01686717.7 1.3195287854 1.5609424292 0.00779 330628.7 0.01689617.8 1.3187497599 1.5625004802 0.00762 323421.3 0.01692617.9 1.3179877165 1.564024567 0.007449 316149.3 0.01695718 1.3172428072 1.5655143857 0.007276 308814.3 0.01699

18.1 1.3165151806 1.5669696388 0.007102 301417.7 0.01702518.2 1.315804982 1.5683900361 0.006926 293960.9 0.01706118.3 1.315112353 1.569775294 0.006749 286445.4 0.01709918.4 1.314437432 1.571125136 0.006571 278872.7 0.0171418.5 1.3137803537 1.5724392927 0.006391 271244.3 0.01718218.6 1.3131412493 1.5737175014 0.00621 263561.8 0.01722718.7 1.3125202465 1.574959507 0.006028 255826.5 0.01727518.8 1.3119174695 1.5761650611 0.005844 248040.1 0.01732518.9 1.3113330387 1.5773339226 0.00566 240204.1 0.01737919 1.3107670711 1.5784658578 0.005474 232320 0.017436

19.1 1.31021968 1.5795606399 0.005287 224389.3 0.01749619.2 1.3096909751 1.5806180497 0.005099 216413.7 0.01756119.3 1.3091810624 1.5816378752 0.00491 208394.6 0.0176319.4 1.3086900442 1.5826199117 0.00472 200333.7 0.01770419.5 1.3082180191 1.5835639618 0.004529 192232.4 0.01778319.6 1.3077650821 1.5844698359 0.004338 184092.5 0.01786919.7 1.3073313243 1.5853373514 0.004145 175915.4 0.01796119.8 1.3069168333 1.5861663333 0.003951 167702.8 0.01806119.9 1.3065216928 1.5869566143 0.003757 159456.3 0.0181720 1.3061459828 1.5877080345 0.003562 151177.4 0.018289

20.1 1.3057897793 1.5884204414 0.003366 142867.8 0.01841920.2 1.3054531549 1.5890936903 0.00317 134529.1 0.01856220.3 1.305136178 1.5897276439 0.002973 126162.9 0.01872120.4 1.3048389136 1.5903221728 0.002775 117770.9 0.01889820.5 1.3045614226 1.5908771548 0.002577 109354.5 0.01909620.6 1.3043037621 1.5913924759 0.002378 100915.6 0.0193220.7 1.3040659854 1.5918680293 0.002178 92455.61 0.01957520.8 1.303848142 1.5923037161 0.001979 83976.3 0.0198720.9 1.3036502775 1.5926994451 0.001778 75479.27 0.02021521 1.3034724336 1.5930551328 0.001578 66966.15 0.020624

21.1 1.3033146483 1.5933707033 0.001377 58438.6 0.02112121.2 1.3031769556 1.5936460887 0.001176 49898.24 0.02173921.3 1.3030593857 1.5938812287 0.000974 41346.73 0.02253721.4 1.3029619647 1.5940760705 0.000772 32785.7 0.02362121.5 1.3028847153 1.5942305695 0.000571 24216.8 0.02521621.6 1.3028276558 1.5943446885 0.000369 15641.67 0.02792221.7 1.3027908009 1.5944183981 0.000166 7061.945 0.03438721.8 1.3027741616 1.5944516767 -3.58E-05 1520.75 0.04208421.9 1.3027777448 1.5944445104 -0.000238 10104.81 0.03119322 1.3028015537 1.5943968926 -0.00044 18688.39 0.026758

22.1 1.3028455872 1.5943088256 -0.000643 27269.52 0.024565

22.2 1.3029098395 1.594180321 -0.000845 35846.27 0.0231922.3 1.3029943003 1.5940113994 -0.001047 44416.7 0.02222522.4 1.3030989547 1.5938020906 -0.001248 52978.9 0.02149922.5 1.3032237833 1.5935524334 -0.00145 61530.94 0.02092922.6 1.3033687621 1.5932624757 -0.001651 70070.91 0.02046622.7 1.3035338628 1.5929322743 -0.001852 78596.9 0.02008222.8 1.3037190524 1.5925618951 -0.002052 87107.01 0.01975622.9 1.3039242935 1.592151413 -0.002253 95599.32 0.01947623 1.3041495441 1.5917009118 -0.002452 104072 0.019233

23.1 1.3043947579 1.5912104843 -0.002651 112523 0.01901923.2 1.304659884 1.590680232 -0.00285 120950.6 0.01882823.3 1.3049448672 1.5901102656 -0.003048 129352.9 0.01865923.4 1.3052496478 1.5895007044 -0.003245 137728 0.01850623.5 1.3055741617 1.5888516766 -0.003442 146074 0.01836723.6 1.3059183404 1.5881633191 -0.003638 154389.1 0.01824223.7 1.3062821111 1.5874357778 -0.003833 162671.4 0.01812723.8 1.3066653965 1.5866692069 -0.004027 170919.1 0.01802123.9 1.3070681151 1.5858637697 -0.004221 179130.4 0.01792424 1.3074901811 1.5850196378 -0.004413 187303.4 0.017834

24.1 1.3079315042 1.5841369915 -0.004605 195436.3 0.01775124.2 1.3083919901 1.5832160197 -0.004796 203527.3 0.01767424.3 1.3088715402 1.5822569197 -0.004985 211574.7 0.01760224.4 1.3093700514 1.5812598972 -0.005174 219576.7 0.01753524.5 1.3098874168 1.5802251663 -0.005361 227531.5 0.01747224.6 1.3104235252 1.5791529496 -0.005547 235437.2 0.01741324.7 1.3109782611 1.5780434777 -0.005732 243292.3 0.01735724.8 1.3115515052 1.5768969896 -0.005916 251095 0.01730524.9 1.3121431338 1.5757137324 -0.006099 258843.5 0.01725625 1.3127530194 1.5744939612 -0.00628 266536.1 0.01721

25.1 1.3133810304 1.5732379393 -0.00646 274171.3 0.01716625.2 1.3140270312 1.5719459377 -0.006639 281747.2 0.01712425.3 1.3146908823 1.5706182355 -0.006816 289262.2 0.01708525.4 1.3153724402 1.5692551195 -0.006991 296714.7 0.01704725.5 1.3160715578 1.5678568844 -0.007165 304103.1 0.01701225.6 1.3167880838 1.5664238323 -0.007338 311425.7 0.01697825.7 1.3175218635 1.5649562731 -0.007509 318681 0.01694625.8 1.318272738 1.5634545241 -0.007678 325867.4 0.01691525.9 1.319040545 1.56191891 -0.007846 332983.3 0.01688626 1.3198251185 1.560349763 -0.008012 340027.2 0.016858

26.1 1.3206262888 1.5587474225 -0.008176 346997.6 0.01683226.2 1.3214438826 1.5571122349 -0.008338 353892.9 0.01680626.3 1.322277723 1.5554445539 -0.008499 360711.7 0.01678226.4 1.3231276299 1.5537447402 -0.008658 367452.5 0.01675926.5 1.3239934194 1.5520131612 -0.008815 374113.8 0.01673726.6 1.3248749043 1.5502501914 -0.00897 380694.3 0.01671526.7 1.3257718941 1.5484562118 -0.009123 387192.5 0.01669526.8 1.326684195 1.5466316101 -0.009274 393607.1 0.01667526.9 1.3276116098 1.5447767805 -0.009423 399936.6 0.016657

27 1.3285539381 1.5428921237 -0.00957 406179.7 0.01663927.1 1.3295109766 1.5409780468 -0.009715 412335.2 0.01662127.2 1.3304825186 1.5390349628 -0.009858 418401.7 0.01660527.3 1.3314683544 1.5370632913 -0.009999 424377.9 0.01658927.4 1.3324682712 1.5350634575 -0.010138 430262.6 0.01657327.5 1.3334820536 1.5330358929 -0.010274 436054.5 0.01655927.6 1.3345094828 1.5309810344 -0.010409 441752.5 0.01654527.7 1.3355503375 1.528899325 -0.010541 447355.2 0.01653127.8 1.3366043935 1.5267912131 -0.01067 452861.7 0.01651827.9 1.3376714237 1.5246571525 -0.010798 458270.7 0.01650528 1.3387511987 1.5224976027 -0.010923 463581.1 0.016493

