Chapter 08 To do this click on the office button in the upper

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Companion program to Geotechnical Engineering: Principles and Practiced, Second Edition Coduto, Yeung, & Kitch (2011)

Finite difference solution for Problem 11, Chapter 8

Soultion to example shown in Figure 8.9, Pg 315

Setup

If you opend this file and received an error message about circular references, you need to set spreadsheet to allow iterative computations.

To do this click on the office button in the upper left corner of the Excel window.

Then click “Excel Options” at the bottom of the tab

<- Blue cells are equipotential boundaried

<-Orange cells are flow boundaries

<-White cells are non-boudary cells

<-Value of upstream head

To perform calculations, enter the upstream head value in the red cells and hit F9

Pore water pressures on bottom of dam -> 4763.36 4673.53 4614.46 4568.51 4530.01 4496. 72 4467. 57 4441.98 4419.66 4400.41 4384.15 4370.84 4360.47 4353.05 4348.59 4347.1 3038.47 3037. 35 3034. 03 3028.52 3020.91 3011.27 2999.71 2986.33 2971.25 2954.59 2936.48 2917.03 2896. 36 2874. 58 2851.78 2828.05 2803.5 2778.18 2752.18 2725.55 2698.36 2670.66 2642.49 2613.89 2584. 91 2555. 57 2525.9 2495.93 2465.67 2435.15 2404.39 2373.39 2342.17 2310.73 2279.08 2247.22 2215. 16 2182. 89 2150.41 2117.71 2084.78 2051.62 2018.2 1984.5 1950.51 1916.19 1881.5 1846.42 1810.88 1774.82 1738. 18 1700. 85 1662.72 1623.65 1583.45 1541.86 1498.53 1452.96 1404.37 1351.42 1291.42 1217. 81 1110. 29

The matrix below is the solut ion to the potenal f unction

2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0 42.5 45.0 47.5 50.0 52.5 55.0 57.5 60.0 62.5 65.0 67.5 70.0 72.5 75.0 77.5 80.0 82.5 85.0 87.5 90.0 92.5 95.0 97.5 100.0 102.5 105.0 107. 5 110.0 112.5 115.0 117.5 120. 0 122.5 125.0 127.5 130. 0 132.5 135.0 137.5 140.0 142. 5 145.0 147.5 150.0 152.5 155. 0 157.5 160.0 162.5 165.0 167.5 170.0 172.5 175. 0 177.5 180.0 182.5 185.0 187. 5 190.0 192.5 195.0 197.5 200. 0 202.5 205.0 207.5 210.0 212. 5 215.0 217.5 220.0 222. 5 225.0 227.5 230.0 232.5 235. 0 237.5 240.0 242.5 245.0 247. 5 250.0 252.5 255.0 257.5 260. 0 262.5 265.0 267.5 270.0 272.5 275.0 277.5 280.0 282. 5 285.0 287.5 290.0 292.5 295. 0 297.5 300.0 302.5 305. 0 307.5 310.0 312.5 315.0 317. 5 320.0 322.5 325.0 327.5 330. 0 332.5 335.0 337.5 340.0 342. 5 345.0 347.5 350.0 352.5 355. 0 357.5 360.0 362.5 365. 0 367.5 370.0 372.5 375.0 377. 5 380.0 382.5 385.0 387. 5 390.0 392.5 395.0 397.5 400. 0 402.5 405.0 407.5 410.0 412. 5 415.0 417.5 420.0 422.5 425. 0 427.5 430.0 432.5 435. 0 437.5 440.0 442.5 445.0 447. 5 450.0 452.5 455.0 457.5 460. 0 462.5 465.0 467.5 470.0 472. 5 475.0 477.5 480.0 482.5 485. 0 487.5 490.0 492.5 495. 0 497.5 500.0

2.5 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 80.3 80.3 80.3 80.3 80. 3 79. 6385 14.0426 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13.3 13. 3 13.3 13.3 13.3 13. 3

5.0 80.229 80.229 80.228 80. 228 80.227 80.227 80.226 80.225 80. 224 80.222 80.221 80.219 80. 217 80.215 80.213 80.210 80.208 80. 205 80.202 80.199 80.195 80.191 80. 188 80.183 80.179 80.174 80. 169 80.164 80.158 80.152 80.145 80. 139 80.131 80.124 80.116 80.107 80. 098 80.088 80.078 80.067 80.055 80. 043 80.029 80.015 80.000 79. 983 79.965 79.946 79.924 79.901 79. 875 79.846 79.813 79.775 79.732 79. 680 79.619 79.544 79.451 79.335 79. 187 78.977 14.785 14.545 14.372 14.234 14. 123 14.034 13.961 13.900 13.849 13. 805 13.768 13.734 13.705 13. 679 13.655 13.634 13.615 13.597 13. 581 13.566 13.552 13.539 13. 527 13.516 13.506 13.496 13.487 13. 478 13.470 13.463 13.456 13.449 13. 443 13.437 13.432 13.426 13.422 13. 417 13.413 13.409 13.405 13.401 13. 398 13.395 13.392 13.390 13. 387 13.385 13.383 13.381 13.379 13. 378 13.376 13.375 13.374 13.373 13. 373 13.372 13.372 13.371 13. 371

7.5 80.157 80.157 80.157 80. 156 80.155 80.154 80.152 80.150 80. 147 80.145 80.142 80.138 80. 135 80.130 80.126 80.121 80.116 80. 110 80.104 80.098 80.091 80.083 80. 075 80.067 80.058 80.048 80. 038 80.027 80.016 80.004 79.991 79. 978 79.963 79.948 79.932 79.915 79. 896 79.877 79.857 79.835 79.811 79. 786 79.760 79.731 79.701 79. 668 79.632 79.593 79.551 79.504 79. 452 79.395 79.330 79.256 79.171 79. 071 78.951 78.806 78.626 78.402 78. 135 77.896 16.007 15.725 15.407 15.140 14. 925 14.751 14.609 14.491 14.391 14. 305 14.230 14.165 14.107 14. 055 14.009 13.966 13.928 13.893 13. 860 13.831 13.803 13.777 13. 754 13.731 13.711 13.691 13.673 13. 656 13.640 13.625 13.611 13.598 13. 585 13.574 13.563 13.552 13.543 13. 534 13.525 13.517 13.510 13.502 13. 496 13.490 13.484 13.479 13. 474 13.470 13.465 13.462 13.458 13. 455 13.453 13.450 13.448 13.446 13. 445 13.444 13.443 13.443 13. 443

10.0 80.086 80.086 80.086 80. 084 80.083 80.081 80.078 80.075 80. 071 80.067 80.063 80.058 80. 052 80.046 80.039 80.032 80.024 80. 016 80.007 79.997 79.987 79.975 79. 964 79.951 79.937 79.923 79. 908 79.892 79.875 79.857 79.838 79. 817 79.796 79.773 79.749 79.723 79. 696 79.667 79.636 79.604 79.569 79. 532 79.492 79.450 79.404 79.355 79. 302 79.244 79.181 79.112 79. 036 78.951 78.856 78.749 78.625 78. 481 78.310 78.102 77.845 77.513 77. 056 76.336 74.896 73.950 73.213 72.596 72.063 71.596 71. 186 70.828 70.519 70.259 70.046 69. 879 69.760 69.689 69.665 48.693 48. 675 48.622 48.534 48.412 48.258 48. 072 47.858 47.616 47.349 47. 059 46.747 46.416 46.067 45.701 45. 321 44.928 44.522 44.105 43.679 43. 243 42.799 42.347 41.889 41.425 40. 955 40.479 39.999 39.514 39.025 38. 532 38.035 37.535 37.031 36. 524 36.013 35.499 34.982 34.462 33. 938 33.410 32.878 32.343 31. 803 31.258 30.708 30.152 29.590 29. 020 28.443 27.855 27.257 26.646 26. 020 25.376 24.709 24.015 23.285 22. 506 21.657 20.696 19.516 17.793 16. 940 16.393 15.994 15.685 15. 437 15.233 15.063 14.918 14.793 14. 684 14.588 14.503 14.426 14. 357 14.295 14.238 14.186 14.137 14. 093 14.052 14.014 13.978 13.945 13. 914 13.885 13.858 13.833 13.809 13. 787 13.766 13.746 13.727 13.710 13. 693 13.678 13.663 13.650 13. 637 13.625 13.614 13.603 13.593 13. 584 13.576 13.568 13.561 13.554 13. 548 13.542 13.537 13.532 13.528 13. 525 13.522 13.519 13.517 13. 516 13.514 13.514 13.514

