ESTRUCTURAS HIDRAULICAS

RIO: LA LECHE - ESTACION PUCHACA

AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC MAX PROM MIN

1960 11.485 26.880 22.802 16.153 19.729 6.954 2.369 15.122 16.192 3.593 3.555 2.410 26.880 12.270 2.369

1961 5.263 10.193 37.221 35.120 13.107 5.667 1.526 1.088 12.911 6.038 3.844 14.835 37.221 12.234 1.088

1962 8.419 41.801 27.522 38.336 15.047 5.222 1.255 2.896 7.520 2.891 12.036 8.177 41.801 14.260 1.255

1963 2.931 3.101 27.202 10.377 5.318 6.440 3.103 0.668 0.253 10.202 6.299 15.263 27.202 7.596 0.253

1964 23.114 10.788 25.125 18.625 6.291 4.682 5.953 14.120 7.393 38.475 24.452 5.800 38.475 15.402 4.682

1965 6.498 23.451 32.375 55.875 10.758 10.531 15.691 7.750 16.247 7.311 21.900 34.220 55.875 20.217 6.498

1966 30.125 13.225 9.947 14.776 34.525 2.229 1.664 7.608 9.287 24.544 7.292 6.055 34.525 13.440 1.664

1967 34.750 31.250 27.707 26.495 4.605 2.914 17.411 5.570 6.492 15.908 5.766 17.829 34.750 16.391 2.914

1968 17.136 3.908 8.138 22.357 7.056 0.570 12.758 8.611 11.257 26.588 11.245 1.987 26.588 10.968 0.570

1969 29.500 23.294 55.125 29.165 22.962 10.713 2.315 12.848 8.404 3.081 12.641 19.654 55.125 19.142 2.315

1970 30.750 12.561 44.867 25.256 28.358 27.350 10.313 5.075 11.471 48.212 30.733 29.666 48.212 25.384 5.075

1971 21.238 18.870 121.250 92.375 22.647 10.827 7.504 15.342 11.652 20.647 21.622 19.065 121.250 31.920 7.504

1972 42.875 36.925 141.312 62.312 11.692 14.220 30.293 13.968 20.129 2.777 6.131 20.291 141.312 33.577 2.777

1973 26.002 105.200 63.450 58.937 17.998 13.260 11.100 11.729 28.363 6.234 15.573 8.620 105.200 30.539 6.234

1974 23.958 38.865 18.349 14.342 9.397 10.125 21.312 9.083 11.932 22.195 11.168 58.216 58.216 20.745 9.083

1975 40.810 30.980 210.131 29.036 11.468 17.604 10.304 15.210 13.947 16.302 23.007 1.686 210.131 35.040 1.686

1976 41.906 47.002 24.970 34.272 19.080 43.523 9.465 11.155 6.915 1.028 1.894 13.239 47.002 21.204 1.028

1977 18.754 40.414 72.299 28.171 15.363 31.663 6.402 3.338 11.901 8.728 9.491 6.694 72.299 21.102 3.338

1978 14.091 14.418 68.725 12.510 13.015 8.844 21.133 10.965 9.326 14.762 24.212 13.780 68.725 18.815 8.844

1979 17.138 10.780 48.401 19.105 6.649 7.612 1.754 2.056 9.279 4.172 0.584 2.403 48.401 10.828 0.584

1980 9.895 6.345 31.550 17.750 11.054 2.410 4.395 2.586 0.634 34.346 14.978 13.641 34.346 12.465 0.634

1981 1.995 30.998 34.835 47.313 3.685 16.547 7.224 4.348 0.639 12.163 5.325 13.783 47.313 14.905 0.639

1982 5.821 5.651 8.636 24.824 6.673 4.790 6.278 1.501 7.582 9.572 7.773 18.980 24.824 9.007 1.501

1983 77.292 46.250 122.500 120.937 215.813 13.475 7.693 4.596 5.202 20.771 10.142 8.738 215.813 54.451 4.596

1984 2.539 92.216 114.538 11.135 13.131 18.793 5.921 10.338 3.471 27.291 6.500 8.468 114.538 26.195 2.539

1985 4.134 20.831 28.938 5.763 15.570 10.725 3.800 6.775 12.988 40.875 0.424 13.472 40.875 13.691 0.424

1986 21.750 5.252 20.743 31.997 14.103 1.777 3.331 9.791 1.024 5.564 13.979 10.413 31.997 11.644 1.024

1987 17.648 20.592 49.077 12.625 8.153 0.798 4.956 4.311 1.408 3.103 2.656 6.700 49.077 11.002 0.798

1988 9.009 10.709 16.447 27.075 11.350 1.906 0.347 0.380 2.538 9.263 13.863 3.772 27.075 8.888 0.347

1989 13.781 58.438 59.031 23.425 6.300 14.081 2.081 1.134 3.003 4.325 1.075 0.398 59.031 15.589 0.398

1990 13.850 14.494 22.288 8.531 4.981 20.544 9.350 0.444 1.084 30.911 18.525 9.438 30.911 12.870 0.444

1991 10.500 40.494 14.272 15.519 6.975 1.088 0.840 0.233 0.500 0.783 2.994 2.971 40.494 8.097 0.233

1992 15.675 21.338 26.950 58.131 4.100 7.594 2.591 3.184 2.730 5.512 5.409 10.101 58.131 13.610 2.591

1993 3.255 12.184 53.306 30.038 6.456 2.806 1.453 2.054 3.181 5.000 3.313 5.413 53.306 10.705 1.453

1994 5.981 14.000 51.781 17.256 7.813 3.447 3.006 1.906 4.238 2.353 14.454 18.306 51.781 12.045 1.906

1995 23.450 23.163 5.672 4.688 5.963 0.844 5.141 0.398 0.729 1.134 3.625 14.688 23.450 7.458 0.398

1996 7.625 11.125 21.000 8.944 4.475 4.013 1.488 1.936 0.850 13.094 8.375 3.388 21.000 7.193 0.850

1997 1.219 21.000 15.069 9.700 5.000 1.163 0.944 1.172 0.731 1.100 7.063 18.250 21.000 6.868 0.731

1998 431.250 579.750 400.000 297.500 99.500 14.125 6.488 2.650 15.375 11.281 24.088 3.381 579.750 157.116 2.650