28.1 1.339843486 1.5203130281 -0.011046 468791.9 0.01648228.2 1.3409480508 1.5181038984 -0.011166 473901.9 0.01647128.3 1.3420646557 1.5158706885 -0.011284 478910.1 0.0164628.4 1.343193061 1.5136138781 -0.0114 483815.4 0.01644928.5 1.3443330242 1.5113339515 -0.011513 488617 0.0164428.6 1.3454843009 1.5090313981 -0.011623 493313.8 0.0164328.7 1.3466466442 1.5067067117 -0.011732 497904.9 0.01642128.8 1.3478198048 1.5043603903 -0.011837 502389.3 0.01641228.9 1.3490035317 1.5019929367 -0.01194 506766.1 0.01640429 1.3501975712 1.4996048576 -0.012041 511034.6 0.016395

29.1 1.351401668 1.4971966639 -0.012139 515193.7 0.01638829.2 1.3526155647 1.4947688706 -0.012234 519242.8 0.0163829.3 1.3538390018 1.4923219963 -0.012327 523181.1 0.01637329.4 1.3550717182 1.4898565636 -0.012417 527007.6 0.01636629.5 1.3563134507 1.4873730986 -0.012505 530721.8 0.01635929.6 1.3575639346 1.4848721308 -0.01259 534322.9 0.01635329.7 1.3588229034 1.4823541933 -0.012672 537810.2 0.01634729.8 1.3600900889 1.4798198223 -0.012751 541183.1 0.01634129.9 1.3613652215 1.4772695571 -0.012828 544440.8 0.01633630 1.36264803 1.47470394 -0.012902 547582.9 0.01633

30.1 1.3639382418 1.4721235164 -0.012973 550608.7 0.01632530.2 1.3652355829 1.4695288342 -0.013042 553517.6 0.01632130.3 1.366539778 1.466920444 -0.013108 556309.2 0.01631630.4 1.3678505506 1.4642988989 -0.013171 558982.8 0.01631230.5 1.3691676228 1.4616647544 -0.013231 561538.1 0.01630830.6 1.3704907159 1.4590185682 -0.013288 563974.7 0.01630430.7 1.3718195499 1.4563609002 -0.013343 566291.9 0.016330.8 1.3731538438 1.4536923123 -0.013395 568489.6 0.01629730.9 1.3744933159 1.4510133683 -0.013444 570567.2 0.01629331 1.3758376833 1.4483246335 -0.01349 572524.5 0.01629

31.1 1.3771866624 1.4456266751 -0.013533 574361.2 0.01628831.2 1.3785399691 1.4429200618 -0.013573 576076.9 0.01628531.3 1.3798973182 1.4402053635 -0.013611 577671.3 0.01628331.4 1.3812584242 1.4374831515 -0.013646 579144.3 0.0162831.5 1.3826230009 1.4347539982 -0.013678 580495.7 0.01627831.6 1.3839907616 1.4320184768 -0.013707 581725.1 0.01627631.7 1.3853614191 1.4292771617 -0.013733 582832.6 0.016275

31.8 1.3867346861 1.4265306278 -0.013756 583817.9 0.01627331.9 1.3881102746 1.4237794508 -0.013776 584680.9 0.01627232 1.3894878966 1.4210242068 -0.013794 585421.7 0.016271

32.1 1.3908672639 1.4182654722 -0.013808 586040 0.0162732.2 1.392248088 1.4155038239 -0.01382 586535.9 0.01626932.3 1.3936300806 1.4127398388 -0.013829 586909.3 0.01626932.4 1.3950129532 1.4099740937 -0.013835 587160.4 0.01626832.5 1.3963964173 1.4072071655 -0.013838 587289.1 0.01626832.6 1.3977801847 1.4044396307 -0.013838 587295.6 0.01626832.7 1.3991639672 1.4016720656 -0.013835 587179.8 0.01626832.8 1.4005474771 1.3989050459 -0.013829 586942 0.01626932.9 1.4019304266 1.3961391467 -0.013821 586582.3 0.01626933 1.4033125287 1.3933749427 -0.01381 586100.9 0.01627

33.1 1.4046934963 1.3906130073 -0.013795 585497.9 0.01627133.2 1.4060730433 1.3878539133 -0.013778 584773.7 0.01627233.3 1.4074508838 1.3850982324 -0.013758 583928.3 0.01627333.4 1.4088267326 1.3823465349 -0.013736 582962.2 0.01627533.5 1.410200305 1.37959939 -0.01371 581875.7 0.01627633.6 1.4115713172 1.3768573655 -0.013682 580668.9 0.01627833.7 1.4129394862 1.3741210277 -0.01365 579342.4 0.0162833.8 1.4143045295 1.371390941 -0.013616 577896.4 0.01628233.9 1.4156661658 1.3686676685 -0.013579 576331.3 0.01628534 1.4170241145 1.365951771 -0.01354 574647.7 0.016287

34.1 1.4183780962 1.3632438076 -0.013497 572845.8 0.0162934.2 1.4197278324 1.3605443353 -0.013452 570926.2 0.01629334.3 1.4210730456 1.3578539087 -0.013404 568889.4 0.01629634.4 1.4224134598 1.3551730804 -0.013353 566735.9 0.01629934.5 1.4237487998 1.3525024005 -0.0133 564466.2 0.01630334.6 1.4250787918 1.3498424163 -0.013244 562080.8 0.01630734.7 1.4264031635 1.3471936729 -0.013185 559580.4 0.01631134.8 1.4277216437 1.3445567125 -0.013123 556965.5 0.01631534.9 1.4290339628 1.3419320744 -0.013059 554236.8 0.01631935 1.4303398524 1.3393202951 -0.012992 551394.9 0.016324

35.1 1.431639046 1.3367219079 -0.012922 548440.4 0.01632935.2 1.4329312784 1.3341374432 -0.01285 545374.2 0.01633435.3 1.434216286 1.331567428 -0.012775 542196.8 0.01633935.4 1.435493807 1.329012386 -0.012698 538908.9 0.01634535.5 1.4367635813 1.3264728374 -0.012618 535511.5 0.01635135.6 1.4380253505 1.323949299 -0.012535 532005.1 0.01635735.7 1.439278858 1.3214422839 -0.01245 528390.7 0.01636435.8 1.4405238492 1.3189523016 -0.012362 524668.9 0.0163735.9 1.4417600712 1.3164798575 -0.012272 520840.7 0.01637736 1.4429872733 1.3140254534 -0.012179 516906.9 0.016384

36.1 1.4442052065 1.311589587 -0.012084 512868.3 0.01639236.2 1.4454136241 1.3091727519 -0.011987 508725.9 0.016436.3 1.4466122813 1.3067754374 -0.011887 504480.6 0.01640836.4 1.4478009356 1.3043981287 -0.011784 500133.2 0.01641636.5 1.4489793467 1.3020413066 -0.011679 495684.7 0.016425

36.6 1.4501472763 1.2997054474 -0.011572 491136.1 0.01643436.7 1.4513044885 1.297391023 -0.011463 486488.4 0.01644436.8 1.4524507497 1.2950985005 -0.011351 481742.5 0.01645436.9 1.4535858288 1.2928283425 -0.011237 476899.5 0.01646437 1.4547094967 1.2905810066 -0.01112 471960.4 0.016475

37.1 1.4558215271 1.2883569458 -0.011002 466926.2 0.01648637.2 1.456921696 1.286156608 -0.010881 461798 0.01649737.3 1.4580097819 1.2839804361 -0.010758 456577 0.01650937.4 1.459085566 1.2818288679 -0.010633 451264.1 0.01652237.5 1.460148832 1.2797023361 -0.010505 445860.5 0.01653537.6 1.461199366 1.277601268 -0.010376 440367.3 0.01654837.7 1.4622369571 1.2755260858 -0.010244 434785.8 0.01656237.8 1.4632613969 1.2734772061 -0.010111 429116.9 0.01657637.9 1.4642724799 1.2714550402 -0.009975 423362 0.01659138 1.4652700031 1.2694599938 -0.009838 417522.2 0.016607