12.5 80.016 80.016 80.015 80. 013 80.011 80.008 80.005 80.001 79. 996 79.991 79.985 79.978 79. 971 79.962 79.953 79.944 79.933 79. 922 79.910 79.897 79.883 79.868 79. 853 79.836 79.818 79.799 79. 779 79.757 79.735 79.711 79.685 79. 658 79.630 79.599 79.567 79.533 79. 497 79.459 79.418 79.375 79.329 79. 280 79.227 79.171 79.111 79.046 78. 976 78.900 78.818 78.727 78. 628 78.518 78.396 78.257 78.100 77. 917 77.704 77.449 77.138 76.748 76. 240 75.555 74.650 73.845 73.154 72.555 72.030 71.567 71. 159 70.803 70.495 70.235 70.022 69. 856 69.737 69.665 69.641 48.711 48. 693 48.639 48.551 48.428 48.273 48. 087 47.871 47.629 47.361 47. 070 46.757 46.425 46.075 45.709 45. 328 44.934 44.527 44.110 43.683 43. 247 42.803 42.351 41.892 41.427 40. 957 40.481 40.001 39.516 39.027 38. 534 38.037 37.536 37.032 36. 525 36.015 35.501 34.984 34.463 33. 939 33.412 32.880 32.345 31. 805 31.261 30.711 30.155 29.594 29. 024 28.447 27.861 27.263 26.654 26. 029 25.387 24.723 24.033 23.309 22. 541 21.714 20.805 19.788 18.678 17. 847 17.231 16.759 16.384 16. 079 15.825 15.610 15.425 15.265 15. 125 15.001 14.890 14.790 14. 700 14.618 14.543 14.474 14.411 14. 352 14.298 14.248 14.201 14.157 14. 116 14.078 14.042 14.008 13.976 13. 947 13.919 13.893 13.868 13.845 13. 823 13.802 13.783 13.765 13. 748 13.732 13.717 13.703 13.690 13. 678 13.667 13.656 13.646 13.638 13. 629 13.622 13.615 13.609 13.604 13. 599 13.595 13.592 13.589 13. 587 13.585 13.584 13.584

15.0 79.946 79.946 79.945 79. 943 79.940 79.937 79.932 79.927 79. 921 79.915 79.907 79.899 79. 889 79.879 79.868 79.856 79.843 79. 829 79.814 79.798 79.781 79.762 79. 743 79.722 79.699 79.676 79. 651 79.624 79.596 79.566 79.534 79. 501 79.465 79.428 79.388 79.346 79. 301 79.253 79.203 79.149 79.092 79. 031 78.966 78.897 78.822 78.742 78. 656 78.563 78.462 78.352 78. 231 78.098 77.950 77.785 77.598 77. 386 77.140 76.852 76.511 76.100 75. 601 74.996 74.303 73.625 73.002 72.439 71.934 71.483 71. 082 70.730 70.424 70.164 69.951 69. 785 69.665 69.593 69.569 48.765 48. 746 48.692 48.601 48.477 48.319 48. 130 47.912 47.666 47.395 47. 101 46.786 46.451 46.099 45.731 45. 348 44.952 44.544 44.125 43.696 43. 259 42.813 42.361 41.901 41.436 40. 965 40.488 40.007 39.522 39.032 38. 539 38.042 37.541 37.037 36. 530 36.019 35.506 34.989 34.468 33. 945 33.417 32.886 32.351 31. 812 31.268 30.719 30.165 29.604 29. 037 28.461 27.877 27.282 26.676 26. 056 25.419 24.763 24.084 23.377 22. 635 21.852 21.022 20.152 19.285 18. 539 17.926 17.426 17.014 16. 669 16.377 16.126 15.908 15.718 15. 550 15.400 15.265 15.144 15. 034 14.934 14.842 14.757 14.679 14. 607 14.540 14.478 14.420 14.366 14. 315 14.267 14.223 14.181 14.142 14. 105 14.070 14.038 14.007 13.978 13. 951 13.926 13.902 13.879 13. 858 13.838 13.819 13.802 13.786 13. 771 13.757 13.744 13.732 13.721 13. 710 13.701 13.693 13.685 13.679 13. 673 13.668 13.663 13.660 13. 657 13.655 13.654 13.654

17.5 79.877 79.877 79.875 79. 873 79.870 79.866 79.860 79.854 79. 847 79.839 79.830 79.820 79. 809 79.797 79.784 79.770 79.754 79. 737 79.719 79.700 79.679 79.657 79. 634 79.609 79.582 79.554 79. 524 79.492 79.459 79.423 79.385 79. 345 79.303 79.258 79.211 79.160 79. 107 79.050 78.990 78.926 78.859 78. 786 78.709 78.627 78.539 78.445 78. 343 78.234 78.115 77.987 77. 846 77.692 77.523 77.334 77.124 76. 886 76.617 76.309 75.953 75.542 75. 066 74.526 73.940 73.352 72.789 72.265 71.785 71.349 70. 957 70.609 70.306 70.047 69.834 69. 667 69.546 69.474 69.450 48.854 48. 835 48.779 48.686 48.558 48.396 48. 203 47.979 47.729 47.453 47. 154 46.834 46.495 46.139 45.767 45. 380 44.981 44.570 44.149 43.718 43. 279 42.832 42.377 41.916 41.449 40. 977 40.500 40.018 39.532 39.042 38. 548 38.050 37.549 37.045 36. 538 36.027 35.513 34.997 34.476 33. 953 33.426 32.896 32.362 31. 823 31.281 30.733 30.180 29.622 29. 056 28.484 27.903 27.313 26.712 26. 098 25.471 24.827 24.164 23.479 22. 770 22.036 21.280 20.514 19.770 19. 096 18.509 18.006 17.576 17. 206 16.887 16.609 16.364 16.148 15. 956 15.784 15.628 15.487 15. 359 15.241 15.133 15.034 14.942 14. 857 14.778 14.704 14.635 14.571 14. 511 14.454 14.401 14.352 14.305 14. 261 14.220 14.181 14.144 14.110 14. 078 14.047 14.019 13.992 13. 967 13.943 13.921 13.900 13.881 13. 863 13.846 13.830 13.816 13.803 13. 790 13.779 13.769 13.760 13.752 13. 745 13.739 13.734 13.730 13. 727 13.725 13.723 13.723

