capitulo 8 ingenieria de rios
DESCRIPTION
inge de riosTRANSCRIPT
INGENIERIA DE RIOS
INGENIERA DE ROS
Ro Magdalena, Rodrigo de Bastidas, 1501http://www.mintransporte.gov.co/portal_servicios/proyecto_yuma/resena.htmParticularidades
Hidrulica compleja
Flujo no permanente
Fronteras y geometra variables
Rugosidad estacional y variable
Interdependencia entre transporte de sedimentos y de agua
Interaccin dinmica entre la forma del lecho y el modo y magnitud del transporte de sedimentos
Problemas de naturaleza estocstica
Difcil verificacin modelo/prototipo
Tema en pleno desarrollo terico y experimental en laboratorio y en campo
Principios bsicos del flujo en canales abiertos
Laminar o turbulento segn el nmero de Reynolds
en ros y canales el flujo es turbulento
Permanente , as Q=f(distancia) o constante
como en los ros canalizados y canales.
uniforme (con , , constantes)
no uniforme con variacinrpida ( = constante, y varan con la posicin )gradual ( = constante, y varan con la posicin )
espacial
No permanente si Q=f(t)
Supercrtico o Subcrtico segn el nmero de Froude
= ancho de la superficie libre
= coeficiente de Coriolis (obtenido de la distribucin de velocidades en la seccin)
Alineamiento
En general, los canales son canales abiertos prismticos En general, los ros son canales abiertos no prismticos.
Los contornos de los canales abiertos formados por el fondo y los lados pueden ser:
fijos, por ejemplo el canal revestido en concreto
variables, como en ros o canales no revestidos sobre material aluvial.
ECUACIONES BSICAS
Para un flujo uniforme son iguales:
la pendiente de la solera,
el gradiente de energa,
la pendiente de friccin,
Balance entre la gravedad y la resistencia a la friccin:
: el esfuerzo cortante medio sobre el permetro del canal
: radio hidrulico
: velocidad de corte
Para flujo turbulento completamente desarrollado se obtiene la ecuacin de Chzy para flujo uniforme:
= Coeficiente de friccin en la ecuacin de Darcy Weisbach:
puede expresarse a partir de la teora de la capa lmite:
: tamao de las rugosidades
espesor de la subcapa laminar
Manning: es decir ,
: tamao en metros de la rugosidades (sedimentos)
Ecuacin dinmica para flujo variado en canal prismtico:
Ecuacin de Saint Venant para flujo no permanente:
TRANSPORTE DE SEDIMENTOS
Los sedimentos segn la fuente en ros y canales:
Carga de lavado: material muy fino que se mueve en suspensin
(!) Carga de material del lecho, determina la erosin morfolgica y la sedimentacin; se mueve como carga:
de fondo, los ms gruesos
suspendida, los menos gruesos
Propiedades de los sedimentos y el transporte:
El tamao de sedimentos () : arcillas, limos, arenas, gravas
La forma (d1, d2, d3)
La densidad (2650 kg/m3)
La velocidad de asentamientos ()
Densidad de cuerpo y porosidad
Concentracin de sedimentos () (volumtrica, en ppm, o mg/L)
Velocidad de asentamiento
: coeficiente de arrastre que depende del nmero de Reynolds.
< 1 (sedimentos muy finos) = 24/; ley de Stokes
> 1000 (para grandes tamaos)
La velocidad de asentamiento vara desde a
El movimiento incipiente esta dado por un valor crtico de esfuerzo cortante, criterio de Shields, para > 103
: vara entre 0.04 y 0.06
como :
MTODO DEL ESFUERZO MXIMO PERMISIBLE, ESFUERZO CORTANTE (0)
Esfuerzo que desarrolla el flujo sobre el lecho del canal. En el flujo uniforme dicho esfuerzo se equilibra con la fuerza motriz.