38.1 1.4662537666 1.2674924669 -0.009698 411598.7 0.01662338.2 1.467223573 1.2655528539 -0.009557 405592.7 0.0166438.3 1.4681792282 1.2636415436 -0.009413 399505.4 0.01665838.4 1.4691205406 1.2617589187 -0.009268 393338.2 0.01667638.5 1.4700473218 1.2599053563 -0.009121 387092.2 0.01669538.6 1.4709593863 1.2580812274 -0.008972 380768.7 0.01671538.7 1.4718565514 1.2562868972 -0.008821 374369.1 0.01673638.8 1.4727386378 1.2545227245 -0.008668 367894.5 0.01675738.9 1.4736054689 1.2527890623 -0.008514 361346.4 0.0167839 1.4744568714 1.2510862572 -0.008358 354726.1 0.016803

39.1 1.4752926751 1.2494146499 -0.0082 348034.8 0.01682839.2 1.4761127128 1.2477745743 -0.008041 341274 0.01685439.3 1.4769168208 1.2461663585 -0.00788 334445 0.0168839.4 1.4777048382 1.2445903237 -0.007718 327549.1 0.01690839.5 1.4784766075 1.243046785 -0.007554 320587.7 0.01693839.6 1.4792319746 1.2415360508 -0.007388 313562.3 0.01696939.7 1.4799707884 1.2400584232 -0.007221 306474.3 0.01700139.8 1.4806929014 1.2386141973 -0.007053 299324.9 0.01703539.9 1.4813981691 1.2372036618 -0.006883 292115.8 0.0170740 1.4820864506 1.2358270988 -0.006712 284848.2 0.017108

40.1 1.4827576083 1.2344847833 -0.006539 277523.7 0.01714740.2 1.4834115081 1.2331769839 -0.006365 270143.6 0.01718940.3 1.484048019 1.2319039621 -0.00619 262709.5 0.01723240.4 1.4846670137 1.2306659726 -0.006014 255222.9 0.01727940.5 1.4852683684 1.2294632632 -0.005836 247685.1 0.01732840.6 1.4858519626 1.2282960748 -0.005657 240097.7 0.0173840.7 1.4864176794 1.2271646411 -0.005477 232462.1 0.01743540.8 1.4869654055 1.2260691891 -0.005296 224780 0.01749340.9 1.4874950308 1.2250099383 -0.005114 217052.7 0.01755541 1.4880064492 1.2239871015 -0.004931 209281.8 0.017622

41.1 1.4884995579 1.2230008842 -0.004747 201468.9 0.01769341.2 1.4889742577 1.2220514846 -0.004562 193615.3 0.01776941.3 1.4894304531 1.2211390938 -0.004376 185722.8 0.017851

41.4 1.4898680521 1.2202638958 -0.004189 177792.8 0.01793941.5 1.4902869665 1.2194260671 -0.004001 169826.8 0.01803541.6 1.4906871115 1.2186257771 -0.003813 161826.5 0.01813841.7 1.4910684061 1.2178631878 -0.003624 153793.3 0.0182541.8 1.4914307731 1.2171384538 -0.003434 145728.9 0.01837341.9 1.4917741388 1.2164517225 -0.003243 137634.8 0.01850742 1.4920984332 1.2158031337 -0.003052 129512.6 0.018656

42.1 1.49240359 1.2151928199 -0.00286 121363.8 0.0188242.2 1.4926895469 1.2146209063 -0.002667 113190.1 0.01900342.3 1.4929562448 1.2140875104 -0.002474 104993 0.01920842.4 1.4932036289 1.2135927423 -0.00228 96774.18 0.01944142.5 1.4934316476 1.2131367047 -0.002086 88535.11 0.01970642.6 1.4936402536 1.2127194928 -0.001891 80277.45 0.02001342.7 1.4938294029 1.2123411943 -0.001697 72002.79 0.02037342.8 1.4939990554 1.2120018891 -0.001501 63712.72 0.02080242.9 1.494149175 1.21170165 -0.001306 55408.85 0.02132443 1.494279729 1.2114405419 -0.00111 47092.79 0.021977

43.1 1.4943906888 1.2112186224 -0.000913 38766.12 0.02282743.2 1.4944820293 1.2110359414 -0.000717 30430.46 0.02399443.3 1.4945537294 1.2108925412 -0.00052 22087.41 0.02574443.4 1.4946057716 1.2107884567 -0.000324 13738.56 0.02882943.5 1.4946381424 1.2107237153 -0.000127 5385.516 0.03717143.6 1.4946508317 1.2106983367 7E-05 2970.146 0.04469243.7 1.4946438334 1.2107123331 0.000267 11326.85 0.03027743.8 1.4946171452 1.2107657096 0.000464 19682.73 0.02643543.9 1.4945707688 1.2108584623 0.000661 28035.91 0.02441844 1.4945047108 1.2109905785 0.000857 36384.5 0.02312

44.1 1.4944189818 1.2111620364 0.001054 44726.62 0.02219544.2 1.4943135972 1.2113728056 0.00125 53060.41 0.02149344.3 1.4941885766 1.2116228469 0.001446 61383.99 0.02093844.4 1.4940439439 1.2119121121 0.001642 69695.52 0.02048544.5 1.4938797277 1.2122405445 0.001838 77993.13 0.02010744.6 1.4936959608 1.2126080785 0.002033 86274.98 0.01978644.7 1.4934926801 1.2130146397 0.002228 94539.21 0.01950944.8 1.4932699274 1.2134601452 0.002422 102784 0.01926844.9 1.4930277483 1.2139445034 0.002616 111007.5 0.01905545 1.4927661931 1.2144676138 0.002809 119207.9 0.018866

45.1 1.4924853162 1.2150293677 0.003001 127383.3 0.01869745.2 1.4921851764 1.2156296473 0.003193 135532 0.01854445.3 1.4918658367 1.2162683266 0.003385 143652.1 0.01840645.4 1.4915273645 1.2169452711 0.003575 151741.8 0.01828145.5 1.4911698313 1.2176603375 0.003765 159799.4 0.01816545.6 1.4907933129 1.2184133743 0.003954 167823 0.0180645.7 1.4903978893 1.2192042215 0.004142 175810.9 0.01796245.8 1.4899836447 1.2200327107 0.00433 183761.3 0.01787245.9 1.4895506674 1.2208986652 0.004516 191672.4 0.01778946 1.48909905 1.2218019 0.004702 199542.5 0.017711

46.1 1.4886288891 1.2227422219 0.004886 207369.9 0.017639

46.2 1.4881402853 1.2237194294 0.005069 215152.8 0.01757146.3 1.4876333435 1.224733313 0.005252 222889.5 0.01750846.4 1.4871081725 1.225783655 0.005433 230578.3 0.01744946.5 1.4865648851 1.2268702298 0.005613 238217.6 0.01739346.6 1.4860035982 1.2279928036 0.005792 245805.5 0.0173446.7 1.4854244325 1.229151135 0.005969 253340.6 0.01729146.8 1.4848275128 1.2303449744 0.006145 260821.1 0.01724446.9 1.4842129676 1.2315740648 0.00632 268245.3 0.017247 1.4835809295 1.2328381411 0.006494 275611.7 0.017158

47.1 1.4829315346 1.2341369308 0.006666 282918.7 0.01711847.2 1.4822649232 1.2354701536 0.006837 290164.6 0.0170847.3 1.481581239 1.2368375221 0.007006 297347.9 0.01704447.4 1.4808806296 1.2382387409 0.007174 304467 0.0170147.5 1.4801632462 1.2396735076 0.00734 311520.3 0.01697847.6 1.4794292438 1.2411415124 0.007505 318506.4 0.01694747.7 1.4786787808 1.2426424384 0.007668 325423.7 0.01691747.8 1.4779120193 1.2441759613 0.007829 332270.7 0.01688947.9 1.4771291249 1.2457417501 0.007989 339046 0.01686248 1.4763302667 1.2473394665 0.008146 345748 0.016837

48.1 1.4755156172 1.2489687656 0.008303 352375.4 0.01681248.2 1.4746853522 1.2506292955 0.008457 358926.7 0.01678848.3 1.4738396511 1.2523206977 0.00861 365400.5 0.01676648.4 1.4729786965 1.254042607 0.00876 371795.4 0.01674448.5 1.4721026741 1.2557946518 0.008909 378110.1 0.01672448.6 1.4712117731 1.2575764538 0.009056 384343.3 0.01670448.7 1.4703061856 1.2593876288 0.009201 390493.5 0.01668548.8 1.4693861071 1.2612277859 0.009344 396559.5 0.01666748.9 1.4684517359 1.2630965283 0.009485 402539.9 0.01664949 1.4675032735 1.2649934531 0.009623 408433.7 0.016632