1999 19.625 62.375 54.125 28.875 44.000 9.800 14.938 2.800 5.619 5.275 3.838 19.513 62.375 22.565 2.800

2000 1.306 22.625 155.000 30.125 10.644 10.438 3.925 31.000 4.075 2.619 0.406 63.125 155.000 27.941 0.406

2001 28.313 91.250 500.000 38.188 15.000 53.175 15.013 1.000 12.463 9.363 13.688 16.500 500.000 66.163 1.000

2002 14.250 58.688 117.500 301.875 17.875 3.719 5.656 2.694 0.575 12.250 19.275 16.175 301.875 47.544 0.575

2003 9.750 105.250 9.594 5.363 20.625 15.775 1.706 0.656 0.881 1.440 2.775 9.438 105.250 15.271 0.656

2004 10.425 2.519 11.500 19.250 5.575 1.794 12.713 0.666 5.691 15.156 9.750 20.000 20.000 9.587 0.666

2005 3.475 40.000 40.000 13.650 1.300 1.700 0.794 0.150 0.080 5.838 4.775 2.925 40.000 9.557 0.080

REGISTRO DE CAUDALES MAXIMOS DIARIOS (M3/S)

ESTRUCTURAS HIDRAULICAS

RIO: MOTUPE - ESTACION CHINIAMA

AÑO ENE FEB MAR ABR MAY JUN JUL AGO SET OCT NOV DIC MAX PROM MIN

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986 2.740 1.760 2.530 6.150 4.980 2.210 1.530 1.550 1.370 1.450 1.330 1.140 6.150 2.395 1.140

1987 0.140 6.410 7.500 5.760 5.120 1.970 2.110 1.580 0.910 0.940 0.030 0.850 7.500 2.777 0.030

1988 0.140 4.050 3.470 4.360 0.000 1.710 0.770 0.680 0.680 1.050 1.520 1.330 4.360 1.647 0.000

1989 4.040 6.900 11.290 6.880 5.400 4.920 3.230 1.820 1.680 1.100 0.750 0.620 11.290 4.053 0.620

1990 0.900 2.550 2.880 3.510 1.680 1.450 0.770 0.000 0.000 0.000 0.000 0.000 3.510 1.145 0.000

1991 0.000 0.000 1.440 0.800 0.280 0.160 0.410 0.560 0.390 0.430 0.340 0.000 1.440 0.401 0.000

1992 0.970 0.230 0.500 1.000 1.120 1.000 0.880 1.070 1.500 1.650 1.300 0.990 1.650 1.017 0.230

1993 1.740 1.520 1.000 1.230 0.760 0.970 1.650 0.500 0.900 1.750 0.970 1.880 1.750 1.239 0.500

1994 1.000 1.800 1.900 2.900 1.500 1.200 1.000 0.600 0.500 0.500 0.400 0.500 2.900 1.150 0.400

1995 0.800 1.800 1.400 1.200 1.000 0.500 0.300 0.300 0.200 0.200 0.500 0.400 1.800 0.717 0.200

1996 0.610 0.700 1.380 1.090 1.020 0.500 0.200 0.070 0.010 0.000 0.120 0.180 1.380 0.490 0.000

1997 0.210 0.590 1.290 1.130 0.740 0.220 0.180 0.060 0.000 0.000 0.370 1.180 1.290 0.498 0.000

1998 21.450 114.700 183.690 50.430 19.550 1.720 1.280 1.160 0.950 0.820 0.840 0.770 183.690 33.113 0.770

1999 0.660 4.290 5.200 3.430 2.590 1.300 0.950 0.719 0.580 0.600 0.464 0.735 5.200 1.793 0.464

2000 0.752 1.520 5.442 2.950 2.229 1.602 1.377 1.238 1.187 1.020 0.780 1.292 5.442 2.236 0.752

2001 1.851 2.119 4.757 2.354 1.607 1.274 1.007 0.820 0.835 0.738 0.938 0.970 4.757 1.606 0.738

2002 0.777 2.373 2.639 5.213 1.683 1.793 1.468 1.069 0.752 0.111 1.216 1.064 5.213 1.679 0.111

2003 1.094 1.614 1.644 1.654 1.468 1.334 0.845 0.466 0.381 0.303 0.349 0.621 1.654 0.981 0.303

2004 0.885 0.690 0.876 0.864 0.604 0.306 0.272 0.149 0.180 0.005 0.458 0.732 0.885 0.502 0.005

2005 0.462 1.110 2.575 1.869 0.775 0.354 0.206 0.117 0.009 0.213 0.281 0.264 2.575 0.686 0.009

REGISTRO DE CAUDALES MAXIMOS DIARIOS (M3/S)