(
Recordar que:
si b > 10y es decir si se tiene un canal ancho
Figura 7-7 VTCH: esfuerzos tractivos mximos en trminos de ySo
Figura 7-10: esfuerzos tractivos permisibles recomendados en materiales no cohesivos; granular: 0 vs D25 Figura 7-11: esfuerzos tractivos permisibles recomendados en materiales cohesivos; cohesivo: 0 vs relacin de vacos
Reduccin de o por sinuosidad:
10%: ligeramente sinuoso
25%: moderadamente sinuoso
40%: muy sinuoso
Procedimiento:
1. Seleccionar seccin mediante experiencia
2. Recolectar suelo y determinar propiedades:
D25 Aristas
Cohesin
3. Determinar la mnima seccin estable con 0:
a. Seleccionar z y b/y y con la figura 7-7 obtener s Lb. Con arista (angular o redondeada) y figura 7-9, encontrar (naturalmente < ); con z encontrar y k. El valor medio de es cerca de 35.c. Disear para s y verificar paraLLA SECCIN HIDRULICAMENTE ESTABLE - SHEEs aquella donde el esfuerzo cortante es constante e igual al mximo permisible
Caractersticas:
Menor rea
Ancho mnimo
Velocidad mxima
Excavacin mnima
En el fondo:
con
( y en movimiento inminente
;en el centro del canal:
x = 0; y = y0 (
Casos que ocurren:
1. La capacidad del canal terico es insuficiente y debe ampliarse
2. La capacidad hidrulica del canal es superior a lo requerido y debe recortarse
y0Profundidad en el talweg de la SHE(Peso especfico del agua
(0Esfuerzo tractivo permisiblen Coeficiente de rugosidad de Manning
VVelocidad media en la seccinT'; T"Correcciones en el ancho del canal
Area mojadaQCaudal que transporta la SHE
(ngulo de reposo del materialQ'Caudal de diseo (Si Q'Q)
TAncho de la SHE Referencia: VTCH 7-15
RELACIN ENTRE FLUJO Y SEDIMENTO
La mayora de los enfoques utilizados pueden ser reducidos a una correlacin entre el parmetro de transporte de sedimentos y el nmero de Froude de la partcula de sedimento:
: transporte de sedimentos (m3/sm)
: parmetro de flujo, que puede incluir el factor de rizos y dunas para incorporar el efecto de la forma del lecho
Ejemplos de correlaciones y tendencias simplificadas entre y
Meyer - Peter y Muller:
Einstein Brown:
Engelund Hansen:
MORFOLOGA DE ROS
La morfologa de ros se relaciona con
la configuracin y geometra del canal
el perfil longitudinal del ro
la edad y el tiempo
el caudal
la entrada de sedimentos
las caractersticas de los sedimentos
el material de la banca
las obras de ingeniera
En curvas libres y limitadas, la profundidad se incrementa de forma gradual hasta un mximo aguas abajo del vrtice de la curva; las curvas se caracterizan por tener flujo en espiral y secciones triangulares, con la mxima profundidad y velocidad en la banca cncava, y mximo transporte de sedimentos en la banca convexa y el talweg (lnea de mxima profundidad) desvindose de la lnea central del ro.
Los cruces son tramos relativamente rectos entre curvas alternas y son casi de seccin rectangular.
Los ros con meandros por lo general tienen una relacin de longitud del canal a longitud del canal a longitud del valle mayor que 1.5 y la longitud del meandro (la distancia entre vrtices de curvas alternas) cerca de 10 veces el ancho del cauce. La relacin de la longitud del meandro al ancho vara entre 2 y 4.
Rango de velocidades en ros:
vmedia vara entre
0,5 m/s para flujos de baja profundidad
4,0 m/s en inundaciones
vmxima = (1,25 a 1,30) vmediaRGIMEN DE ROS
Un ro aluvial se considera que est en rgimen si su canal es geomtricamente estable en un promedio largo de tiempo.