49.1 1.4665409243 1.2669181514 0.00976 414239.4 0.01661649.2 1.4655648957 1.2688702085 0.009895 419955.9 0.01660149.3 1.464575398 1.270849204 0.010028 425582 0.01658649.4 1.4635726441 1.2728547118 0.010158 431116.4 0.01657149.5 1.4625568499 1.2748863001 0.010286 436558.2 0.01655849.6 1.461528234 1.276943532 0.010412 441906 0.01654449.7 1.4604870176 1.2790259649 0.010536 447158.8 0.01653249.8 1.4594334244 1.2811331512 0.010657 452315.6 0.01651949.9 1.4583676809 1.2832646382 0.010777 457375.2 0.01650750 1.4572900159 1.2854199681 0.010894 462336.6 0.016496

50.1 1.4562006609 1.2875986782 0.011008 467198.9 0.01648550.2 1.4550998494 1.2898003011 0.01112 471960.9 0.01647550.3 1.4539878177 1.2920243646 0.01123 476621.8 0.01646550.4 1.452864804 1.2942703921 0.011338 481180.6 0.01645550.5 1.4517310488 1.2965379023 0.011443 485636.4 0.01644650.6 1.4505867951 1.2988264099 0.011545 489988.2 0.01643750.7 1.4494322874 1.3011354251 0.011645 494235.3 0.01642850.8 1.4482677729 1.3034644542 0.011743 498376.8 0.0164250.9 1.4470935003 1.3058129993 0.011838 502411.7 0.016412

51 1.4459097205 1.3081805589 0.01193 506339.5 0.01640451.1 1.4447166862 1.3105666275 0.01202 510159.2 0.01639751.2 1.443514652 1.3129706961 0.012108 513870.2 0.0163951.3 1.4423038739 1.3153922521 0.012193 517471.6 0.01638351.4 1.4410846102 1.3178307797 0.012275 520962.9 0.01637751.5 1.4398571203 1.3202857595 0.012355 524343.3 0.01637151.6 1.4386216654 1.3227566692 0.012432 527612.3 0.01636551.7 1.4373785083 1.3252429834 0.012506 530769.1 0.01635951.8 1.4361279131 1.3277441738 0.012578 533813.2 0.01635451.9 1.4348701454 1.3302597092 0.012647 536744 0.01634952 1.4336054721 1.3327890558 0.012713 539561 0.016344

52.1 1.4323341613 1.3353316773 0.012777 542263.7 0.01633952.2 1.4310564825 1.337887035 0.012838 544851.6 0.01633552.3 1.4297727062 1.3404545876 0.012896 547324.2 0.01633152.4 1.428483104 1.343033792 0.012952 549681 0.01632752.5 1.4271879486 1.3456241027 0.013004 551921.7 0.01632352.6 1.4258875137 1.3482249726 0.013054 554045.9 0.0163252.7 1.4245820738 1.3508358524 0.013102 556053.2 0.01631652.8 1.4232719043 1.3534561914 0.013146 557943.3 0.01631352.9 1.4219572815 1.3560854371 0.013188 559715.8 0.01631153 1.4206384821 1.3587230358 0.013227 561370.6 0.016308

53.1 1.4193157839 1.3613684322 0.013263 562907.2 0.01630553.2 1.417989465 1.3640210699 0.013297 564325.6 0.01630353.3 1.4166598042 1.3666803915 0.013327 565625.4 0.01630153.4 1.4153270808 1.3693458385 0.013355 566806.6 0.01629953.5 1.4139915742 1.3720168515 0.01338 567868.9 0.01629853.6 1.4126535647 1.3746928706 0.013402 568812.2 0.01629653.7 1.4113133325 1.3773733351 0.013422 569636.5 0.01629553.8 1.4099711581 1.3800576838 0.013438 570341.6 0.01629453.9 1.4086273224 1.3827453552 0.013452 570927.5 0.01629354 1.4072821062 1.3854357877 0.013463 571394.2 0.016292

54.1 1.4059357904 1.3881284192 0.013471 571741.6 0.01629254.2 1.404588656 1.3908226879 0.013477 571969.8 0.01629154.3 1.403240984 1.3935180321 0.013479 572078.8 0.01629154.4 1.401893055 1.39621389 0.013479 572068.8 0.01629154.5 1.4005451497 1.3989097006 0.013476 571939.7 0.01629154.6 1.3991975485 1.401604903 0.01347 571691.8 0.01629254.7 1.3978505314 1.4042989371 0.013462 571325.1 0.01629254.8 1.3965043783 1.4069912434 0.01345 570839.9 0.01629354.9 1.3951593685 1.409681263 0.013436 570236.3 0.01629455 1.3938157808 1.4123684384 0.013419 569514.6 0.016295

55.1 1.3924738937 1.4150522127 0.013399 568675 0.01629655.2 1.3911339848 1.4177320303 0.013377 567717.7 0.01629855.3 1.3897963315 1.420407337 0.013351 566643.1 0.016355.4 1.3884612102 1.4230775796 0.013323 565451.5 0.01630155.5 1.3871288966 1.4257422069 0.013292 564143.1 0.01630355.6 1.3857996656 1.4284006688 0.013259 562718.5 0.01630655.7 1.3844737914 1.4310524172 0.013222 561177.9 0.016308

55.8 1.3831515471 1.4336969057 0.013183 559521.8 0.01631155.9 1.381833205 1.4363335899 0.013142 557750.5 0.01631456 1.3805190363 1.4389619273 0.013097 555864.6 0.016317

56.1 1.3792093111 1.4415813777 0.01305 553864.6 0.0163256.2 1.3779042985 1.4441914031 0.013 551750.8 0.01632356.3 1.3766042662 1.4467914676 0.012948 549523.9 0.01632756.4 1.375309481 1.4493810381 0.012893 547184.4 0.01633156.5 1.3740202081 1.4519595838 0.012835 544732.8 0.01633556.6 1.3727367116 1.4545265768 0.012775 542169.8 0.0163456.7 1.3714592542 1.4570814917 0.012712 539495.9 0.01634456.8 1.3701880969 1.4596238061 0.012646 536711.7 0.01634956.9 1.3689234997 1.4621530006 0.012578 533818 0.01635457 1.3676657207 1.4646685586 0.012507 530815.4 0.016359

57.1 1.3664150165 1.4671699671 0.012434 527704.5 0.01636557.2 1.3651716421 1.4696567158 0.012358 524486.1 0.01637157.3 1.3639358508 1.4721282983 0.01228 521160.9 0.01637757.4 1.3627078944 1.4745842112 0.012199 517729.7 0.01638357.5 1.3614880225 1.4770239549 0.012115 514193.2 0.01638957.6 1.3602764833 1.4794470334 0.01203 510552.3 0.01639657.7 1.3590735229 1.4818529542 0.011941 506807.6 0.01640357.8 1.3578793856 1.4842412288 0.011851 502960.2 0.01641157.9 1.3566943136 1.4866113727 0.011758 499010.7 0.01641958 1.3555185474 1.4889629052 0.011662 494960.1 0.016427

58.1 1.3543523252 1.4912953497 0.011564 490809.3 0.01643558.2 1.3531958831 1.4936082338 0.011464 486559.1 0.01644458.3 1.3520494553 1.4959010894 0.011362 482210.5 0.01645358.4 1.3509132737 1.4981734527 0.011257 477764.4 0.01646258.5 1.3497875679 1.5004248642 0.01115 473221.7 0.01647258.6 1.3486725654 1.5026548691 0.011041 468583.6 0.01648258.7 1.3475684914 1.5048630171 0.010929 463850.8 0.01649358.8 1.3464755687 1.5070488626 0.010816 459024.5 0.01650458.9 1.3453940178 1.5092119645 0.0107 454105.6 0.01651559 1.3443240566 1.5113518868 0.010582 449095.3 0.016527

59.1 1.3432659008 1.5134681984 0.010461 443994.5 0.01653959.2 1.3422197635 1.515560473 0.010339 438804.3 0.01655259.3 1.3411858553 1.5176282894 0.010215 433525.8 0.01656559.4 1.3401643842 1.5196712316 0.010088 428160.1 0.01657959.5 1.3391555557 1.5216888886 0.00996 422708.4 0.01659359.6 1.3381595725 1.523680855 0.009829 417171.7 0.01660859.7 1.3371766348 1.5256467304 0.009697 411551.3 0.01662359.8 1.33620694 1.52758612 0.009563 405848.2 0.0166459.9 1.3352506828 1.5294986344 0.009426 400063.6 0.01665660 1.3343080551 1.5313838898 0.009288 394198.8 0.016674