20.0 79.809 79.808 79.807 79. 804 79.800 79.796 79.790 79.783 79. 774 79.765 79.755 79.743 79. 730 79.716 79.701 79.684 79.666 79. 647 79.626 79.603 79.579 79.554 79. 527 79.498 79.467 79.434 79. 400 79.363 79.324 79.282 79.239 79. 192 79.143 79.091 79.036 78.978 78. 916 78.851 78.782 78.708 78.630 78. 547 78.458 78.363 78.262 78.154 78. 038 77.913 77.779 77.633 77. 475 77.302 77.113 76.905 76.675 76. 420 76.134 75.813 75.452 75.047 74. 595 74.102 73.580 73.052 72.537 72.048 71.591 71.170 70. 787 70.445 70.143 69.885 69.670 69. 501 69.380 69.306 69.282 48.982 48. 962 48.903 48.806 48.673 48.505 48. 305 48.074 47.817 47.534 47. 228 46.902 46.556 46.194 45.817 45. 426 45.022 44.608 44.183 43.749 43. 306 42.857 42.400 41.937 41.468 40. 995 40.516 40.033 39.546 39.055 38. 560 38.062 37.561 37.056 36. 549 36.038 35.524 35.008 34.488 33. 965 33.439 32.909 32.376 31. 839 31.298 30.752 30.202 29.645 29. 083 28.515 27.938 27.354 26.760 26. 155 25.539 24.909 24.265 23.606 22. 931 22.242 21.546 20.854 20.186 19. 567 19.008 18.513 18.077 17. 694 17.356 17.058 16.792 16.555 16. 342 16.150 15.976 15.817 15. 672 15.539 15.416 15.303 15.198 15. 100 15.010 14.925 14.846 14.772 14. 703 14.638 14.577 14.519 14.465 14. 415 14.367 14.322 14.280 14.240 14. 202 14.167 14.134 14.103 14. 074 14.046 14.020 13.996 13.974 13. 953 13.934 13.916 13.899 13.883 13. 869 13.857 13.845 13.835 13.825 13. 817 13.810 13.804 13.800 13. 796 13.793 13.792 13.791

22.5 79.742 79.741 79.739 79. 736 79.732 79.727 79.720 79.712 79. 703 79.692 79.680 79.667 79. 652 79.636 79.619 79.600 79.580 79. 557 79.534 79.508 79.481 79.452 79. 421 79.388 79.353 79.316 79. 277 79.235 79.191 79.144 79.094 79. 042 78.986 78.928 78.865 78.799 78. 730 78.656 78.577 78.494 78.406 78. 312 78.212 78.106 77.993 77.872 77. 742 77.603 77.453 77.292 77. 118 76.929 76.723 76.499 76.253 75. 983 75.685 75.357 74.995 74.598 74. 167 73.706 73.226 72.739 72.260 71.798 71.361 70.953 70. 578 70.239 69.938 69.678 69.461 69. 289 69.165 69.089 69.064 49.148 49. 127 49.065 48.963 48.822 48.646 48. 437 48.197 47.929 47.637 47. 322 46.987 46.634 46.265 45.881 45. 484 45.074 44.655 44.225 43.787 43. 341 42.888 42.429 41.963 41.492 41. 017 40.536 40.052 39.563 39.071 38. 576 38.077 37.575 37.070 36. 562 36.051 35.538 35.022 34.502 33. 980 33.455 32.926 32.394 31. 859 31.320 30.776 30.228 29.675 29. 117 28.553 27.982 27.404 26.818 26. 224 25.620 25.006 24.382 23.748 23. 105 22.456 21.808 21.170 20.555 19. 976 19.443 18.960 18.525 18. 135 17.786 17.473 17.192 16.938 16. 708 16.499 16.308 16.134 15. 974 15.826 15.690 15.564 15.446 15. 337 15.235 15.140 15.051 14.968 14. 890 14.817 14.748 14.683 14.622 14. 565 14.511 14.460 14.412 14.367 14. 325 14.285 14.247 14.212 14. 179 14.148 14.119 14.091 14.066 14. 042 14.020 13.999 13.981 13.963 13. 947 13.933 13.919 13.908 13.897 13. 888 13.880 13.873 13.868 13. 864 13.861 13.859 13.858

25.0 79.676 79.675 79.673 79. 670 79.665 79.659 79.651 79.642 79. 632 79.620 79.607 79.592 79. 576 79.558 79.539 79.517 79.495 79. 470 79.443 79.415 79.385 79.352 79. 318 79.281 79.242 79.201 79. 157 79.110 79.061 79.008 78.953 78. 895 78.833 78.767 78.698 78.624 78. 547 78.465 78.378 78.285 78.187 78. 084 77.973 77.856 77.731 77.598 77. 455 77.303 77.140 76.964 76. 776 76.572 76.352 76.114 75.855 75. 573 75.267 74.934 74.573 74.183 73. 768 73.330 72.877 72.420 71.966 71.524 71.101 70.703 70. 332 69.994 69.692 69.428 69.206 69. 029 68.901 68.822 68.796 49.357 49. 334 49.267 49.157 49.007 48.820 48. 599 48.347 48.067 47.763 47. 437 47.091 46.728 46.350 45.958 45. 553 45.137 44.711 44.276 43.833 43. 383 42.926 42.463 41.995 41.521 41. 043 40.561 40.074 39.584 39.091 38. 594 38.095 37.592 37.087 36. 579 36.068 35.554 35.038 34.519 33. 998 33.474 32.946 32.416 31. 882 31.345 30.804 30.259 29.710 29. 156 28.597 28.033 27.462 26.886 26. 302 25.711 25.113 24.509 23.898 23. 284 22.670 22.060 21.462 20.886 20. 339 19.829 19.358 18.928 18. 536 18.180 17.857 17.564 17.296 17. 053 16.829 16.625 16.436 16. 263 16.102 15.953 15.815 15.686 15. 567 15.454 15.350 15.252 15.159 15. 073 14.992 14.915 14.844 14.776 14. 712 14.652 14.596 14.542 14.492 14. 445 14.400 14.358 14.319 14. 282 14.247 14.215 14.184 14.156 14. 129 14.105 14.082 14.061 14.041 14. 023 14.007 13.992 13.979 13.967 13. 957 13.948 13.941 13.935 13. 930 13.927 13.925 13.924

27.5 79.611 79.610 79.608 79. 605 79.599 79.593 79.584 79.574 79. 563 79.550 79.535 79.519 79. 501 79.481 79.460 79.437 79.411 79. 384 79.355 79.324 79.290 79.255 79. 217 79.176 79.133 79.087 79. 039 78.988 78.933 78.876 78.815 78. 751 78.683 78.611 78.534 78.454 78. 369 78.279 78.183 78.082 77.975 77. 861 77.741 77.613 77.477 77.332 77. 178 77.014 76.838 76.650 76. 448 76.232 75.999 75.749 75.479 75. 188 74.875 74.539 74.179 73.795 73. 391 72.969 72.535 72.096 71.659 71.231 70.817 70.424 70. 055 69.714 69.407 69.136 68.906 68. 721 68.586 68.503 68.475 49.610 49. 585 49.512 49.392 49.229 49.028 48. 791 48.524 48.229 47.910 47. 571 47.212 46.838 46.449 46.047 45. 633 45.210 44.777 44.335 43.887 43. 432 42.970 42.503 42.031 41.555 41. 074 40.589 40.101 39.609 39.114 38. 616 38.115 37.612 37.106 36. 598 36.087 35.573 35.058 34.539 34. 019 33.495 32.969 32.441 31. 909 31.374 30.837 30.295 29.750 29. 201 28.647 28.090 27.527 26.959 26. 387 25.809 25.227 24.641 24.053 23. 464 22.878 22.300 21.734 21.188 20. 666 20.175 19.717 19.292 18. 901 18.542 18.212 17.909 17.632 17. 376 17.141 16.925 16.724 16. 539 16.366 16.206 16.057 15.918 15. 788 15.666 15.552 15.445 15.345 15. 251 15.162 15.078 15.000 14.925 14. 856 14.790 14.728 14.669 14.614 14. 562 14.513 14.467 14.424 14. 383 14.345 14.309 14.275 14.244 14. 215 14.188 14.163 14.139 14.118 14. 098 14.080 14.064 14.049 14.036 14. 025 14.015 14.007 14.000 13. 995 13.992 13.989 13.989