Concepto diferente al de estabilidad de la seccin (SHE)
La seccin transversal y la pendiente longitudinal de un canal en rgimen son funciones de la descarga Q formadora del lecho:
ancho,
profundidad,
pendiente,
Tramo aguas abajoSeccin
Suelo gruesoCauce altoSuelo finoCauce bajo
Teora de Esfuerzo cortanteTeora del Rgimende Lacey
B
Y
S
RS
V
con ,d en m, V en m/s
y varan con el dimetro de los sedimentos(*)
(*) Lacey y Pemberton (d>2mm) 0,250,1 mm)
ESTUDIOS DE CAMPO - Cartografa
Se necesitan mapas confiables para: investigacin, diseo, ejecucin, operacin, administracin y mantenimiento de obras de ingeniera
Herramientas disponibles hoy: Aerofotografa
Fotointerpretacin
Interpretacin de imgenes de satlite
SIG
Posicionamiento total
Topografa: fechas, referencias, BM, AX
Batimetra
Ecosondas
Radar
Sensores remotos
NIVELES DE AGUA
Los niveles de agua se obtienen de medidores instalados en estaciones de medicin.
tipo registrador de flotador: limngrafo
tipo no registrador: limnmetro
miras en vados
miras en pilas de puentes
rayos pticos
Registrar fecha, hora, nivel, condicin de flujo
Escala y limngrafo registrador en el Ao Grande, Ushuaia, ArgentinaCOTAS DE FONDO
Barra de sondeo con una placa de base fija en el extremo inferior
Tcnicas de sonido, complementadas con telemetra y SIG
Actividad peridica
Pantalla de control de la sonda multihaz "SeaBeam"
MEDICIN DE CAUDALES
Mtodos rea-velocidadQ= A1V1 + A2V2 + A3V3 + . . .Ejecucin de aforo por vadeo en el ro Lasifashaj, Argentina
1- Flotadores
Tcnica utilizada con frecuencia en la etapa de reconocimiento.
Los flotadores de superficie son muy tiles para identificar patrones de flujo en estuarios, costas, golfos, confluencias, ramificaciones.
2- Correntmetros o molinentes
MEDICIN DE CAUDALES
Mtodos de dilucin
Alternativa en corrientes con gradientes empinados y en torrentes poco profundos donde no pueden utilizarse las tcnicas convencionales de medida de la corriente.
Una solucin de un trazador de una intensidad conocida (por ejemplo, NaCl, tintura rodamina etc) se inyecta al flujo a una tasa constante (o mediante inyeccin repentina) en una seccin transversal, tomndose muestras en el extremo aguas abajo a intervalos de tiempo regulares. Tan pronto como la intensidad de las muestras alcanza un valor constante (nivel meseta) el caudal es:
Q : tasa de flujo
: tasa de inyeccin del trazador
: concentracin de la solucin inyectada
: concentracin en la meseta de la muestra
: concentracin antecedente ya presente en la corriente.
Si la inyeccin es abrupta o repentina:
Q : tasa de flujo
: volumen de la solucin inyectada
: concentracin del trazador en los puntos de muestreo durante cada
http://www.borstad.com/spanish/papers/s-dye.htmlMEDICIN DE CAUDALES
Estructuras de aforo
estructuras convencionales de aforo
se construyen a travs o dentro de la corriente
control artificial
el flujo se pasa por la estructura, creando condiciones de flujo crtico
vertedero de cresta ancha
vertedero de cresta delgada
vertedero crump
canaleta Venturi: Palmer, Bowlus, Parshall
se establece la relacin
y dependen del tipo de estructura, que a su vez, depende del tamao de la corriente y de los rangos de los caudales que van a ser aforados y de la carga de sedimentos transportados
Las estructuras de medida pueden ser divididas en dos categoras:
(a) Vertederos de cresta delgada (placa delgada), vertederos de abertura o corte, desages, vertederos de cresta ancha o vertederos Crump
http://www.usbr.gov/wrrl/fmt/wmm/figures.html
(b) Canaletas Venturi, Parshall o de pendiente empinada
MEDICIN DE CAUDALES
Tcnicas no obstructivas de aforo
1. Medidor electromagntico de flujo bobina enterrada a travs y debajo del lecho del ro se magnetiza mediante una fuente externa
el movimiento del agua a travs de la bobina induce una fuerza electromotriz (fem)
la fem es proporcional a la velocidad promedio de la seccin transversal.
complejo sistema de sonda para percibir la fem inducida
requiere personal especializado
montaje y operacin costosa.