60.1 1.3333792461 1.5332415078 0.009148 388254.9 0.01669260.2 1.3324644421 1.5350711159 0.009006 382233.2 0.0167160.3 1.3315638264 1.5368723473 0.008862 376134.8 0.0167360.4 1.3306775796 1.5386448409 0.008717 369961.1 0.0167560.5 1.3298058793 1.5403882415 0.00857 363713.2 0.016772

60.6 1.3289489001 1.5421021998 0.008421 357392.6 0.01679460.7 1.3281068138 1.5437863725 0.00827 351000.3 0.01681760.8 1.3272797888 1.5454404223 0.008118 344537.7 0.01684160.9 1.326467991 1.5470640181 0.007964 338006.2 0.01686661 1.3256715826 1.5486568348 0.007809 331407 0.016893

61.1 1.3248907233 1.5502185535 0.007652 324741.5 0.0169261.2 1.3241255692 1.5517488616 0.007493 318010.9 0.01694961.3 1.3233762736 1.5532474529 0.007333 311216.8 0.01697961.4 1.3226429863 1.5547140273 0.007171 304360.3 0.01701161.5 1.3219258543 1.5561482914 0.007008 297442.9 0.01704461.6 1.321225021 1.557549958 0.006844 290466 0.01707961.7 1.3205406267 1.5589187466 0.006678 283430.9 0.01711561.8 1.3198728084 1.5602543831 0.006511 276339 0.01715461.9 1.3192217 1.5615566 0.006343 269191.8 0.01719462 1.3185874317 1.5628251366 0.006173 261990.7 0.017237

62.1 1.3179701307 1.5640597385 0.006002 254737 0.01728262.2 1.3173699207 1.5652601585 0.00583 247432.3 0.01732962.3 1.3167869221 1.5664261558 0.005657 240078 0.0173862.4 1.3162212517 1.5675574966 0.005482 232675.4 0.01743362.5 1.3156730232 1.5686539537 0.005307 225226.2 0.0174962.6 1.3151423465 1.569715307 0.00513 217731.7 0.0175562.7 1.3146293284 1.5707413433 0.004953 210193.3 0.01761462.8 1.314134072 1.5717318561 0.004774 202612.7 0.01768262.9 1.3136566769 1.5726866461 0.004594 194991.3 0.01775663 1.3131972395 1.573605521 0.004414 187330.6 0.017834

63.1 1.3127558523 1.5744882954 0.004232 179632 0.01791863.2 1.3123326044 1.5753347911 0.00405 171897.1 0.01800963.3 1.3119275815 1.5761448369 0.003867 164127.3 0.01810763.4 1.3115408656 1.5769182688 0.003683 156324.3 0.01821463.5 1.3111725351 1.5776549299 0.003499 148489.5 0.0183363.6 1.3108226648 1.5783546704 0.003313 140624.5 0.01845663.7 1.3104913261 1.5790173478 0.003127 132730.8 0.01859563.8 1.3101785866 1.5796428268 0.002941 124809.8 0.01874863.9 1.3098845103 1.5802309793 0.002754 116863.3 0.01891864 1.3096091577 1.5807816846 0.002566 108892.6 0.019107

64.1 1.3093525854 1.5812948291 0.002377 100899.4 0.0193264.2 1.3091148467 1.5817703066 0.002189 92885.26 0.01956264.3 1.308895991 1.582208018 0.001999 84851.63 0.01983864.4 1.308696064 1.5826078719 0.00181 76800.13 0.02015764.5 1.308515108 1.582969784 0.001619 68732.3 0.02053364.6 1.3083531613 1.5832936773 0.001429 60649.71 0.02098264.7 1.3082102588 1.5835794823 0.001238 52553.92 0.02153164.8 1.3080864316 1.5838271368 0.001047 44446.5 0.02222264.9 1.307981707 1.584036586 0.000856 36329.01 0.02312765 1.3078961088 1.5842077824 0.000665 28203.02 0.024387

65.1 1.307829657 1.584340686 0.000473 20070.09 0.02631665.2 1.3077823679 1.5844352641 0.000281 11931.78 0.02987565.3 1.3077542543 1.5844914913 8.929E-05 3789.65 0.041349

65.4 1.3077453252 1.5845093496 -0.000103 4354.76 0.03961265.5 1.3077555859 1.5844888283 -0.000295 12499.88 0.02952365.6 1.307785038 1.584429924 -0.000486 20643.89 0.02614565.7 1.307833679 1.584332642 -0.000678 28784.93 0.0242865.8 1.3079015019 1.5841969962 -0.00087 36921.17 0.02305265.9 1.3079884954 1.5840230093 -0.001061 45050.8 0.02216466 1.3080946438 1.5838107124 -0.001253 53172 0.021485

66.1 1.3082199274 1.5835601452 -0.001444 61282.95 0.02094466.2 1.3083643219 1.5832713561 -0.001635 69381.84 0.020566.3 1.3085277991 1.5829444019 -0.001825 77466.87 0.02012966.4 1.3087103261 1.5825793478 -0.002015 85536.24 0.01981366.5 1.3089118661 1.5821762678 -0.002205 93588.16 0.01953966.6 1.309132378 1.581735244 -0.002394 101620.8 0.019366.7 1.3093718164 1.5812563672 -0.002583 109632.4 0.01908966.8 1.3096301318 1.5807397364 -0.002771 117621.3 0.01890166.9 1.3099072704 1.5801854593 -0.002959 125585.5 0.01873367 1.3102031742 1.5795936516 -0.003146 133523.4 0.018581

67.1 1.3105177812 1.5789644375 -0.003332 141433.1 0.01844367.2 1.3108510252 1.5782979496 -0.003518 149313 0.01831767.3 1.3112028357 1.5775943286 -0.003703 157161.3 0.01820267.4 1.3115731383 1.5768537235 -0.003887 164976.2 0.01809667.5 1.3119618543 1.5760762914 -0.00407 172756.1 0.01799967.6 1.3123689012 1.5752621976 -0.004253 180499.1 0.01790967.7 1.3127941922 1.5744116156 -0.004434 188203.6 0.01782567.8 1.3132376366 1.5735247269 -0.004615 195868 0.01774767.9 1.3136991396 1.5726017208 -0.004795 203490.4 0.01767468 1.3141786025 1.571642795 -0.004973 211069.2 0.017606

68.1 1.3146759227 1.5706481546 -0.005151 218602.8 0.01754368.2 1.3151909935 1.5696180131 -0.005327 226089.5 0.01748368.3 1.3157237043 1.5685525913 -0.005502 233527.7 0.01742768.4 1.3162739409 1.5674521182 -0.005676 240915.6 0.01737468.5 1.316841585 1.5663168301 -0.005849 248251.8 0.01732468.6 1.3174265144 1.5651469712 -0.006021 255534.5 0.01727768.7 1.3180286034 1.5639427932 -0.006191 262762.2 0.01723268.8 1.3186477224 1.5627045553 -0.00636 269933.4 0.0171968.9 1.319283738 1.5614325241 -0.006528 277046.4 0.0171569 1.3199365132 1.5601269736 -0.006694 284099.7 0.017112

69.1 1.3206059074 1.5587881852 -0.006859 291091.8 0.01707569.2 1.3212917763 1.5574164474 -0.007022 298021.1 0.01704169.3 1.321993972 1.556012056 -0.007184 304886.2 0.01700869.4 1.3227123432 1.5545753137 -0.007344 311685.5 0.01697769.5 1.3234467348 1.5531065303 -0.007503 318417.6 0.01694769.6 1.3241969886 1.5516060227 -0.00766 325081 0.01691969.7 1.3249629428 1.5500741144 -0.007815 331674.4 0.01689269.8 1.3257444321 1.5485111359 -0.007969 338196.1 0.01686669.9 1.326541288 1.5469174241 -0.008121 344645 0.01684170 1.3273533386 1.5452933228 -0.008271 351019.5 0.016817