80.0 78.771 78.770 78.765 78. 757 78.745 78.730 78.712 78.691 78. 666 78.637 78.605 78.569 78. 530 78.487 78.440 78.389 78.334 78. 275 78.211 78.143 78.071 77.994 77. 912 77.825 77.733 77.635 77. 532 77.423 77.308 77.187 77.059 76. 925 76.784 76.635 76.480 76.316 76. 145 75.965 75.776 75.579 75.372 75. 156 74.930 74.693 74.446 74.188 73. 919 73.638 73.345 73.039 72. 720 72.389 72.043 71.684 71.310 70. 921 70.517 70.097 69.661 69.208 68. 739 68.251 67.746 67.222 66.680 66.118 65.537 64.936 64. 315 63.675 63.015 62.337 61.642 60. 931 60.207 59.472 58.728 57.980 57. 230 56.482 55.739 55.002 54.274 53. 556 52.850 52.156 51.474 50. 804 50.146 49.499 48.864 48.239 47. 623 47.017 46.420 45.830 45.247 44. 672 44.102 43.539 42.980 42.427 41. 878 41.333 40.793 40.256 39.722 39. 191 38.664 38.139 37.618 37. 098 36.582 36.068 35.557 35.048 34. 542 34.038 33.537 33.039 32. 544 32.052 31.564 31.078 30.597 30. 119 29.645 29.176 28.712 28.252 27. 798 27.349 26.907 26.470 26.040 25. 618 25.202 24.794 24.394 24.002 23. 619 23.244 22.879 22.522 22. 175 21.838 21.510 21.192 20.884 20. 585 20.297 20.018 19.748 19. 489 19.239 18.998 18.766 18.543 18. 330 18.125 17.928 17.739 17.559 17. 386 17.221 17.064 16.913 16.770 16. 633 16.503 16.379 16.261 16.149 16. 042 15.942 15.846 15.756 15. 671 15.591 15.515 15.444 15.377 15. 315 15.257 15.203 15.153 15.107 15. 064 15.025 14.990 14.959 14.931 14. 906 14.885 14.867 14.852 14. 841 14.833 14.828 14.826

82.5 78.763 78.762 78.757 78. 748 78.737 78.722 78.704 78.682 78. 657 78.628 78.596 78.560 78. 521 78.477 78.430 78.379 78.324 78. 264 78.200 78.132 78.059 77.982 77. 899 77.812 77.719 77.621 77. 517 77.408 77.292 77.171 77.043 76. 908 76.766 76.617 76.460 76.296 76. 124 75.943 75.754 75.556 75.348 75. 131 74.904 74.667 74.419 74.160 73. 890 73.608 73.313 73.007 72. 687 72.355 72.008 71.648 71.273 70. 883 70.478 70.057 69.620 69.166 68. 695 68.207 67.701 67.176 66.633 66.071 65.489 64.888 64. 269 63.630 62.972 62.297 61.606 60. 901 60.182 59.453 58.717 57.976 57. 233 56.491 55.753 55.021 54.297 53. 582 52.878 52.184 51.503 50. 833 50.174 49.526 48.890 48.263 47. 647 47.039 46.440 45.849 45.265 44. 688 44.117 43.553 42.993 42.439 41. 889 41.344 40.802 40.265 39.730 39. 200 38.672 38.147 37.625 37. 105 36.589 36.075 35.563 35.055 34. 549 34.045 33.545 33.047 32. 552 32.061 31.573 31.088 30.607 30. 130 29.657 29.188 28.725 28.266 27. 812 27.365 26.923 26.487 26.058 25. 636 25.221 24.814 24.415 24.023 23. 641 23.267 22.902 22.546 22. 199 21.862 21.534 21.216 20.908 20. 610 20.321 20.042 19.772 19. 512 19.262 19.021 18.789 18.566 18. 351 18.146 17.949 17.760 17.579 17. 405 17.240 17.082 16.931 16.787 16. 649 16.519 16.394 16.276 16.163 16. 056 15.955 15.859 15.769 15. 683 15.602 15.526 15.455 15.388 15. 326 15.267 15.213 15.163 15.116 15. 073 15.035 14.999 14.968 14.939 14. 915 14.893 14.875 14.861 14. 849 14.841 14.836 14.835

85.0 78.758 78.757 78.752 78. 743 78.732 78.717 78.699 78.677 78. 652 78.623 78.591 78.555 78. 515 78.471 78.424 78.373 78.317 78. 258 78.194 78.125 78.052 77.974 77. 892 77.804 77.711 77.613 77. 509 77.399 77.283 77.161 77.032 76. 897 76.755 76.606 76.449 76.284 76. 111 75.930 75.741 75.542 75.334 75. 116 74.889 74.651 74.402 74.143 73. 872 73.589 73.295 72.988 72. 667 72.334 71.987 71.626 71.250 70. 860 70.454 70.033 69.595 69.140 68. 669 68.180 67.673 67.148 66.605 66.042 65.461 64.860 64. 241 63.603 62.947 62.274 61.585 60. 882 60.167 59.442 58.710 57.973 57. 234 56.496 55.761 55.032 54.310 53. 597 52.894 52.201 51.520 50. 850 50.191 49.543 48.905 48.278 47. 660 47.052 46.452 45.860 45.275 44. 698 44.126 43.561 43.001 42.446 41. 896 41.350 40.808 40.270 39.736 39. 204 38.676 38.151 37.629 37. 110 36.593 36.079 35.568 35.059 34. 553 34.050 33.549 33.052 32. 557 32.066 31.578 31.094 30.613 30. 136 29.664 29.196 28.732 28.274 27. 821 27.374 26.932 26.497 26.069 25. 647 25.233 24.826 24.427 24.036 23. 654 23.280 22.915 22.560 22. 213 21.876 21.549 21.231 20.923 20. 624 20.335 20.056 19.787 19. 527 19.276 19.034 18.802 18.579 18. 364 18.158 17.961 17.772 17.590 17. 417 17.251 17.093 16.941 16.797 16. 659 16.528 16.403 16.285 16.172 16. 065 15.963 15.867 15.776 15. 691 15.610 15.533 15.462 15.395 15. 332 15.273 15.219 15.168 15.122 15. 079 15.040 15.005 14.973 14.945 14. 920 14.898 14.880 14.866 14. 854 14.846 14.841 14.840