ESTRUCTURAS HIDRAULICAS

METODO NASHRIO LA LECHE - Estacion de Aforos : Puchaca n = 44 años

m Q max.Anual T T / ( T - 1 ) X Q * X1 579.750 45.000 1.023 -2.011 -1165.621 336110.063 4.0422 500.000 22.500 1.047 -1.705 -852.282 250000.000 2.9063 301.875 15.000 1.071 -1.523 -459.880 91128.516 2.3214 215.813 11.250 1.098 -1.393 -300.695 46575.251 1.9415 210.130 9.000 1.125 -1.291 -271.306 44154.617 1.6676 179.250 7.500 1.154 -1.207 -216.278 32130.563 1.4567 155.000 6.429 1.184 -1.134 -175.791 24025.000 1.2868 133.800 5.625 1.216 -1.071 -143.236 17902.440 1.1469 114.538 5.000 1.250 -1.014 -116.099 13118.953 1.02710 105.250 4.500 1.286 -0.962 -101.250 11077.563 0.92511 105.250 4.091 1.324 -0.915 -96.261 11077.563 0.83612 88.906 3.750 1.364 -0.871 -77.405 7904.277 0.75813 72.299 3.462 1.406 -0.830 -59.976 5227.145 0.68814 68.725 3.214 1.452 -0.791 -54.354 4723.126 0.62515 62.380 3.000 1.500 -0.754 -47.051 3891.264 0.56916 59.031 2.813 1.552 -0.719 -42.466 3484.659 0.51817 58.220 2.647 1.607 -0.686 -39.940 3389.568 0.47118 58.130 2.500 1.667 -0.654 -38.014 3379.097 0.42819 55.880 2.368 1.731 -0.623 -34.813 3122.574 0.38820 53.310 2.250 1.800 -0.593 -31.613 2841.956 0.35221 51.500 2.143 1.875 -0.564 -29.038 2652.250 0.31822 51.130 2.045 1.957 -0.535 -27.374 2614.277 0.28723 49.077 1.957 2.045 -0.508 -24.908 2408.552 0.25824 47.313 1.875 2.143 -0.480 -22.719 2238.520 0.23125 47.002 1.800 2.250 -0.453 -21.303 2209.188 0.20526 41.800 1.731 2.368 -0.427 -17.832 1747.240 0.18227 40.875 1.667 2.500 -0.400 -16.357 1670.766 0.16028 40.494 1.607 2.647 -0.374 -15.141 1639.764 0.14029 40.000 1.552 2.813 -0.348 -13.907 1600.000 0.12130 38.480 1.500 3.000 -0.321 -12.366 1480.710 0.10331 34.750 1.452 3.214 -0.295 -10.248 1207.563 0.08732 34.530 1.406 3.462 -0.268 -9.261 1192.321 0.07233 34.346 1.364 3.750 -0.241 -8.280 1179.648 0.05834 30.911 1.324 4.091 -0.213 -6.596 955.490 0.04635 27.770 1.286 4.500 -0.185 -5.136 771.173 0.03436 27.200 1.250 5.000 -0.156 -4.231 739.840 0.02437 27.075 1.216 5.625 -0.125 -3.381 733.056 0.01638 24.824 1.184 6.429 -0.093 -2.297 616.231 0.00939 23.982 1.154 7.500 -0.058 -1.390 575.136 0.00340 23.450 1.125 9.000 -0.020 -0.477 549.902 0.00041 21.000 1.098 11.250 0.022 0.455 441.000 0.00042 21.000 1.071 15.000 0.070 1.479 441.000 0.00543 20.000 1.047 22.500 0.131 2.621 400.000 0.01744 17.260 1.023 45.000 0.218 3.768 297.908 0.048

Σ 3993.306 -26.367 -4568.245 945625.728 26.774

Qp = 90.757 m³/sg.

Xm = -0.599

Q2 X2

ESTRUCTURAS HIDRAULICAS

Calculo de los parametros a y b

a = 209.548

b = Σ Xi*Qi - N*Xm*Qm b = -198.231 Σ Xi² - N*Xm²

Calculo del Caudal Maximo : T= 50 años T para 50 años = 1.0204

Qmax. = 617.271 m³/sg.

Calculo de las desviaciones estandar y la covarianza :

Sxx = N Σ Xi^2 - ( Σ Xi )^2 Sxx = 482.8214307

Sqq = N Σ Qi^2 - ( Σ Qi )^2 Sqq = 25661039.21

Sxq = N Σ Qi*Xi - ( Σ Qi )( Σ Xi ) Sxq = -95710.29986

X i = -2.056806117

ΔQ = 63.52752037

Calculo del caudal maximo de diseño:

Qd = 680.799 m³/sg.

T (años) P (%) X

5 80.00 -1.01363 410.482 448.685

10 90.00 -1.33954 475.086 519.313

25 96.00 -1.75132 556.715 611.341

50 98.00 -2.05681 617.27 680.799

100 99.00 -2.36004 677.381 750.341

200 99.50 -2.66216 737.271 820.019

1000 99.90 -3.36200 876.00135 982.316

a = Qm - b*Xm

Qmax. = a + b log log ( T / T - 1)

Qd = Qmax. + ΔQ

Qmax(m3/s) Qd (m3/s)

ESTRUCTURAS HIDRAULICAS

METODO NASHRIO MOTUPE - Estacion de Aforos : Chiniama n = 44 años

m Q max.Anual T T / ( T - 1 ) X Q * X1 300.000 45.000 1.023 -2.011 -603.167 90000.000 4.0422 255.000 22.500 1.047 -1.705 -434.664 65025.000 2.9063 183.690 15.000 1.071 -1.523 -279.835 33742.016 2.3214 36.000 11.250 1.098 -1.393 -50.159 1296.000 1.9415 23.180 9.000 1.125 -1.291 -29.928 537.312 1.6676 19.200 7.500 1.154 -1.207 -23.166 368.640 1.4567 19.200 6.429 1.184 -1.134 -21.775 368.640 1.2868 12.500 5.625 1.216 -1.071 -13.382 156.250 1.1469 11.920 5.000 1.250 -1.014 -12.082 142.086 1.02710 10.590 4.500 1.286 -0.962 -10.188 112.148 0.92511 10.000 4.091 1.324 -0.915 -9.146 100.000 0.83612 10.000 3.750 1.364 -0.871 -8.706 100.000 0.75813 10.000 3.462 1.406 -0.830 -8.296 100.000 0.68814 9.440 3.214 1.452 -0.791 -7.466 89.114 0.62515 9.039 3.000 1.500 -0.754 -6.818 81.704 0.56916 9.000 2.813 1.552 -0.719 -6.474 81.000 0.51817 7.338 2.647 1.607 -0.686 -5.034 53.846 0.47118 7.200 2.500 1.667 -0.654 -4.708 51.840 0.42819 7.000 2.368 1.731 -0.623 -4.361 49.000 0.38820 6.510 2.250 1.800 -0.593 -3.860 42.380 0.35221 6.200 2.143 1.875 -0.564 -3.496 38.440 0.31822 6.000 2.045 1.957 -0.535 -3.212 36.000 0.28723 5.500 1.957 2.045 -0.508 -2.791 30.250 0.25824 5.442 1.875 2.143 -0.480 -2.613 29.615 0.23125 5.240 1.800 2.250 -0.453 -2.375 27.458 0.20526 5.213 1.731 2.368 -0.427 -2.224 27.175 0.18227 5.200 1.667 2.500 -0.400 -2.081 27.040 0.16028 4.757 1.607 2.647 -0.374 -1.779 22.629 0.14029 4.420 1.552 2.813 -0.348 -1.537 19.536 0.12130 4.200 1.500 3.000 -0.321 -1.350 17.640 0.10331 3.700 1.452 3.214 -0.295 -1.091 13.690 0.08732 3.430 1.406 3.462 -0.268 -0.920 11.765 0.07233 3.360 1.364 3.750 -0.241 -0.810 11.290 0.05834 2.850 1.324 4.091 -0.213 -0.608 8.123 0.04635 2.575 1.286 4.500 -0.185 -0.476 6.631 0.03436 2.530 1.250 5.000 -0.156 -0.394 6.401 0.02437 1.900 1.216 5.625 -0.125 -0.237 3.610 0.01638 1.800 1.184 6.429 -0.093 -0.167 3.240 0.00939 1.654 1.154 7.500 -0.058 -0.096 2.736 0.00340 1.380 1.125 9.000 -0.020 -0.028 1.904 0.00041 1.290 1.098 11.250 0.022 0.028 1.664 0.00042 1.260 1.071 15.000 0.070 0.089 1.588 0.00543 1.130 1.047 22.500 0.131 0.148 1.277 0.01744 0.885 1.023 45.000 0.218 0.193 0.783 0.048