70.1 1.3281804089 1.5436391822 -0.008419 357318.4 0.016794

70.2 1.3290223205 1.5419553589 -0.008566 363540.2 0.01677270.3 1.329878892 1.540242216 -0.00871 369683.7 0.01675170.4 1.3307499387 1.5385001226 -0.008853 375747.5 0.01673170.5 1.3316352729 1.5367294542 -0.008994 381730.4 0.01671270.6 1.3325347038 1.5349305923 -0.009133 387631 0.01669470.7 1.3334480378 1.5331039243 -0.00927 393448.1 0.01667670.8 1.3343750782 1.5312498436 -0.009405 399180.6 0.01665970.9 1.3353156253 1.5293687493 -0.009539 404827.2 0.01664271 1.3362694768 1.5274610463 -0.00967 410386.6 0.016627

71.1 1.3372364275 1.5255271449 -0.009798 415857.8 0.01661271.2 1.3382162694 1.5235674612 -0.009925 421239.6 0.01659771.3 1.3392087919 1.5215824163 -0.01005 426530.9 0.01658371.4 1.3402137816 1.5195724368 -0.010172 431730.5 0.0165771.5 1.3412310227 1.5175379546 -0.010293 436837.5 0.01655771.6 1.3422602967 1.5154794065 -0.010411 441850.7 0.01654471.7 1.3433013828 1.5133972343 -0.010527 446769.1 0.01653271.8 1.3443540576 1.5112918848 -0.01064 451591.6 0.01652171.9 1.3454180954 1.5091638093 -0.010752 456317.5 0.0165172 1.346493268 1.5070134639 -0.010861 460945.5 0.016499

72.1 1.3475793453 1.5048413095 -0.010967 465474.9 0.01648972.2 1.3486760946 1.5026478109 -0.011072 469904.6 0.01647972.3 1.3497832812 1.5004334377 -0.011174 474233.8 0.0164772.4 1.3509006683 1.4981986634 -0.011273 478461.7 0.01646172.5 1.3520280171 1.4959439659 -0.011371 482587.3 0.01645272.6 1.3531650866 1.4936698268 -0.011465 486609.9 0.01644472.7 1.3543116342 1.4913767317 -0.011558 490528.6 0.01643672.8 1.355467415 1.48906517 -0.011648 494342.8 0.01642872.9 1.3566321827 1.4867356346 -0.011735 498051.5 0.01642173 1.3578056889 1.4843886222 -0.01182 501654.2 0.016413

73.1 1.3589876837 1.4820246327 -0.011902 505150 0.01640773.2 1.3601779154 1.4796441693 -0.011982 508538.4 0.016473.3 1.3613761307 1.4772477385 -0.012059 511818.7 0.01639473.4 1.3625820751 1.4748358498 -0.012134 514990.2 0.01638873.5 1.3637954921 1.4724090157 -0.012206 518052.4 0.01638273.6 1.3650161242 1.4699677515 -0.012276 521004.6 0.01637773.7 1.3662437124 1.4675125752 -0.012343 523846.4 0.01637273.8 1.3674779963 1.4650440074 -0.012407 526577.1 0.01636773.9 1.3687187144 1.4625625713 -0.012469 529196.3 0.01636274 1.3699656039 1.4600687922 -0.012528 531703.6 0.016358

74.1 1.371218401 1.457563198 -0.012584 534098.4 0.01635374.2 1.3724768408 1.4550463184 -0.012638 536380.4 0.01634974.3 1.3737406573 1.4525186854 -0.012689 538549.1 0.01634674.4 1.3750095837 1.4499808326 -0.012738 540604.1 0.01634274.5 1.3762833522 1.4474332956 -0.012783 542545.2 0.01633974.6 1.3775616942 1.4448766115 -0.012826 544372 0.01633674.7 1.3788443405 1.4423113191 -0.012867 546084.1 0.01633374.8 1.3801310208 1.4397379584 -0.012904 547681.3 0.0163374.9 1.3814214646 1.4371570708 -0.012939 549163.4 0.016328

75 1.3827154005 1.4345691991 -0.012972 550530.2 0.01632675.1 1.3840125567 1.4319748867 -0.013001 551781.4 0.01632375.2 1.3853126608 1.4293746783 -0.013028 552916.8 0.01632275.3 1.3866154403 1.4267691194 -0.013052 553936.3 0.0163275.4 1.387920622 1.424158756 -0.013073 554839.8 0.01631875.5 1.3892279325 1.4215441349 -0.013092 555627.2 0.01631775.6 1.3905370984 1.4189258033 -0.013107 556298.4 0.01631675.7 1.3918478457 1.4163043086 -0.013121 556853.4 0.01631575.8 1.3931599006 1.4136801988 -0.013131 557292.1 0.01631475.9 1.3944729892 1.4110540217 -0.013138 557614.5 0.01631476 1.3957868374 1.4084263252 -0.013143 557820.7 0.016314

76.1 1.3971011714 1.4057976571 -0.013145 557910.7 0.01631376.2 1.3984157175 1.4031685651 -0.013145 557884.5 0.01631376.3 1.3997302018 1.4005395963 -0.013141 557742.3 0.01631476.4 1.4010443512 1.3979112977 -0.013135 557484.2 0.01631476.5 1.4023578923 1.3952842154 -0.013127 557110.3 0.01631576.6 1.4036705525 1.3926588949 -0.013115 556620.8 0.01631676.7 1.4049820594 1.3900358812 -0.013101 556015.9 0.01631776.8 1.406292141 1.387415718 -0.013084 555295.8 0.01631876.9 1.4076005259 1.3847989482 -0.013064 554460.7 0.01631977 1.4089069432 1.3821861136 -0.013042 553511 0.016321

77.1 1.4102111227 1.3795777546 -0.013017 552446.8 0.01632277.2 1.4115127947 1.3769744105 -0.012989 551268.5 0.01632477.3 1.4128116905 1.374376619 -0.012959 549976.4 0.01632677.4 1.4141075419 1.3717849162 -0.012925 548570.9 0.01632977.5 1.4154000817 1.3691998367 -0.01289 547052.4 0.01633177.6 1.4166890435 1.3666219131 -0.012851 545421.2 0.01633477.7 1.4179741618 1.3640516763 -0.01281 543677.8 0.01633777.8 1.4192551724 1.3614896553 -0.012766 541822.5 0.0163477.9 1.4205318116 1.3589363767 -0.01272 539856 0.01634378 1.4218038174 1.3563923653 -0.012671 537778.6 0.016347

78.1 1.4230709284 1.3538581432 -0.01262 535590.9 0.01635178.2 1.4243328847 1.3513342305 -0.012565 533293.4 0.01635578.3 1.4255894277 1.3488211445 -0.012509 530886.6 0.01635978.4 1.4268402999 1.3463194002 -0.012449 528371.2 0.01636478.5 1.4280852453 1.3438295095 -0.012388 525747.7 0.01636878.6 1.429324009 1.3413519819 -0.012323 523016.7 0.01637378.7 1.4305563381 1.3388873238 -0.012256 520178.8 0.01637878.8 1.4317819806 1.3364360388 -0.012187 517234.8 0.01638478.9 1.4330006864 1.3339986272 -0.012115 514185.3 0.01638979 1.4342122069 1.3315755861 -0.012041 511030.9 0.016395

79.1 1.4354162952 1.3291674097 -0.011964 507772.4 0.01640279.2 1.4366127058 1.3267745884 -0.011885 504410.6 0.01640879.3 1.4378011953 1.3243976095 -0.011803 500946.1 0.01641579.4 1.4389815218 1.3220369564 -0.011719 497379.8 0.01642279.5 1.4401534454 1.3196931092 -0.011633 493712.4 0.01642979.6 1.441316728 1.3173665441 -0.011544 489944.8 0.01643779.7 1.4424711332 1.3150577335 -0.011453 486077.8 0.016445

79.8 1.443616427 1.312767146 -0.011359 482112.1 0.01645379.9 1.444752377 1.3104952461 -0.011264 478048.8 0.01646280 1.4458787529 1.3082424943 -0.011166 473888.6 0.016471