78.757 78.755 78.750 78.742 78. 730 78.715 78.697 78.675 78.650 78. 621 78.589 78.553 78.513 78. 469 78.422 78.371 78.315 78.255 78. 191 78.123 78.050 77.972 77.889 77. 801 77.708 77.610 77.506 77. 396 77.280 77.158 77.029 76.894 76. 751 76.602 76.445 76.280 76.107 75. 926 75.736 75.537 75.329 75.111 74. 884 74.646 74.397 74.137 73.866 73. 583 73.289 72.981 72.661 72. 327 71.980 71.619 71.243 70.852 70. 446 70.024 69.586 69.132 68.660 68. 171 67.664 67.139 66.595 66.033 65.451 64.851 64.232 63. 594 62.939 62.266 61.578 60.876 60. 163 59.439 58.708 57.972 57.235 56. 498 55.764 55.036 54.314 53.602 52. 899 52.207 51.525 50.855 50. 196 49.548 48.910 48.283 47.665 47. 056 46.456 45.864 45.279 44.701 44. 129 43.564 43.004 42.449 41.898 41. 352 40.810 40.272 39.737 39.206 38. 678 38.153 37.631 37.111 36. 594 36.080 35.569 35.060 34.554 34. 051 33.551 33.053 32.559 32.068 31. 580 31.096 30.615 30.138 29. 666 29.198 28.735 28.277 27.824 27. 377 26.935 26.500 26.072 25.651 25. 236 24.830 24.431 24.040 23.658 23. 285 22.920 22.564 22.218 21. 881 21.554 21.236 20.928 20.629 20. 340 20.061 19.791 19.531 19. 281 19.039 18.807 18.583 18.369 18. 163 17.965 17.776 17.594 17.421 17. 255 17.096 16.945 16.800 16.662 16. 531 16.406 16.288 16.175 16.068 15. 966 15.870 15.779 15.693 15. 612 15.536 15.464 15.397 15.334 15. 275 15.221 15.170 15.124 15.081 15. 042 15.006 14.975 14.946 14.921 14. 900 14.882 14.867 14.856 14. 848 14.843 14.841

2.5 80.1108 79.9217 79.646 79.3471 79. 0393 78.7264 78.4088 78.0866 77.7593 77. 4262 77.0868 76.7403 76.386 76.0233 75.6512 75.269 74. 8758 74.4709 74.0533 73.6221 73. 1763 72.7149 72.2369 71.7413 71.2268 70. 6923 70.1366 69.5584 68.9562 68.3287 67. 6744 66.9917 66.2787 65.5339 64. 7551 63.9405 63.0877 62.1945 61.2583 60. 2763 59.2457 58.1631 57.025 55.8275 54.5662 53. 2362 51.8321 50.3475 48.7753 47.1071 45. 3332 43.4419 41.4191 39.2478 36.9069 34. 3704 31.6064 28.5768 25.2405 21. 5643 17.5518 13.3 13.3 17.9619 22.3401 26.32 29.8972 33.1118 36.0138 38.6494 41.058 43.2713 45. 3155 47.2117 48.977 50.626 52.1705 53.6207 54. 9854 56.2719 57.4869 58.636 59.7243 60.7563 61.736 62.667 63. 5527 64.396 65.1997 65.9662 66.698 67.3971 68.0655 68. 7051 69.3176 69.9047 70.4678 71.0084 71. 5279 72.0275 72.5085 72.972 73.4191 73.8509 74. 2684 74.6725 75.0641 75.4442 75.8136 76.173 76. 5235 76.8655 77.2001 77.5277 77.8491 78.165 78. 4759 78.7822 79.0841 79.3809 79. 6693 79.9351 80.1176

5.0 80.3 79.9649 79.6577 79.3514 79. 0419 78.7286 78.4112 78.0892 77.7621 77. 4294 77.0903 76.7442 76.3903 76. 0279 75.6562 75.2744 74.8817 74.4773 74. 0601 73.6293 73.184 72.7232 72.2458 71.7507 71. 2368 70.7029 70.1479 69.5703 68. 9689 68.3422 67.6887 67.0067 66.2947 65. 5508 64.7731 63.9595 63.1079 62.216 61.2811 60. 3007 59.2717 58.1909 57.0547 55.8594 54. 6005 53.2733 51.8723 50.3913 48.8232 47.16 45.3919 43.5076 41.4934 39. 3326 37.0047 34.4842 31.7392 28.7302 25. 4105 21.7324 17.6715 13.3 13.3 18.1036 22. 5394 26.5213 30.0784 33.2681 36.1469 38.763 41. 1555 43.3559 45.3896 47.277 49.0352 50.6782 52. 2176 53.6635 55.0244 56.3077 57.5198 58. 6664 59.7525 60.7824 61.7603 62. 6897 63.5739 64.4158 65.2182 65.9836 66. 7143 67.4124 68.0799 68.7186 69.3303 69. 9166 70.4791 71.019 71.5379 72.0369 72.5173 72. 9802 73.4268 73.8581 74.2751 74.6787 75. 0699 75.4495 75.8185 76.1776 76. 5276 76.8693 77.2035 77.5308 77.8519 78. 1675 78.4782 78.7844 79.0866 79.3851 79. 6806 79.9768 80.3

7.5 80.3 79.9802 79.6685 79.359 79.0484 78.735 78. 4181 78.0968 77.7707 77.4389 77.1009 76. 7558 76.4031 76.0418 75.6714 75.2908 74. 8994 74.4963 74.0805 73.6512 73. 2074 72.7481 72.2723 71.7789 71.2667 70. 7347 70.1816 69.6061 69.0068 68.3824 67. 7313 67.0519 66.3426 65.6015 64. 8269 64.0166 63.1685 62.2803 61.3496 60. 3736 59.3494 58.2739 57.1437 55.9548 54. 7032 53.3842 51.9924 50.5221 48.9665 47. 3177 45.5668 43.7032 41.7142 39. 5845 37.2951 34.8225 32.136 29.1942 25.9389 22. 2832 18.1019 13.3 13.3 18.6133 23.1923 27.1475 30. 6271 33.7353 36.5428 39.1002 41.4452 43. 6073 45.6098 47.4717 49.2087 50. 8339 52.3583 53.7913 55.1411 56.4147 57. 6183 58.7574 59.8367 60.8607 61. 8331 62.7576 63.6373 64.4752 65.2738 66. 0358 66.7632 67.4583 68.1231 68.7592 69. 3685 69.9525 70.5128 71.0507 71.5676 72. 0648 72.5435 73.0048 73.4498 73. 8796 74.2951 74.6973 75.0872 75.4656 75. 8333 76.1912 76.5401 76.8807 77.2138 77. 5401 77.8602 78.1749 78.4848 78.7906 79. 0929 79.3925 79.691 79.9916 80.3

10.0 80.3 79.9874 79.6771 79.3678 79. 0575 78.745 78.4292 78.1094 77.7848 77.4547 77. 1184 76.7752 76.4243 76.065 75.6966 75.3181 74. 9288 74.5279 74.1144 73.6875 73. 2462 72.7895 72.3164 71.8258 71.3166 70. 7877 70.2378 69.6657 69.07 68.4493 67.8022 67.127 66.4222 65.6859 64.9163 64. 1114 63.2692 62.3873 61.4633 60.4947 59. 4785 58.4118 57.2912 56.113 54.8734 53.5677 52. 1912 50.7383 49.2028 47.5775 45.8545 44. 0242 42.0757 39.9959 37.7689 35.3748 32. 7879 29.9718 26.8677 23.3595 19.153 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 13.3 19.8573 24.4691 28.2493 31.5473 34. 5031 37.1888 39.6497 41.9179 44.0182 45. 9706 47.7913 49.494 51.0904 52.5903 54.0023 55.334 56. 5917 57.7813 58.908 59.9763 60.9904 61.9539 62. 8703 63.7426 64.5737 65.3661 66. 1223 66.8445 67.5347 68.1948 68.8266 69. 4319 70.0121 70.5688 71.1034 71.6171 72. 1113 72.5871 73.0456 73.488 73.9153 74.3284 74. 7284 75.116 75.4922 75.8579 76.2139 76.5608 76. 8996 77.2309 77.5555 77.874 78.1872 78.4957 78. 8003 79.1017 79.401 79.6993 79.9985 80.3