Σ 1038.723 -26.367 -1571.043 192847.461 26.774

Qp = 23.607 m³/sg.

Xm = -0.599

Q2 X2

ESTRUCTURAS HIDRAULICAS

Calculo de los parametros a y b

a = 75.410

b = Σ Xi*Qi - N*Xm*Qm b = -86.445 Σ Xi² - N*Xm²

Calculo del Caudal Maximo : T= 50 años T para 50 años = 1.0204

Qmax. = 253.211 m³/sg.

Calculo de las desviaciones estandar y la covarianza :

Sxx = N Σ Xi^2 - ( Σ Xi )^2 Sxx = 482.8214307

Sqq = N Σ Qi^2 - ( Σ Qi )^2 Sqq = 7406342.801

Sxq = N Σ Qi*Xi - ( Σ Qi )( Σ Xi ) Sxq = -41737.6297

X i = -2.056806117

ΔQ = 44.13134814

Calculo del Caudal Maximo de Diseño:

Qd = 297.343 m³/sg.

T (años) P (%) X

5 80.00 -1.01363 163.03380 185.046

10 90.00 -1.33954 191.20687 218.892

25 96.00 -1.75132 226.80362 263.550

50 98.00 -2.05681 253.21 297.34

100 99.00 -2.36004 279.42404 331.181

200 99.50 -2.66216 305.54110 365.075

1000 99.90 -3.36200 366.03903 443.979

a = Qm - b*Xm

Qmax. = a + b log log ( T / T - 1)

Qd = Qmax. + ΔQ

Qmax (m3/s) Qd(m3/s)

ESTRUCTURAS HIDRAULICAS

METODO LEBEDIEVRIO LA LECHE - Estacion de Aforos : Puchaca

AÑO Q max Q/Qm - 11962 41.800 -0.539 0.291 -0.1571963 27.200 -0.700 0.490 -0.3431964 38.480 -0.576 0.332 -0.1911965 55.880 -0.384 0.148 -0.0571966 34.530 -0.620 0.384 -0.2381967 34.750 -0.617 0.381 -0.2351968 27.770 -0.694 0.482 -0.3341969 51.500 -0.433 0.187 -0.0811970 51.130 -0.437 0.191 -0.0831971 133.800 0.474 0.225 0.1071972 179.250 0.975 0.951 0.9271973 105.250 0.160 0.026 0.0041974 58.220 -0.359 0.129 -0.0461975 210.130 1.315 1.730 2.2761976 47.002 -0.482 0.232 -0.1121977 72.299 -0.203 0.041 -0.0081978 68.725 -0.243 0.059 -0.0141979 23.982 -0.736 0.541 -0.3981980 34.346 -0.622 0.386 -0.2401981 47.313 -0.479 0.229 -0.1101982 24.824 -0.726 0.528 -0.3831983 215.813 1.378 1.899 2.6161984 114.538 0.262 0.069 0.0181985 40.875 -0.550 0.302 -0.1661986 88.906 -0.020 0.000 0.0001987 49.077 -0.459 0.211 -0.0971988 27.075 -0.702 0.492 -0.3451989 59.031 -0.350 0.122 -0.0431990 30.911 -0.659 0.435 -0.2871991 40.494 -0.554 0.307 -0.1701992 58.130 -0.359 0.129 -0.0461993 53.310 -0.413 0.170 -0.0701994 17.260 -0.810 0.656 -0.5311995 23.450 -0.742 0.550 -0.4081996 21.000 -0.769 0.591 -0.4541997 21.000 -0.769 0.591 -0.4541998 579.750 5.388 29.030 156.4111999 62.380 -0.313 0.098 -0.0312000 155.000 0.708 0.501 0.3552001 500.000 4.509 20.333 91.6862002 301.875 2.326 5.411 12.5872003 105.250 0.160 0.026 0.0042004 20.000 -0.780 0.608 -0.4742005 40.000 -0.559 0.313 -0.175

Σ 3993.306 70.805 260.208

N = 44

Qm = Σ Qi / NQm = 90.757

(Q/Qm - 1)2 (Q/Qm - 1)3

m3/s.

ESTRUCTURAS HIDRAULICAS

Coeficiente de Variación Cv:

Cv= √((Σ(Qi/Qm - 1)^2 / N))Cv= 1.269

Coeficiente de Asimetría Cs:Considerando que la avenida es producida por una tormenta:

Cs= (Σ (Qi/Qm - 1)^3) / (N*Cv^3) Cs= 3*CvCs= 2.89704 Cs= 3.8056

Escogemos el mayor: = Cs= 3.806

Para el período de retorno de 50 años, el valor P es:

T= 50 años P= 0.02P= 2 %

Con P (%) y Cs, se obtiene el valor K de la Tabla 6.17 (Hidrología, Máximo Villón Béjar)

K= 3.181124636855

Con P (%) y Cv, se obtiene el valor de Er de la figura 6.3

Er = 1.75

Cálculo del caudal máximo Qmax :

Qmax = Qm (K*Cv + 1)

Qmax = 456.996 m3/s

ESTRUCTURAS HIDRAULICAS

Cáculo del intervalo de confianza: Para N = 44 años (N>40 años) se toma A= 0.7

A= 0.7

ΔQ = + (A*Er*Qmax)/√N

ΔQ = 84.3961311

Cálculo del caudal de diseño Qd :

Qd = Qmax + ΔQQd = 541.3925 m3/s

T (años) P (%) K Er5 20.00 0.24 1.36 118.388 135.379

10 10.00 1.00 1.38 205.886 235.86925 4.00 2.43 1.53 369.945 429.48050 2.00 3.18 1.75 456.996 541.393

100 1.00 4.29 1.78 584.660 694.483200 0.50 5.40 1.87 712.453 853.048

1000 0.10 7.97 2.01 1008.334 1222.216

METODO LEBEDIEV

m3/s

Qmax (m3/s) Qd (m3/s)

K; Er:Obtenidos de tabla, para T (años).