2. Medidor ultrasnico de flujo instalacin de transmisores y receptores en cada orilla siguiendo una lnea que forma un ngulo con la corriente
se mide la diferencia en el tiempo de viaje de los dos pulsos con las direcciones opuestas
la diferencia de tiempo se relaciona con la velocidad media de la corriente
requiere equipos electrnicos complejos
se utiliza en corrientes libres de maleza, con agua clara y lecho estable
gran precisin en la medida del caudal
instalacin y operacin costosa
3. Flotadores integradores tcnica basada en el principio de movimiento de flotadores
los flotadores son burbujas de aire lanzadas a intervalos regulares desde agujas localizadas en una lnea de aire comprimido colocada a travs del lecho de la corriente
la difusin area de las burbujas que salen a la superficie del agua (fotografiadas con un equipo especial) da la medida de la velocidad media de la corriente.
MEDICIN DE CAUDALES
Control natural
http://www.noor-scientific.com/enviro_water_management_and_hydrology.htmEl control natural de un tramo de un ro es una seccin particular (estacin de aforo) donde se mide el caudal y su correspondiente nivel y se establece una nica relacin (denominada curva de calibracin) entre estos dos valores. Tal relacin puede ser utilizada para estimar el caudal a partir del nivel observado.
: nivel
, y (nivel para el caudal cero) son los parmetros relativos a la seccin de control.
Si se seleccionan tres valores de caudal , y de la curva de calibracin tal que el nivel para la descarga cero puede ser obtenido de:
, y son los niveles correspondientes, respectivamente, a los tres caudales seleccionados.
TRANSPORTE DE SEDIMENTOS
El muestreo real es el mtodo ms confiable de medida de la tasa de transporte de sedimentos en un ro.
Recoleccin de muestras de sedimentos en suspensin (concentracin):
trampas de vlvula de gozne accionadas con resortes
muestreadores de bombeo continuo o intermitente
para la medicin de la carga de sedimentos suspendidos se utilizan muestreadores de sedimentos tipo integradores-puntuales o integradores en profundidad, con boquillas orientadas contra la direccin del flujo y paralelas a l y muestreadores perfilados de tal manera que se logra a la entrada una verdadera velocidad no distorsionada de la corriente en la toma.
muestreadores que constan de un tubo recolector que descarga en una botella
http://fisp.wes.army.mil/Catalog_Page_US_D-95.htm
Recoleccin de muestras de sedimentos de material del lecho:
1. Muestreador de sedimentos, por ejemplo, un dispositivo colocado temporalmente en el lecho, que altere lo menos posible el movimiento de la carga del lecho.
2. Otros mtodos(i) Investigacin de depsitos de sedimentos en la desembocadura del ro
(ii) Seguimiento de dunas
(iii) Sensores remotos
(iv) Trazadores
(v) Detectores acsticos
CALIDAD DEL AGUA
La calidad del agua se define de acuerdo con:
su uso: riego, consumo humano, consumo industrial
la conveniencia para la vida acutica
La calidad se define y monitorea mediante varios parmetros:
pH
DBO, demanda biolgica de oxgeno
DQO, demanda qumica de oxgeno
COT, carbono orgnico total
OD oxgeno disuelto
SS, slidos suspendidos
temperatura
amonaco
http://www.noor-scientific.comTRNSITO DE CRECIENTES EN ROS
Hidrgrafas de caudal en el trnsito de la hidrgrafa de la descarga de la creciente mxima de diseo a partir de la presa de La FeEl trnsito de crecientes es el procedimiento de transformar un caudal de entrada cuando pasa por un tramo de ro (o un embalse) en un caudal de salida.
Durante este proceso:
SYMBOL 183 \f "Symbol" \s 10 \h El hidrograma de entrada de la creciente cambia su forma
SYMBOL 183 \f "Symbol" \s 10 \h El caudal pico por lo general se reduce
SYMBOL 183 \f "Symbol" \s 10 \h El tiempo base se incrementa, es decir, la creciente se amortigua.