12.5 80.3 79.9921 79.6848 79.3775 79. 0689 78.7582 78.4445 78.1268 77.8045 77. 4767 77.1429 76.8022 76.454 76.0974 75.7318 75. 3562 74.9699 74.5721 74.1618 73. 7383 73.3004 72.8473 72.3779 71.8913 71. 3862 70.8616 70.3162 69.7488 69.1581 68. 5427 67.9011 67.2318 66.5332 65. 8035 65.041 64.2437 63.4095 62.5363 61.6217 60. 6633 59.6582 58.6035 57.4962 56.3328 55. 1095 53.8222 52.4664 51.0371 49.5288 47. 9352 46.2494 44.4635 42.5686 40.5546 38. 4096 36.1199 33.6691 31.0373 28. 2005 25.1342 21.8507 18.6214 17.2182 16.4671 15.9872 15.6367 15.3546 15. 1114 14.8907 14.683 14.4825 14.2854 14.0894 13. 8931 13.6961 13.4983 13.3 13.3 13.4479 13.594 13.7369 13. 8751 14.0074 14.1329 14.2509 14. 3611 14.4634 14.5578 14.6445 14.7239 14. 7963 14.8623 14.9222 14.9765 15.0259 15. 0706 15.1111 15.1479 15.1813 15.2117 15. 2394 15.2647 15.2879 15.3092 15. 3288 15.3471 15.3641 15.3802 15.3953 15. 4098 15.4238 15.4374 15.4509 15.4642 15. 4778 15.4916 15.5058 15.5208 15. 5366 15.5535 15.5717 15.5916 15.6135 15. 6379 15.6651 15.6958 15.7308 15.771 15.8176 15. 8722 15.937 16.0148 16.1101 16.2292 16.3825 16. 5873 16.876 17.3152 18.0614 19.5371 23.0469 26. 5776 29.8332 32.8096 35.541 38.0597 40.3918 42. 5584 44.5771 46.463 48.2288 49.8857 51.4433 52. 9102 54.2938 55.6007 56.8368 58. 0073 59.117 60.1702 61.1706 62.1218 63.027 63.8891 64. 7109 65.4947 66.243 66.9577 67.6411 68.2948 68. 9207 69.5203 70.0953 70.647 71.1768 71.6861 72. 1761 72.6479 73.1026 73.5414 73. 9651 74.3749 74.7717 75.1562 75.5295 75. 8923 76.2455 76.5898 76.9259 77.2547 77. 5769 77.8931 78.2041 78.5105 78.8132 79. 1128 79.4103 79.7068 80.0031 80.3

15.0 80.3 79.9964 79.6926 79.3883 79. 0825 78.7746 78.4636 78.1488 77.8295 77. 5048 77.1742 76.8368 76.492 76.1389 75.7768 75.405 75. 0226 74.6287 74.2226 73.8033 73. 3698 72.9213 72.4568 71.9752 71.4753 70. 9562 70.4166 69.8553 69.2709 68.6622 68. 0277 67.3659 66.6753 65.954 65.2005 64.4128 63. 5889 62.7268 61.8241 60.8785 59. 8873 58.848 57.7574 56.6124 55.4096 54.1451 52. 8151 51.4149 49.94 48.385 46.7443 45.0117 43.1807 41.2442 39.1951 37.0261 34.7313 32.308 29. 7627 27.1262 24.4939 22.1169 20.4843 19.3629 18.545 17.9048 17.3705 16. 9002 16.4683 16.059 15.6617 15.2697 14.8789 14.487 14.093 13. 6971 13.3 13.3 13.5974 13.8914 14.1786 14.4561 14. 7216 14.9731 15.2096 15.4302 15.6347 15. 8233 15.9964 16.1548 16.2992 16.4305 16. 5499 16.6582 16.7563 16.8453 16.926 16.9992 17. 0657 17.1261 17.1812 17.2315 17.2776 17.32 17.3591 17.3954 17.4293 17. 4612 17.4913 17.5202 17.548 17.5751 17.6018 17. 6284 17.6552 17.6827 17.711 17.7407 17.772 17.8056 17. 8418 17.8812 17.9246 17.9728 18. 0267 18.0874 18.1565 18.2356 18.3272 18. 4343 18.5608 18.7122 18.8963 19.1243 19. 4135 19.7908 20.3014 21.0232 22.0935 23. 7399 26.2154 28.9614 31.6964 34.3167 36. 7917 39.1173 41.2994 43.3467 45. 2689 47.0754 48.7753 50.3766 51.8871 53. 3134 54.6619 55.9382 57.1474 58. 2941 59.3826 60.4168 61.4001 62.3358 63. 2268 64.0761 64.8859 65.6589 66.397 67.1025 67. 7771 68.4227 69.0409 69.6334 70.2017 70.747 71. 2709 71.7745 72.2591 72.7257 73.1756 73. 6097 74.029 74.4345 74.8271 75.2077 75.5772 75. 9363 76.2859 76.6268 76.9596 77. 2852 77.6042 77.9174 78.2255 78.5291 78.829 79.126 79. 4208 79.7143 80.0072 80.3

17.5 80.3 80.0007 79.701 79.4004 79.0983 78. 7939 78.4865 78.1754 77.8598 77.539 77.2122 76. 8789 76.5382 76.1894 75.8317 75.4644 75. 0866 74.6976 74.2965 73.8824 73. 4543 73.0115 72.5528 72.0772 71.5838 71. 0714 70.5387 69.9848 69.4081 68.8076 68. 1816 67.5289 66.8479 66.1369 65. 3942 64.6181 63.8066 62.9577 62.0693 61. 1391 60.1648 59.1436 58.073 56.9499 55.7712 54. 5337 53.2338 51.8676 50.4313 48.9206 47. 3311 45.6585 43.8983 42.0466 40.1003 38.058 35. 9219 33.7007 31.4161 29.1138 26.882 24.8681 23.239 21.9554 20.9251 20.0672 19. 3225 18.6505 18.0235 17.4228 16.8354 16. 2528 15.6697 15.083 14.4919 13.897 13.3 13.3 13.7505 14.1955 14. 6298 15.0491 15.4496 15.8286 16.1842 16. 5154 16.822 17.1043 17.3631 17.5996 17.815 18.0109 18. 1887 18.3499 18.496 18.6284 18.7484 18.8572 18.956 19. 0459 19.1278 19.2025 19.271 19.334 19.3922 19.4461 19. 4965 19.5439 19.5887 19.6315 19. 6728 19.7131 19.7527 19.7923 19.8321 19. 8728 19.9149 19.9589 20.0053 20.055 20.1086 20. 1669 20.231 20.302 20.3814 20.4707 20.572 20.6878 20.8214 20. 9769 21.1597 21.3769 21.6386 21.9584 22. 3562 22.861 23.5156 24.3829 25.5496 27.1136 29. 1135 31.356 33.6741 35.9693 38.1916 40.3186 42. 3418 44.2602 46.0763 47.7946 49.4202 50. 9585 52.4148 53.7945 55.1023 56. 3428 57.5205 58.6392 59.7026 60.7142 61. 6771 62.5943 63.4685 64.3023 65.098 65. 8578 66.5838 67.278 67.9421 68.5779 69.1869 69. 7708 70.3309 70.8686 71.3852 71.8819 72.36 72.8204 73.2643 73.6928 74.1067 74.507 74. 8946 75.2704 75.6352 75.9899 76.3352 76. 6718 77.0006 77.3223 77.6375 77. 9469 78.2513 78.5514 78.8478 79.1413 79. 4327 79.7225 80.0114 80.3