ESTRUCTURAS HIDRAULICAS

RIO LA LECHE - Estacion de Aforos : PuchacaAÑO Q max Q/Qm - 11962 7.000 -0.923 0.852 -0.7861963 1.260 -0.986 0.972 -0.9591964 2.530 -0.972 0.945 -0.9191965 6.000 -0.934 0.872 -0.8141966 19.200 -0.788 0.622 -0.4901967 9.039 -0.900 0.811 -0.7301968 7.338 -0.919 0.845 -0.7771969 10.000 -0.890 0.792 -0.7051970 1.900 -0.979 0.959 -0.9391971 9.440 -0.896 0.803 -0.7191972 255.000 1.810 3.275 5.9271973 19.200 -0.788 0.622 -0.4901974 3.430 -0.962 0.926 -0.8911975 23.180 -0.745 0.554 -0.4131976 10.590 -0.883 0.780 -0.6891977 6.510 -0.928 0.862 -0.8001978 10.000 -0.890 0.792 -0.7051979 11.920 -0.869 0.755 -0.6551980 3.700 -0.959 0.920 -0.8831981 36.000 -0.603 0.364 -0.2201982 3.360 -0.963 0.927 -0.8931983 300.000 2.306 5.315 12.2551984 12.500 -0.862 0.744 -0.6411985 5.240 -0.942 0.888 -0.8371986 4.420 -0.951 0.905 -0.8611987 7.200 -0.921 0.848 -0.7801988 4.200 -0.954 0.910 -0.8671989 5.500 -0.939 0.882 -0.8291990 2.850 -0.969 0.938 -0.9091991 1.130 -0.988 0.975 -0.9631992 10.000 -0.890 0.792 -0.7051993 9.000 -0.901 0.812 -0.7311994 6.200 -0.932 0.868 -0.8091995 1.800 -0.980 0.961 -0.9421996 1.380 -0.985 0.970 -0.9551997 1.290 -0.986 0.972 -0.9581998 183.690 1.024 1.049 1.0741999 5.200 -0.943 0.889 -0.8382000 5.442 -0.940 0.884 -0.8312001 4.757 -0.948 0.898 -0.8512002 5.213 -0.943 0.888 -0.8372003 1.654 -0.982 0.964 -0.9462004 0.885 -0.990 0.981 -0.971

2005 2.575 -0.972 0.944 -0.917

Σ 1038.723 44.523 -13.197

N = 44

Qm = Σ Qi / N

Qm = 23.607

(Q/Qm - 1)2 (Q/Qm - 1)3

m3/s.

ESTRUCTURAS HIDRAULICAS

Coeficiente de Variación Cv:

Cv= √((Σ(Qi/Qm - 1)^2 / N))Cv= 1.006

Coeficiente de Asimetría Cs:Considerando que la avenida es producida por una tormenta:

Cs= (Σ (Qi/Qm - 1)^3) / (N*Cv^3) Cs= 3*CvCs= -0.29467 Cs= 3.0178

Escogemos el mayor: = Cs= 3.018

Para el período de retorno de 50 años, el valor P es:

T= 50 años P= 0.02P= 2 %

Con P (%) y Cs, se obtiene el valor K de la Tabla 6.17 (Hidrología, Máximo Villón Béjar)

K= 3.14

Con P (%) y Cv, se obtiene el valor de Er de la figura 6.3

Er = 1.38

Cálculo del caudal máximo Qmax :

Qmax = Qm (K*Cv + 1)

Qmax = 98.173 m3/s

ESTRUCTURAS HIDRAULICAS

Cáculo del intervalo de confianza: Para N = 44 años (N>40 años) se toma A= 0.7

A= 0.7

ΔQ = + (A*Er*Qmax)/√N

ΔQ = 14.2969798

Cálculo del caudal de diseño Qd :

Qd = Qmax + ΔQQd = 112.4703 m3/s

T (años) P (%) K Er5 20.00 0.39 1.09 32.87 36.632

10 10.00 1.00 1.13 47.35 52.97625 4.00 2.31 1.27 78.46 88.97950 2.00 3.14 1.38 98.173 112.470

100 1.00 4.05 1.41 119.78 137.606200 0.50 4.96 1.49 141.39 163.625

1000 0.10 7.11 1.57 192.45 224.335

m3/s

Qmax (m3/s) Qd (m3/s)

K; Er:Obtenidos de tabla, para T (años).