La tarea usual es determinar la reduccin-atenuacin del pico de la creciente entre la entrada y la salida- y el tiempo de desfase entre los picos. La creciente amortiguada es controlada por la resistencia local, por la debida a la friccin, por los trminos de la aceleracin presentes en la ecuacin de movimiento y por el almacenamiento.
El trnsito de crecientes en un embalseslo considera los efectos del almacenamiento
Existen tres enfoques posibles de trnsito de crecientes en un canal:
1. El mtodo hidrulico (solucin dinmica exacta) se basa en la solucin mediante diferencias finitas de las ecuaciones de Saint Venant, se requiere informacin sobre la forma del canal y los coeficientes de friccin.
2. La analoga de la difusin (solucin dinmica aproximada) se basa en las analogas entre la transformacin de la creciente y los procesos de dispersin y difusin.
3. El mtodo hidrolgico (solucin cinemtica) popularizado despus de la aparicin del mtodo Muskingum-Cunge
MTODO MUSKINGUM-CUNGE
S: almacenamiento
K: constante de almacenamiento
O: caudal de salida
I: caudal de entrada
x: factor de ponderacin
t: tiempo
L: longitud del tramo
Qp: caudal pico
vp: velocidad del caudal pico
so: pendiente media del lecho
B: ancho medio del canal
OBRAS FLUVIALES
Los objetivos de las obras de mejoramiento de los ros son:
Ayudar a la navegacin
Prevenir inundaciones
Recuperar terrenos
Proteger terrenos
Suministrar el agua necesaria para el riego
Desarrollar hidroelctricas
Aprovechar el agua en uso domstico
Aprovechar el agua en uso industrial
Aprovechamiento mltiple
Aspectos que deben considerarse:
Leyes de Rgimen de ros
Anlisis B/C
Reglamentacin del valle del ro.
En control de inundaciones reglamentar para varios niveles
Estabilizacin del canal y de las bancas
Encauzamiento con diques
Contemplar las consecuencias atrs y delante de la intervencin
ESPIGONES
Los espigones son pequeos espolones, permeables y slidos, de madera, tablestacado, vegetacin y mampostera de piedra. Su propsito es reducir el ancho del canal y remover el peligro de socavacin existente sobre la orilla.
Barcelona
Cartagena de IndiasBaluartes de San Lucas y Santa Catalina. A la derecha de ellos, el Espign, que desde 1779 impide el acceso a la playa creada por Antonio de Arvalo para proteger de las olas la muralla de la Marina.
DIQUESLos diques longitudinales son ms econmicos que los espigones, pueden ser en piedra, roca o trabajos en fajina. Los diques de aguas altas se utilizan para proteccin contra inundaciones. El encauzamiento de ros a base de hormign y venga muros y diques es un arma de matar para las generaciones futuras. En la fotografa el ro Limia en Xinzo, no dejaron ni orillas.http://galeon.hispavista.com/marialor/encauza.htm
Diques de encauzamiento contra los sedimentos que aterraban la entrada del Pasig. 1757. SGE Durante el siglo XVIII se realizaron obras y campaas de dragado contra la acumulacin de arena en la desembocadura del ro, que dificultaba la navegacin y la entrada al puerto fluvial.http://www.cedex.es/cehopu/expomanila/p20.htmDEFLECTORESLos deflectores se construyen de tableros de madera o metal, pueden utilizarse para desviar el flujo que erosiona la banca del ro o para inducir erosin del lecho y profundizacin local del flujo.
TRAVIESAS (umbrales de fondo)
Las traviesas estabilizan los lechos del ro expuestos a erosiones intensas, cubren el ancho total del cauce del ro, con la mayor altura hacia las orillas y una pendiente suave hacia el centro de la corriente. Los materiales mas frecuentes son terraplenes en piedra, encofrados llenos de tierra y concreto.