20.0 80.3 80.0054 79.7103 79.4142 79. 1164 78.8163 78.5132 78.2064 77.8953 77.579 77. 2569 76.9283 76.5925 76.2487 75.8962 75. 5342 75.1619 74.7786 74.3834 73. 9754 73.5537 73.1174 72.6656 72.1972 71. 7113 71.2066 70.6822 70.1369 69.5693 68. 9782 68.3624 67.7203 67.0504 66. 3513 65.6213 64.8587 64.0616 63.2282 62. 3563 61.444 60.489 59.4888 58.441 57.3429 56.1918 54.9847 53. 7187 52.3905 50.997 49.5349 48.0011 46.3927 44. 7074 42.9436 41.1015 39.1838 37.1976 35. 1569 33.0873 31.0309 29.0523 27.2342 25. 6484 24.2944 23.1329 22.1162 21.2017 20.3557 19.5525 18.7733 18. 0044 17.2366 16.4639 15.6833 14.8946 14. 0992 13.3 13.3 13.909 14.5101 15.0962 15.661 16.1992 16.7074 17. 1831 17.6251 18.0335 18.4087 18.7521 19. 0654 19.3504 19.6093 19.844 20.0567 20.2493 20. 4238 20.5819 20.7252 20.8553 20. 9736 21.0814 21.1798 21.27 21.3529 21.4294 21.5005 21.5668 21.6291 21.6881 21.7444 21. 7987 21.8517 21.9038 21.9558 22.0082 22. 0617 22.1169 22.1746 22.2355 22. 3005 22.3706 22.4468 22.5305 22.623 22.7261 22. 8419 22.9729 23.1223 23.2938 23.4923 23. 7241 23.9973 24.3226 24.7144 25.192 25.7814 26. 5172 27.4431 28.6081 30.0516 31.7689 33. 6751 35.6748 37.6947 39.687 41.6235 43.489 45.2759 46. 9816 48.6065 50.1524 51.6223 53. 0194 54.3473 55.6098 56.8104 57.9525 59. 0395 60.0744 61.0603 61.9999 62. 8959 63.7507 64.5666 65.3459 66.0905 66. 8025 67.4835 68.1354 68.7598 69.3581 69. 9319 70.4825 71.0113 71.5194 72.0081 72. 4785 72.9316 73.3686 73.7904 74.1979 74. 5921 74.9739 75.3441 75.7034 76. 0528 76.393 76.7248 77.0488 77.3657 77.6764 77. 9814 78.2815 78.5773 78.8696 79.1589 79.446 79. 7315 80.016 80.3

22.5 80.3 80.0106 79.7206 79.4295 79. 1368 78.8417 78.5436 78.2419 77.9359 77. 6248 77.3081 76.985 76.6548 76.3167 75.9702 75. 6143 75.2484 74.8715 74.4831 74.082 73. 6676 73.2389 72.795 72.3348 71.8574 71.3617 70. 8467 70.3112 69.7539 69.1738 68.5693 67. 9393 67.2823 66.5967 65.8811 65.1338 64.353 63.537 62. 6839 61.7917 60.8583 59.8816 58.8592 57.789 56. 6683 55.4947 54.2657 52.9787 51. 6312 50.2209 48.7456 47.2039 45.5948 43. 9189 42.1783 40.3782 38.5277 36.6421 34. 7451 32.8704 31.062 29.3682 27.8258 26.4409 25.196 24.063 23.0125 22.0181 21.0575 20.1134 19. 1724 18.2252 17.2659 16.2919 15.304 14.305 13.3 13.3 14.0753 14. 8399 15.584 16.2992 16.979 17.6187 18.2156 18.7687 19.278 19.745 20. 1713 20.5595 20.9121 21.2318 21.5214 21. 7836 22.0209 22.2356 22.4301 22.6065 22. 7665 22.9119 23.0444 23.1654 23. 2762 23.3781 23.4722 23.5595 23.641 23.7176 23. 7901 23.8593 23.9261 23.9911 24.0551 24. 1189 24.1832 24.2487 24.3164 24.387 24.4615 24. 5409 24.6264 24.7193 24.821 24.9333 25. 0582 25.198 25.3556 25.5346 25.739 25.9743 26.247 26.5655 26.9402 27. 3847 27.916 28.5554 29.3287 30.2641 31. 3883 32.7159 34.2352 35.9008 37.6554 39. 4476 41.238 42.9996 44.7147 46.3727 47.9678 49. 4974 50.9608 52.3588 53.693 54.9657 56. 1793 57.3364 58.4397 59.4918 60.4953 61. 4526 62.3663 63.2386 64.0717 64.8676 65. 6284 66.356 67.052 67.7183 68.3563 68.9677 69.5539 70. 1162 70.656 71.1746 71.673 72.1525 72.6142 73.059 73.488 73.9022 74. 3025 74.6897 75.0648 75.4285 75.7816 76.125 76. 4594 76.7854 77.1039 77.4155 77.721 78.0209 78.316 78. 6068 78.8942 79.1787 79.4609 79.7415 80.021 80.3

25.0 80.3 80.0163 79.732 79.4466 79.1595 78.87 78.5777 78.2817 77.9815 77.6764 77. 3657 77.0487 76.7249 76.3933 76. 0534 75.7045 75.3456 74.9762 74.5953 74. 2021 73.7959 73.3756 72.9405 72.4896 72. 0218 71.5362 71.0317 70.5072 69. 9615 69.3935 68.8019 68.1854 67.5426 66. 8722 66.1726 65.4422 64.6796 63.8829 63. 0505 62.1805 61.2709 60.32 59.3255 58.2854 57.1977 56.0602 54.8707 53. 6274 52.3283 50.9718 49.5567 48.0824 46. 5492 44.9589 43.3147 41.6228 39.8928 38. 1389 36.3806 34.6434 32.9571 31.3509 29. 8458 28.4475 27.1471 25.9273 24.7673 23.6465 22.5462 21.4504 20. 3467 19.2259 18.0824 16.9146 15.7243 14. 5168 13.3 13.3 14.2523 15.1902 16.1007 16.9729 17. 7987 18.5727 19.292 19.9558 20.5651 21.1218 21. 6287 22.0891 22.5065 22.8844 23. 2262 23.5353 23.8149 24.0677 24.2966 24.504 24. 6922 24.8632 25.0189 25.1612 25.2914 25. 4112 25.5218 25.6244 25.7201 25.8101 25. 8953 25.9767 26.0551 26.1315 26. 2066 26.2815 26.3569 26.4337 26.5129 26. 5955 26.6826 26.7753 26.8749 26.9829 27.101 27.231 27. 3752 27.5362 27.717 27.9213 28.1535 28.419 28.7243 29. 0774 29.488 29.9681 30.5318 31.1957 31.9779 32. 8964 33.9651 35.1885 36.5553 38.0375 39. 5985 41.2022 42.818 44.422 45.9974 47.5325 49.0196 50. 4544 51.8344 53.159 54.4282 55.6432 56. 8053 57.9163 58.9781 59.9927 60.9622 61. 8887 62.7741 63.6205 64.4298 65.2038 65. 9442 66.6529 67.3313 67.9812 68. 6039 69.2009 69.7735 70.3231 70.8508 71. 3579 71.8456 72.3148 72.7667 73.2022 73. 6223 74.028 74.4201 74.7995 75.167 75.5234 75.8696 76. 2062 76.534 76.8537 77.166 77.4715 77.7711 78.0652 78. 3546 78.6399 78.9217 79.2007 79.4774 79. 7525 80.0265 80.3