ESTRUCTURAS HIDRAULICAS

ESTRUCTURAS HIDRAULICAS

Tabla 6.17 Valores de K

C s Probabilidad P en (%)0.01 0.1 0.5 1 2 3 5 10 20

3.05 7.16 4.98 4.07 3.14 2.66 1.97 1.12 0.38

3.10 7.23 5.01 4.09 3.14 2.66 1.97 1.11 0.37

3.15 7.29 5.04 4.10 3.14 2.66 1.96 1.10 0.36

3.20 7.35 5.08 4.11 3.14 2.66 1.96 1.09 0.35

3.25 7.39 5.11 4.13 3.14 2.66 1.95 1.06 0.34

3.30 7.44 5.14 4.15 3.14 2.66 1.95 1.08 0.33

3.35 7.49 5.16 4.16 3.14 2.66 1.94 1.07 0.32

3.40 7.54 5.19 4.18 3.15 2.66 1.94 1.06 0.31

3.45 7.59 5.22 4.19 3.15 2.66 1.93 1.05 0.30

3.50 7.64 5.25 4.21 3.16 2.66 1.93 1.04 0.29

3.55 7.68 5.27 4.22 3.16 2.66 1.93 1.03 0.28

3.60 7.72 5.30 4.24 3.17 2.66 1.93 1.03 0.28

3.65 7.79 5.32 4.25 3.17 2.66 1.92 1.02 0.27

3.70 7.86 5.35 4.26 3.18 2.66 1.91 1.01 0.26

3.75 7.91 5.37 4.27 3.18 2.66 1.90 1.00 0.25

3.80 7.97 5.40 4.29 3.18 2.65 1.90 1.00 0.24

3.85 8.02 5.42 4.31 3.19 2.65 1.90 0.99 0.23

3.90 8.08 5.45 4.32 3.20 2.65 1.90 0.98 0.23

3.95 8.12 5.47 4.33 3.20 2.65 1.90 0.97 0.22

4.00 8.17 5.50 4.34 3.20 2.65 1.90 0.96 0.21

4.05 8.23 5.52 4.35 3.21 2.65 1.89 0.95 0.20

4.10 8.29 5.55 4.36 3.21 2.65 1.89 0.95 0.20

4.15 8.33 5.57 4.37 3.22 2.65 1.88 0.94 0.19

4.20 8.38 5.60 4.39 3.23 2.65 1.88 0.93 0.19

4.25 8.43 5.62 4.39 3.24 2.64 1.87 0.92 0.184.30 8.49 5.65 4.40 3.24 2.64 1.87 0.92 0.17

4.35 8.54 5.67 4.41 3.24 2.64 1.86 0.91 0.16

4.40 8.60 5.69 4.42 3.25 2.63 1.86 0.91 0.15

4.45 8.64 5.71 4.43 3.25 2.63 1.85 0.90 0.14

4.50 8.69 5.74 4.44 3.26 2.62 1.85 0.89 0.14

ESTRUCTURAS HIDRAULICAS

3.05

3.10

3.15

3.20

3.25

3.30

3.35

3.40

3.45

3.50

3.55

3.60

3.65

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

4.30

4.35

4.40

4.45

4.50

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Column J

Column K

Column L

Column M

Column N

Column O

10

20

ESTRUCTURAS HIDRAULICAS

3.05

3.10

3.15

3.20

3.25

3.30

3.35

3.40

3.45

3.50

3.55

3.60

3.65

3.70

3.75

3.80

3.85

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

4.30

4.35

4.40

4.45

4.50

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Column J

Column K

Column L

Column M

Column N

Column O

10

20

METODO DE LOGARITMO PEARSON IIIRIO LA LECHE - Estacion de Aforos : Puchaca

UTILIZANDO LOS CAUDALES MAXIMOS

AñoCaudales (m3/s)

Max. Descendentes log Q (logQ-logQp)^2

1962 41.800 579.750 2.763 7.635 21.10 0.994

1963 27.200 500.000 2.699 7.284 19.66 0.870

1964 38.480 301.875 2.480 6.150 15.25 0.5091965 55.880 215.813 2.334 5.448 12.72 0.3221966 34.530 210.130 2.322 5.394 12.53 0.3091967 34.750 179.250 2.253 5.078 11.44 0.2371968 27.770 155.000 2.190 4.798 10.51 0.1801969 51.500 133.800 2.126 4.522 9.62 0.1301970 51.130 114.538 2.059 4.239 8.73 0.0861971 133.800 105.250 2.022 4.089 8.27 0.0661972 179.250 105.250 2.022 4.089 8.27 0.0661973 105.250 88.906 1.949 3.798 7.40 0.0331974 58.220 72.299 1.859 3.456 6.43 0.0091975 210.130 68.725 1.837 3.375 6.20 0.0051976 47.002 62.380 1.795 3.222 5.78 0.0011977 72.299 59.031 1.771 3.137 5.56 0.0001978 68.725 58.220 1.765 3.115 5.50 0.0001979 23.982 58.130 1.764 3.113 5.49 0.0001980 34.346 55.880 1.747 3.053 5.33 0.0001981 47.313 53.310 1.727 2.982 5.15 0.0021982 24.824 51.500 1.712 2.930 5.02 0.0031983 215.813 51.130 1.709 2.920 4.99 0.0031984 114.538 49.077 1.691 2.859 4.83 0.0061985 40.875 47.313 1.675 2.806 4.70 0.0081986 88.906 47.002 1.672 2.796 4.68 0.0091987 49.077 41.800 1.621 2.628 4.26 0.0211988 27.075 40.875 1.611 2.597 4.18 0.0241989 59.031 40.494 1.607 2.584 4.15 0.0251990 30.911 40.000 1.602 2.567 4.11 0.0271991 40.494 38.480 1.585 2.513 3.98 0.0331992 58.130 34.750 1.541 2.375 3.66 0.0511993 53.310 34.530 1.538 2.366 3.64 0.0521994 17.260 34.346 1.536 2.359 3.62 0.0531995 23.450 30.911 1.490 2.220 3.31 0.0761996 21.000 27.770 1.444 2.084 3.01 0.1041997 21.000 27.200 1.435 2.058 2.95 0.1101998 579.750 27.075 1.433 2.052 2.94 0.1111999 62.380 24.824 1.395 1.946 2.71 0.1382000 155.000 23.982 1.380 1.904 2.63 0.1492001 500.000 23.450 1.370 1.877 2.57 0.1572002 301.875 21.000 1.322 1.748 2.31 0.1972003 105.250 21.000 1.322 1.748 2.31 0.1972004 20.000 20.000 1.301 1.693 2.20 0.2162005 40.000 17.260 1.237 1.530 1.89 0.280Σ = 3993.31 77.72 143.14 275.60 5.870

log Q 2 log Q 3

PROMEDIO

X = 1.766

DESVIACION ESTANDAR

S = 0.3695

3. Calculo del Coeficiente de Sesgo (Csy):

n = 44

Csy = 0.99

4. Calculo de la Variable intermedia W:

T = 50 años

P = 0.02 0 < P < 0.5 OK

W = 2.7971

5. Calculo de la Variable Estandarizada Z:

Z = 2.0537

6. Calculo del Factor de Frecuencia K:

C = 0.164442817

K = 2.537064101

7. Calculo del caudal maximo (Qmax):

Log (Qmax) = 2.7037

Qmax = 505.431 m³/s

T (años) P (%) K Log Q

5 80.00 0.75490 2.045 110.966

10 90.00 1.33471 2.259 181.727

25 96.00 2.03599 2.519 330.009

50 98.00 2.53706 2.70366 505.431

100 99.00 3.02146 2.883 763.194

200 99.50 3.49372 3.057 1140.573

1000 99.90 4.55846 3.451 2821.765

Q (m3/s)