80.1 1.4469953266 1.3060093469 -0.011065 469632.5 0.0164880.2 1.448101872 1.303796256 -0.010963 465281.3 0.0164980.3 1.4491981653 1.3016036694 -0.010858 460836.1 0.016580.4 1.4502839848 1.2994320305 -0.010751 456297.7 0.0165180.5 1.4513591109 1.2972817781 -0.010642 451667.2 0.01652180.6 1.4524233267 1.2951533467 -0.010531 446945.4 0.01653280.7 1.453476417 1.2930471659 -0.010418 442133.5 0.01654480.8 1.4545181696 1.2909636608 -0.010302 437232.4 0.01655680.9 1.4555483742 1.2889032516 -0.010184 432243.2 0.01656881 1.4565668232 1.2868663536 -0.010065 427166.8 0.016581

81.1 1.4575733113 1.2848533774 -0.009943 422004.5 0.01659581.2 1.4585676359 1.2828647282 -0.00982 416757.1 0.01660981.3 1.4595495967 1.2809008065 -0.009694 411425.9 0.01662481.4 1.4605189962 1.2789620076 -0.009566 406012 0.01663981.5 1.4614756393 1.2770487213 -0.009437 400516.3 0.01665581.6 1.4624193338 1.2751613325 -0.009306 394940.2 0.01667181.7 1.4633498898 1.2733002205 -0.009172 389284.8 0.01668981.8 1.4642671204 1.2714657592 -0.009037 383551.1 0.01670681.9 1.4651708414 1.2696583172 -0.0089 377740.4 0.01672582 1.4660608713 1.2678782573 -0.008762 371853.9 0.016744

82.1 1.4669370315 1.2661259371 -0.008621 365892.8 0.01676482.2 1.467799146 1.264401708 -0.008479 359858.2 0.01678582.3 1.4686470419 1.2627059161 -0.008335 353751.5 0.01680782.4 1.4694805492 1.2610389016 -0.00819 347573.8 0.0168382.5 1.4702995006 1.2594009987 -0.008042 341326.4 0.01685382.6 1.471103732 1.257792536 -0.007894 335010.6 0.01687882.7 1.471893082 1.256213836 -0.007743 328627.6 0.01690482.8 1.4726673925 1.254665215 -0.007591 322178.7 0.01693182.9 1.4734265082 1.2531469835 -0.007438 315665.3 0.01695983 1.474170277 1.251659446 -0.007283 309088.6 0.016989

83.1 1.4748985498 1.2502029004 -0.007126 302449.9 0.0170283.2 1.4756111806 1.2487776388 -0.006968 295750.6 0.01705283.3 1.4763080266 1.2473839468 -0.006809 288992 0.01708683.4 1.476988948 1.2460221039 -0.006649 282175.5 0.01712283.5 1.4776538085 1.244692383 -0.006487 275302.4 0.01715983.6 1.4783024746 1.2433950508 -0.006323 268374.1 0.01719983.7 1.4789348162 1.2421303675 -0.006159 261392 0.0172483.8 1.4795507066 1.2408985868 -0.005993 254357.4 0.01728483.9 1.4801500221 1.2396999558 -0.005826 247271.7 0.0173384 1.4807326424 1.2385347152 -0.005658 240136.4 0.017379

84.1 1.4812984505 1.2374030989 -0.005489 232952.9 0.01743184.2 1.4818473328 1.2363053344 -0.005318 225722.5 0.01748684.3 1.4823791788 1.2352416423 -0.005147 218446.7 0.01754484.4 1.4828938817 1.2342122366 -0.004975 211126.9 0.01760684.5 1.4833913377 1.2332173245 -0.004801 203764.6 0.017672

84.6 1.4838714468 1.2322571064 -0.004627 196361.2 0.01774284.7 1.484334112 1.231331776 -0.004451 188918.2 0.01781784.8 1.4847792401 1.2304415199 -0.004275 181437 0.01789884.9 1.485206741 1.2295865181 -0.004098 173919.1 0.01798585 1.4856165283 1.2287669435 -0.00392 166366 0.018078

85.1 1.4860085189 1.2279829622 -0.003741 158779.1 0.0181885.2 1.4863826334 1.2272347332 -0.003562 151160 0.01828985.3 1.4867387957 1.2265224086 -0.003381 143510 0.01840985.4 1.4870769332 1.2258461335 -0.0032 135830.8 0.01853985.5 1.487396977 1.225206046 -0.003019 128123.8 0.01868285.6 1.4876988615 1.2246022769 -0.002837 120390.5 0.0188485.7 1.4879825249 1.2240349503 -0.002654 112632.4 0.01901685.8 1.4882479086 1.2235041828 -0.00247 104851 0.01921285.9 1.4884949579 1.2230100842 -0.002287 97047.83 0.01943286 1.4887236214 1.2225527571 -0.002102 89224.44 0.019683

86.1 1.4889338516 1.2221322968 -0.001918 81382.33 0.0199786.2 1.4891256042 1.2217487916 -0.001732 73523.01 0.02030386.3 1.4892988387 1.2214023226 -0.001547 65648.02 0.02069586.4 1.4894535182 1.2210929636 -0.001361 57758.87 0.02116586.5 1.4895896093 1.2208207814 -0.001175 49857.09 0.02174286.6 1.4897070823 1.2205858353 -0.000988 41944.22 0.02247486.7 1.4898059111 1.2203881778 -0.000802 34021.79 0.0234486.8 1.489886073 1.2202278539 -0.000615 26091.32 0.02480386.9 1.4899475493 1.2201049015 -0.000428 18154.34 0.02694287 1.4899903244 1.2200193512 -0.000241 10212.38 0.031106

87.1 1.4900143867 1.2199712265 -5.34E-05 2266.95 0.04891287.2 1.4900197281 1.2199605438 0.000134 5680.434 0.03659587.3 1.4900063439 1.2199873122 0.000321 13628.21 0.02888787.4 1.4899742332 1.2200515336 0.000508 21574.57 0.02588287.5 1.4899233993 1.2201532014 0.000695 29517.73 0.0241587.6 1.4898538498 1.2202923004 0.000883 37455.9 0.02298587.7 1.4897655964 1.2204688071 0.001069 45387.3 0.02213287.8 1.4896586551 1.2206826898 0.001256 53310.17 0.02147487.9 1.489533046 1.220933908 0.001443 61222.74 0.02094788 1.4893887933 1.2212224134 0.001629 69123.26 0.020513

88.1 1.4892259255 1.2215481491 0.001815 77009.95 0.02014888.2 1.489044475 1.2219110499 0.002 84881.07 0.01983788.3 1.4888444787 1.2223110425 0.002185 92734.86 0.01956688.4 1.4886259774 1.2227480453 0.00237 100569.6 0.0193388.5 1.4883890159 1.2232219683 0.002554 108383.5 0.0191288.6 1.4881336432 1.2237327136 0.002737 116174.9 0.01893488.7 1.4878599125 1.224280175 0.00292 123942 0.01876688.8 1.487567881 1.224864238 0.003103 131683.2 0.01861588.9 1.4872576098 1.2254847803 0.003284 139396.6 0.01847789 1.4869291643 1.2261416713 0.003466 147080.6 0.018352

89.1 1.4865826138 1.2268347725 0.003646 154733.6 0.01823789.2 1.4862180314 1.2275639371 0.003825 162353.7 0.01813189.3 1.4858354946 1.2283290108 0.004004 169939.3 0.018033

89.4 1.4854350845 1.2291298309 0.004182 177488.8 0.01794389.5 1.4850168864 1.2299662272 0.004359 185000.5 0.01785989.6 1.4845809894 1.2308380213 0.004535 192472.6 0.01778189.7 1.4841274864 1.2317450272 0.00471 199903.7 0.01770889.8 1.4836564744 1.2326870512 0.004884 207292 0.0176489.9 1.4831680541 1.2336638918 0.005057 214635.9 0.01757690 1.4826623301 1.2346753398 0.005229 221933.8 0.017516

90.1 1.4821394108 1.2357211784 0.0054 229184.2 0.01745990.2 1.4815994083 1.2368011834 0.00557 236385.3 0.01740690.3 1.4810424385 1.2379151229 0.005738 243535.7 0.01735690.4 1.4804686211 1.2390627579 0.005905 250633.7 0.01730890.5 1.4798780792 1.2402438416 0.006071 257677.9 0.01726390.6 1.4792709399 1.2414581202 0.006236 264666.7 0.01722190.7 1.4786473338 1.2427053325 0.006399 271598.5 0.0171890.8 1.4780073949 1.2439852102 0.006561 278471.9 0.01714290.9 1.477351261 1.2452974779 0.006722 285285.3 0.01710591 1.4766790734 1.2466418531 0.006881 292037.3 0.017071