27.5 80.3 80.0225 79.7445 79.4653 79. 1845 78.9013 78.6153 78.3257 78.032 77.7335 77. 4295 77.1194 76.8026 76.4783 76.1458 75. 8045 75.4535 75.0922 74.7197 74. 3353 73.9381 73.5273 73.1019 72.6612 72.204 71. 7295 71.2367 70.7243 70.1914 69.6368 69. 0594 68.4577 67.8307 67.1768 66. 4948 65.7831 65.0402 64.2647 63.4547 62. 6088 61.7251 60.8018 59.8373 58.8296 57. 7769 56.6775 55.5297 54.3319 53.0827 51. 7813 50.4269 49.0198 47.5609 46.0526 44. 4988 42.9056 41.282 39.6399 37.995 36.3657 34.772 33.2323 31. 7592 30.356 29.0175 27.7317 26. 4829 25.2545 24.0302 22.7954 21.5381 20. 2491 18.9234 17.5598 16.1619 14.738 13.3 13.3 14.4436 15. 5679 16.6557 17.6931 18.6703 19.5815 20. 4239 21.1976 21.9047 22.5484 23.1326 23. 6618 24.1405 24.5731 24.9638 25. 3167 25.6356 25.9238 26.1846 26.4207 26.635 26. 8297 27. 007 27.1688 27.3171 27.4534 27.5793 27. 6961 27.8051 27.9075 28.0044 28.097 28.1862 28. 2731 28.3585 28.4435 28.5291 28. 6163 28.7061 28.7996 28.8981 29.0027 29.115 29. 2365 29.3691 29.5146 29.6756 29.8546 30. 0549 30.2801 30.5347 30.8239 31.1538 31. 5317 31.9664 32.4679 33.0475 33.7176 34. 4909 35.3783 36.3872 37.5176 38. 7599 40.0953 41.4989 42.9449 44.4095 45. 8732 47.3206 48.7401 50.1238 51.4661 52. 7637 54.0145 55.2178 56.3735 57. 4824 58.5453 59.5636 60.5387 61.4722 62. 3658 63. 221 64.0396 64.8232 65.5734 66.2918 66.98 67.6393 68.2712 68.8772 69. 4584 70.0162 70.5517 71.0662 71.5608 72. 0365 72.4945 72.9356 73.3608 73.7711 74. 1674 74.5504 74.9211 75.2803 75.6287 75. 9671 76.2962 76.6167 76.9293 77.2347 77. 5336 77.8265 78.1143 78.3973 78. 6764 78.9521 79.225 79.4956 79.7647 80.0326 80.3

30.0 80.3 80.0293 79.7581 79.4858 79. 2118 78.9355 78.6564 78.3739 78.0873 77.796 77. 4994 77.1969 76.8878 76.5714 76.2471 75. 9141 75.5718 75.2194 74.8561 74. 4812 74. 094 73.6934 73.2788 72.8492 72.4037 71. 9413 71.4611 70.962 70.4431 69.9031 69.341 68.7555 68. 1455 67.5096 66.8466 66.1551 65.4336 64. 6807 63. 895 63.0749 62.2187 61.325 60.3922 59. 4186 58.4028 57.3433 56.2386 55.0877 53. 8895 52.6437 51.3499 50.0089 48.622 47.1918 45. 7222 44.2189 42.6895 41.1438 39.5937 38. 0523 36. 533 35.0473 33.6024 32. 2 30.8354 29.499 28.1782 26.8584 25. 5246 24.1629 22. 761 21.3093 19.8022 18.2391 16. 6255 14.9733 13.3 13.3 14.6541 15.982 17.261 18.4735 19.6081 20. 6589 21.6243 22.5061 23.3078 24.0344 24. 6916 25. 285 25.8206 26.3035 26.7392 27.1322 27. 4869 27.8073 28.0971 28.3594 28.5974 28. 8136 29.0104 29.1902 29.3548 29. 5061 29.6459 29.7755 29.8966 30.0103 30. 1179 30.2207 30.3197 30.416 30.5108 30.605 30.6998 30. 7963 30.8956 30.9988 31.1073 31.2225 31. 3459 31.4791 31.6241 31.7828 31. 9578 32.1517 32.3678 32.6096 32.8813 33.188 33. 5352 33.9294 34.3781 34.8895 35.4726 36. 1364 36.8896 37.739 38.6879 39.7347 40.8716 42. 0849 43. 357 44.6688 46.0021 47.3408 48.6715 49. 9836 51.2693 52.5227 53.7396 54.9175 56. 0548 57.1508 58.2054 59.219 60.1923 61. 1264 62.0222 62.8811 63.7045 64.4936 65.25 65.9749 66.6697 67.3359 67. 9747 68.5873 69.1751 69.7393 70.281 70.8014 71. 3016 71.7825 72.2453 72.6909 73.1203 73. 5343 73.9339 74.3199 74.6931 75.0544 75. 4044 75. 744 76.0739 76.3947 76.7073 77.0121 77.31 77.6015 77.8873 78.1679 78. 4441 78.7163 78.9853 79.2515 79.5155 79. 7779 80.0392 80.3

32.5 80.3 80.0367 79.7729 79.5079 79. 2414 78.9726 78.701 78.4261 78.1473 77.8639 77. 5753 77. 281 76.9802 76.6724 76.357 76.0331 75.7001 75. 3574 75.0041 74.6396 74.2631 73. 8737 73.4706 73.0531 72.6201 72.1709 71. 7044 71.2196 70.7157 70.1915 69.6459 69. 0778 68.4861 67.8696 67.2269 66.557 65.8583 65. 1297 64.3697 63.5769 62.7499 61. 8874 60.9879 60.05 59.0725 58.0541 56.9938 55.8907 54.7441 53.5539 52.3202 51. 0438 49.7264 48.3704 46.9794 45.5583 44. 1133 42.6522 41.1837 39.7168 38. 2604 36.8213 35.4034 34.0061 32.6249 31.2509 29.8725 28.4761 27.047 25.5707 24. 0337 22.4248 20.737 18.9691 17.1278 15.2296 13.3 13.3 14. 8908 16.4452 17.9327 19.3317 20.6296 21. 8217 22.9086 23.8945 24.7859 25. 5899 26.3142 26.9662 27.5531 28.0814 28. 5572 28.9859 29.3725 29.7215 30.037 30.3226 30. 5815 30.8168 31.031 31.2266 31.4057 31.5704 31. 7225 31.8637 31.9954 32.1192 32.2363 32.3481 32. 4558 32.5606 32.6636 32.766 32.8689 32.9735 33.081 33. 1927 33.3099 33.4342 33.5669 33.71 33.8652 34.0348 34.2211 34.4268 34. 6549 34. 909 35.1931 35.5116 35.8695 36.2726 36.727 37. 2395 37.8169 38.4659 39.1922 40 40.8906 41.8617 42.9068 44.0158 45. 1754 46.3713 47.5893 48.8163 50.0409 51. 2537 52.4472 53.6156 54.7546 55. 8611 56.9332 57.9695 58.9694 59.933 60.8604 61. 7521 62.6091 63.4321 64.2222 64.9805 65. 7082 66.4064 67.0763 67.7192 68. 3361 68.9282 69.4968 70.0427 70.5673 71. 0714 71.5561 72.0224 72.4713 72.9036 73. 3203 73.7223 74.1103 74.4852 74.8478 75. 1988 75.5389 75.869 76.1897 76.5016 76.8055 77.102 77. 3916 77.6752 77.9531 78.2261 78. 4948 78.7596 79.0212 79.2801 79.5369 79. 7922 80.0463 80.3

Equipotential Lines

Flow Lines

1000

0.000

10.000

20.000

140.0 190.0 240.0 290.0 340.0 390.0

Uplift Pressure on Base of Dam