W=ln ( 1P2 )

METODO DE LOGARITMO PEARSON IIIRIO MOTUPE - Estacion de Aforos : Chiniama

UTILIZANDO LOS CAUDALES MAXIMOS

AñoCaudales (m3/s)

Max. Descendentes log Q (logQ-logQp)^2

1962 7.000 300.000 2.477 6.136 15.20 0.505

1963 1.260 255.000 2.407 5.791 13.94 0.410

1964 2.530 183.690 2.264 5.126 11.61 0.248

1965 6.000 36.000 1.556 2.422 3.77 0.044

1966 19.200 23.180 1.365 1.864 2.54 0.161

1967 9.039 19.200 1.283 1.647 2.11 0.233

1968 7.338 19.200 1.283 1.647 2.11 0.233

1969 10.000 12.500 1.097 1.203 1.32 0.448

1970 1.900 11.920 1.076 1.158 1.25 0.476

1971 9.440 10.590 1.025 1.050 1.08 0.550

1972 255.000 10.000 1.000 1.000 1.00 0.587

1973 19.200 10.000 1.000 1.000 1.00 0.587

1974 3.430 10.000 1.000 1.000 1.00 0.587

1975 23.180 9.440 0.975 0.951 0.93 0.626

1976 10.590 9.039 0.956 0.914 0.87 0.656

1977 6.510 9.000 0.954 0.911 0.87 0.659

1978 10.000 7.338 0.866 0.749 0.65 0.811

1979 11.920 7.200 0.857 0.735 0.63 0.826

1980 3.700 7.000 0.845 0.714 0.60 0.849

1981 36.000 6.510 0.814 0.662 0.54 0.908

1982 3.360 6.200 0.792 0.628 0.50 0.948

1983 300.000 6.000 0.778 0.606 0.47 0.976

1984 12.500 5.500 0.740 0.548 0.41 1.052

1985 5.240 5.442 0.736 0.541 0.40 1.062

1986 4.420 5.240 0.719 0.517 0.37 1.096

1987 7.200 5.213 0.717 0.514 0.37 1.101

1988 4.200 5.200 0.716 0.513 0.37 1.103

1989 5.500 4.757 0.677 0.459 0.31 1.186

1990 2.850 4.420 0.645 0.417 0.27 1.256

1991 1.130 4.200 0.623 0.388 0.24 1.307

1992 10.000 3.700 0.568 0.323 0.18 1.435

1993 9.000 3.430 0.535 0.287 0.15 1.515

1994 6.200 3.360 0.526 0.277 0.15 1.537

1995 1.800 2.850 0.455 0.207 0.09 1.720

1996 1.380 2.575 0.411 0.169 0.07 1.837

1997 1.290 2.530 0.403 0.163 0.07 1.858

1998 183.690 1.900 0.279 0.078 0.02 2.213

1999 5.200 1.800 0.255 0.065 0.02 2.283

2000 5.442 1.654 0.219 0.048 0.01 2.395

log Q 2 log Q 3

2001 4.757 1.380 0.140 0.020 0.00 2.645

2002 5.213 1.290 0.111 0.012 0.00 2.741

2003 1.654 1.260 0.100 0.010 0.00 2.775

2004 0.885 1.130 0.053 0.003 0.00 2.935

2005 2.575 0.885 -0.053 0.003 0.00 3.310

Σ = 1038.72 36.25 43.47 67.48 52.695

PROMEDIO

X = 0.824

DESVIACION ESTANDAR

S = 0.562650968

3. Calculo del Coeficiente de Sesgo (Csy):

n = 44

Csy = 1.26

4. Calculo de la Variable intermedia W:

T = 50 años

P = 0.02 0 < P < 0.5 Ok

W = 2.7971

5. Calculo de la Variable Estandarizada Z:

Z = 2.0537

6. Calculo del Factor de Frecuencia K:

C = 0.210669696

K = 2.65132873

7. Calculo del caudal maximo (Qmax):

Log (Qmax) = 2.3156

Qmax = 206.818 m³/s

T (años) P (%) K Log Q

5 80.00 0.71803 1.228 16.897

10 90.00 1.33045 1.572 37.359

25 96.00 2.09369 2.002 100.423

50 98.00 2.65133 2.31559 206.818

100 99.00 3.19864 2.624 420.274

200 99.50 3.73908 2.928 846.470

1000 99.90 4.97876 3.625 4218.111

Q (m3/s)

Determinación Caudal de DiseñoRIO LA LECHE - Estacion de Aforos : Puchaca

n = 44 años

m T (años) Q (m3/s) Lebediev

1 45.000 579.750 T (años) Qd (m3/s)

2 22.500 500.000 5 135.379

3 15.000 301.875 10 235.869

4 11.250 215.813 25 429.480

5 9.000 210.131 50 541.393

6 7.500 155.000 100 694.483

7 6.429 141.312 200 853.048

8 5.625 121.250 1000 1222.216

9 5.000 114.538

10 4.500 105.250 Nash

11 4.091 105.200 T (años) Qd(m3/s)

12 3.750 72.299 5 448.685

13 3.462 68.725 10 519.313

14 3.214 62.375 25 611.341

15 3.000 59.031 50 680.799

16 2.813 58.216 100 750.341

17 2.647 58.131 200 820.019

18 2.500 55.875 1000 982.316

19 2.368 55.125

20 2.250 53.306 Log-Pearson III

21 2.143 51.781 T (años) Q (m3/s)

22 2.045 49.077 5 110.966

23 1.957 48.401 10 181.727

24 1.875 48.212 25 330.009

25 1.800 47.313 50 505.431

26 1.731 47.002 100 763.194

27 1.667 41.801 200 1140.573

28 1.607 40.875 1000 2821.765

29 1.552 40.494

30 1.500 40.000

31 1.452 38.475

32 1.406 37.221

33 1.364 34.750

34 1.324 34.525

35 1.286 34.346

36 1.250 31.997

37 1.216 30.911

38 1.184 27.202

39 1.154 27.075

40 1.125 26.880

41 1.098 26.588

42 1.071 24.824

43 1.047 23.450

44 1.023 21.000

1 10 100 10000

500

1000

1500

2000

2500

3000

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

T=(n+1m )