91.1 1.4759909768 1.2480180464 0.007039 298726.4 0.01703891.2 1.4752871193 1.2494257614 0.007195 305351.2 0.01700691.3 1.4745676526 1.2508646949 0.007349 311910.2 0.01697691.4 1.4738327315 1.2523345369 0.007502 318402 0.01694791.5 1.4730825145 1.2538349711 0.007654 324825.2 0.0169291.6 1.472317163 1.255365674 0.007803 331178.5 0.01689491.7 1.471536842 1.256926316 0.007951 337460.5 0.01686891.8 1.4707417195 1.258516561 0.008098 343669.7 0.01684491.9 1.4699319668 1.2601360665 0.008242 349805 0.01682192 1.4691077582 1.2617844837 0.008385 355864.9 0.016799

92.099999999999 1.4682692712 1.2634614577 0.008526 361848.3 0.01677892.199999999999 1.4674166863 1.2651666275 0.008665 367753.7 0.01675892.299999999999 1.466550187 1.266899626 0.008802 373580 0.01673892.399999999999 1.4656699598 1.2686600804 0.008938 379326 0.0167292.499999999999 1.464776194 1.2704476119 0.009071 384990.3 0.01670292.599999999999 1.463869082 1.272261836 0.009203 390571.9 0.01668592.699999999999 1.4629488187 1.2741023626 0.009332 396069.5 0.01666892.799999999999 1.462015602 1.275968796 0.00946 401482 0.01665292.899999999999 1.4610696324 1.2778607352 0.009585 406808.2 0.01663792.999999999999 1.4601111132 1.2797777737 0.009709 412047.1 0.01662293.099999999999 1.4591402501 1.2817194998 0.00983 417197.5 0.01660893.199999999999 1.4581572516 1.2836854967 0.009949 422258.4 0.01659493.299999999999 1.4571623287 1.2856753426 0.010066 427228.7 0.01658193.399999999999 1.4561556947 1.2876886105 0.010181 432107.5 0.01656993.499999999999 1.4551375655 1.2897248689 0.010294 436893.6 0.01655793.599999999999 1.4541081593 1.2917836814 0.010405 441586.1 0.01654593.699999999999 1.4530676966 1.2938646068 0.010513 446184.1 0.01653493.799999999999 1.4520164001 1.2959671997 0.010619 450686.5 0.016523

93.9 1.450954495 1.29809101 0.010723 455092.6 0.01651394 1.4498822083 1.3002355835 0.010824 459401.4 0.016503

94.1 1.4487997692 1.3024004616 0.010924 463612 0.016493

94.2 1.4477074092 1.3045851817 0.01102 467723.6 0.01648494.3 1.4466053614 1.3067892772 0.011115 471735.3 0.01647594.4 1.4454938612 1.3090122776 0.011207 475646.4 0.01646794.5 1.4443731457 1.3112537087 0.011297 479456.1 0.01645994.6 1.4432434538 1.3135130924 0.011384 483163.6 0.01645194.7 1.4421050263 1.3157899474 0.011469 486768.2 0.01644394.8 1.4409581056 1.3180837887 0.011552 490269.2 0.01643694.9 1.4398029359 1.3203941281 0.011632 493666 0.01642995 1.4386397629 1.3227204742 0.011709 496957.7 0.016423

95.1 1.4374688339 1.3250623322 0.011784 500143.9 0.01641695.2 1.4362903976 1.3274192048 0.011857 503223.9 0.0164195.3 1.4351047042 1.3297905915 0.011927 506197.1 0.01640595.4 1.4339120054 1.3321759891 0.011995 509063 0.01639995.5 1.4327125541 1.3345748918 0.012059 511821 0.01639495.6 1.4315066044 1.3369867913 0.012122 514470.6 0.01638995.7 1.4302944117 1.3394111767 0.012182 517011.3 0.01638495.8 1.4290762325 1.341847535 0.012239 519442.7 0.0163895.9 1.4278523245 1.3442953509 0.012294 521764.3 0.01637596 1.4266229464 1.3467541072 0.012346 523975.7 0.016371

96.1 1.4253883577 1.3492232845 0.012395 526076.5 0.01636896.2 1.4241488191 1.3517023617 0.012442 528066.4 0.01636496.3 1.422904592 1.3541908161 0.012487 529945 0.01636196.4 1.4216559385 1.356688123 0.012528 531712 0.01635896.5 1.4204031217 1.3591937567 0.012567 533367.1 0.01635596.6 1.4191464051 1.3617071897 0.012604 534910 0.01635296.7 1.4178860532 1.3642278936 0.012637 536340.5 0.0163596.8 1.4166223307 1.3667553385 0.012668 537658.4 0.01634796.9 1.4153555031 1.3692889938 0.012697 538863.4 0.01634597 1.4140858361 1.3718283278 0.012722 539955.5 0.016343

97.1 1.412813596 1.3743728079 0.012745 540934.4 0.01634297.2 1.4115390494 1.3769219012 0.012766 541800 0.0163497.3 1.4102624631 1.3794750737 0.012784 542552.3 0.01633997.4 1.4089841043 1.3820317914 0.012799 543191.2 0.01633897.5 1.4077042401 1.3845915197 0.012811 543716.6 0.01633797.6 1.406423138 1.3871537239 0.012821 544128.5 0.01633697.7 1.4051410654 1.3897178691 0.012828 544426.9 0.01633697.8 1.4038582898 1.3922834205 0.012832 544611.8 0.01633597.9 1.4025750784 1.3948498432 0.012834 544683.3 0.01633598 1.4012916987 1.3974166027 0.012833 544641.4 0.016335

98.1 1.4000084176 1.3999831648 0.012829 544486.2 0.01633698.2 1.3987255021 1.4025489958 0.012823 544217.9 0.01633698.3 1.3974432188 1.4051135624 0.012814 543836.6 0.01633798.4 1.396161834 1.407676332 0.012802 543342.4 0.01633898.5 1.3948816135 1.410236773 0.012788 542735.6 0.01633998.6 1.3936028228 1.4127943543 0.012771 542016.3 0.0163498.7 1.3923257269 1.4153485462 0.012751 541184.9 0.01634198.8 1.3910505901 1.4178988197 0.012729 540241.4 0.01634398.9 1.3897776763 1.4204446473 0.012704 539186.3 0.016345

99 1.3885072486 1.4229855027 0.012677 538019.8 0.01634799.1 1.3872395695 1.4255208611 0.012647 536742.2 0.01634999.2 1.3859749005 1.428050199 0.012614 535353.9 0.01635199.3 1.3847135026 1.4305729948 0.012579 533855.3 0.01635499.4 1.3834556358 1.4330887285 0.012541 532246.7 0.01635799.5 1.382201559 1.4355968819 0.0125 530528.6 0.0163699.6 1.3809515306 1.4380969388 0.012457 528701.3 0.01636399.7 1.3797058074 1.4405883851 0.012412 526765.4 0.01636699.8 1.3784646456 1.4430707087 0.012363 524721.4 0.0163799.9 1.3772283001 1.4455433999 0.012313 522569.6 0.016374100 1.3759970244 1.4480059511 0.01226 520310.7 0.016378

100.1 1.3747710713 1.4504578574 0.012204 517945.1 0.016382100.2 1.3735506919 1.4528986163 0.012146 515473.5 0.016387100.3 1.372336136 1.4553277279 0.012085 512896.4 0.016392100.4 1.3711276524 1.4577446952 0.012022 510214.4 0.016397100.5 1.3699254881 1.4601490239 0.011956 507428.1 0.016402100.6 1.3687298888 1.4625402225 0.011888 504538.2 0.016408100.7 1.3675410986 1.4649178028 0.011817 501545.3 0.016414100.8 1.3663593603 1.4672812794 0.011744 498450.1 0.01642

0 20 40 60 80 100 1201.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.65Liquid Height in Tank 1

Liquid Height in Tank 2

Time (s)

Heig

ht (m

)

This spreadsheet models the transient flow of liquid between two tanks connected by a pipe.The liquid momentum causes the liquid height in each tank tank to oscillate to an equilibrium.The spreadsheet solves the governing differential equations that describe the flowrate in the pipeand the height of liquid in each tank with a simple Euler routine