LebedievT (años) Qd (m3/s) T = 50 años

5 135.379

10 235.869 Qd' = 541.393 m3/s25 429.480

50 541.393

100 694.483

200 853.048

1000 1222.216

A este caudal se le considerará aportes y pérdidas:

Pérdidas:Pérdida por infiltración -15%Aportes:Quebradas 15%Aguas Subterráneas 10%Área de influencia (precip.) 40%

Q diseño = 812.089 m3/s

En el gráfico T vs. Q, se observa que la distribución que más se acerca a la distribución registrada, es la distribución por el Metodo de Lebediev, por lo cual asumiremos esta distribución para calcular el Qd:

Determinación Caudal de DiseñoRIO LA LECHE - Estacion de Aforos : Puchaca

n = 44 años

m T (años) Q (m3/s) Lebediev

1 45.000 579.750 T (años) Qd (m3/s)

2 22.500 500.000 5 36.632

3 15.000 301.875 10 52.976

4 11.250 215.813 25 88.979

5 9.000 210.131 50 112.470

6 7.500 155.000 100 137.606

7 6.429 141.312 200 163.625

8 5.625 121.250 1000 224.335

9 5.000 114.538

10 4.500 105.250 Nash

11 4.091 105.200 T (años) Qd(m3/s)

12 3.750 72.299 5 185.046

13 3.462 68.725 10 218.892

14 3.214 62.375 25 263.550

15 3.000 59.031 50 297.343

16 2.813 58.216 100 331.181

17 2.647 58.131 200 365.075

18 2.500 55.875 1000 443.979

19 2.368 55.125

20 2.250 53.306 Log-Pearson III

21 2.143 51.781 T (años) Q (m3/s)

22 2.045 49.077 5 16.897

23 1.957 48.401 10 37.359

24 1.875 48.212 25 100.423

25 1.800 47.313 50 206.818

26 1.731 47.002 100 420.274

27 1.667 41.801 200 846.470

28 1.607 40.875 1000 4218.111

29 1.552 40.494

30 1.500 40.000

31 1.452 38.475

32 1.406 37.221

33 1.364 34.750

34 1.324 34.525

35 1.286 34.346

36 1.250 31.997

37 1.216 30.911

38 1.184 27.202

39 1.154 27.075

40 1.125 26.880

41 1.098 26.588

42 1.071 24.824

43 1.047 23.450

44 1.023 21.000

1 10 100 10000

500

1000

1500

2000

2500

3000

3500

4000

4500

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

T=(n+1m )

Nash

T (años) Qd (m3/s) T = 50 años5 185.046

10 218.892 Qd = 297.343 m3/s25 263.550

50 297.343

100 331.181

200 365.075

1000 443.979

A este caudal se le considerará aportes y pérdidas:

Pérdidas:Pérdida por infiltración -15%Aportes:Quebradas 15%Aguas Subterráneas 10%Área de influencia (precip.) 40%

Q diseño = 446.014

Q diseño = 812.089 + 446.014

Q diseño = 1258.103

m3/s

m3/seg

En el gráfico T vs. Q, se observa que la distribución que más se acerca a la distribución registrada, es la distribución por el Metodo de Nash, por lo cual asumiremos esta distribución para calcular el Qd:

Debido a la confluencia de los rios La Leche y Motupe, el Caudal Maximo se obtiene de la suma de los caudales de los rios mencionados.

1 10 100 10000

500

1000

1500

2000

2500

3000

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

1 10 100 10000

500

1000

1500

2000

2500

3000

3500

4000

4500

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

1 10 100 10000

500

1000

1500

2000

2500

3000

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

1 10 100 10000

500

1000

1500

2000

2500

3000

3500

4000

4500

T VS Q

Registro

Lebediev

Nash

Log-Pearson III

Tiempo de Retorno (años)

Cau

dal

(m

3/s)

1.-Valores basicos de n recomendados (n1)Cauces en grava fina 0.014 escogidoCauces en grava gruesa 0.028Cauces en roca 0.015Cauces en tierra 0.010

2.- Aumento del coeficiente n que se recomienda para tomar en cuenta el grado de irregularidad (n2)Cauces parejos 0.000Moderados 0.010Muy irregulares 0.020Poco irregulares 0.005 escogido

3.- Aumento del coeficiente n que se recomienda para tomar en cuenta el cambio de diemnsiones y de forma de seccion transversal (n3)Graduales 0.000Ocasionales 0.005 escogidoFrecuentes 0.010 0.015

4.- Aumento del coeficiente n que se recomienda para tomar en cuenta obstrucciones formadas por arrastres, raices, etc. (n4)efecto inapreciable 0.000poco efecto 0.010 escogidoefecto apreciable 0.030mucho efecto 0.060

5.- Aumento del coeficiente n que se recomienda para toamr en cuenta la vegetación. (n5)poco efecto 0.005 0.010efecto medio 0.010 0.025mucho efecto 0.025 0.050muchisimo efecto 0.050 0.100

6.- Aumento del coeficiente n que se recomienda para tomar según la tortuosidad del cauce (n6)Ls= Longitud del tramo recto 1Lm= Longitud del tramo con meandros 1

Lm/Ls= 1

Lm/Ls1 1.0-1.2 0.00*n6 0.000001.2 1.2-1.5 0.15*n6 0.006301.5 >1.5 0.30*n6 0.01260

n6= Suma de conceptos 1+2+3+4+5 = 0.042

VALORES PROMEDIO PARA CALCULO DE "n"(referencia Rocha)

(poco efecto, efecto medio, mucho efecto, muchisimo efecto)

2.- Aumento del coeficiente n que se recomienda para tomar en cuenta el grado de irregularidad (n2)

3.- Aumento del coeficiente n que se recomienda para tomar en cuenta el cambio de diemnsiones y de forma de seccion transversal (n3)

4.- Aumento del coeficiente n que se recomienda para tomar en cuenta obstrucciones formadas por arrastres, raices, etc. (n4)

(poco efecto, efecto medio, mucho efecto, muchisimo efecto) escogido