PROTECCIN DE LA BANCA
SYMBOL 183 \f "Symbol" \s 10 \h Plantas
SYMBOL 183 \f "Symbol" \s 10 \h Fajinas (atados o manojos de ramas, por lo general sauce)
SYMBOL 183 \f "Symbol" \s 10 \h Blago
SYMBOL 183 \f "Symbol" \s 10 \h Zarzas
SYMBOL 183 \f "Symbol" \s 10 \h Colchacretos
SYMBOL 183 \f "Symbol" \s 10 \h Mampostera
SYMBOL 183 \f "Symbol" \s 10 \h Piedra lanzada
SYMBOL 183 \f "Symbol" \s 10 \h Gaviones
SYMBOL 183 \f "Symbol" \s 10 \h Bolsacretos
SYMBOL 183 \f "Symbol" \s 10 \h Placas de concreto o de asfalto
SYMBOL 183 \f "Symbol" \s 10 \h Unidades de concreto prefabricado entrelazadas con o sin vegetacin
SYMBOL 183 \f "Symbol" \s 10 \h Colchacretos articulados
SYMBOL 183 \f "Symbol" \s 10 \h Bloques de suelo
SYMBOL 183 \f "Symbol" \s 10 \h Geotextiles
SYMBOL 183 \f "Symbol" \s 10 \h Llantas usadas
VENTAJAS!
dy
dx
Tr segn el propsito
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Seccin 1 (km 0.0)
Seccin 16 (km 6.36)
Seccin 38 (km 20.41)
Seccin 60 (km32.24)
Seccin 70 (km 38.33)
Tiempo (h)
Q (m3/s)
Hoja1
seccin 1Seccin 16Seccin 38seccin 60seccin 70
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9.402123.82220.842097.91329.442073.14466.271964.52270.741879.713792240.86
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9.802123.72204.162097.84307.582073.10453.521964.57290.961879.902768258.59
9.902123.69200.002097.83302.372073.09448.231964.58296.001879.951536263.04
10.002123.66195.842097.81297.412073.08445.991964.59301.041879.997256267.48
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10.302123.58183.322097.76282.152073.05433.021964.63316.191880.14356280.76
10.402123.55179.162097.74276.772073.03429.371964.64321.231880.18928285.18
10.502123.52175.002097.72271.532073.02424.161964.65326.271880.238048289.60
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10.802123.43162.512097.67256.152072.98410.421964.69341.421880.384352302.85
10.902123.40158.322097.65251.112072.97407.561964.70346.461880.43312307.27
11.002123.37154.162097.63246.072072.96403.711964.71351.501880.481888311.68
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11.202123.30145.832097.59236.192072.93394.341964.73361.611880.582472320.55
11.302123.27141.672097.57231.072072.92390.091964.74366.651880.63124324.96
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11.502123.20133.342097.53219.822072.89381.231964.76376.731880.731824333.80
11.602123.15129.152097.51214.532072.88376.441964.76374.861880.78364338.22
11.702123.07124.992097.48209.352072.87372.451964.75372.991880.832408342.63
11.802123.10120.832097.46204.222072.86367.611964.75371.121880.884224347.05
11.902123.06116.672097.44199.122072.84363.671964.74369.251880.932992351.47
12.002123.02112.502097.42194.032072.83358.801964.74367.381880.984808355.86
12.102123.01110.832097.40188.992072.82354.921964.73365.091881.000048355.63
12.202122.99109.162097.37184.142072.81350.001964.73362.821881.018336355.38
12.302122.97107.492097.35179.902072.79346.171964.73360.561881.033576355.15
12.402122.96105.822097.33176.502072.78341.191964.72358.291881.048816354.90
12.502122.94104.182097.32173.782072.77337.451964.72356.031881.064056354.67
12.602122.93102.512097.31171.432072.76332.411964.71353.731881.070152352.94
12.702122.91100.842097.30169.222072.74328.701964.71351.441881.0732351.21
12.802122.8999.172097.29167.072072.73323.601964.70349.181881.079296349.49
12.902122.8897.492097.28164.972072.72318.451964.70346.881881.082344347.76
13.002122.8695.822097.27162.912072.71314.321964.69344.591881.08844346.03
13.102122.8494.152097.26160.812072.69309.841964.69342.321881.091488343.99
13.202122.8392.512097.25158.742072.68305.451964.68340.031881.091488341.95
13.302122.8190.842097.24156.682072.67301.041964.68337.761881.094536339.92
13.402122.7989.172097.23154.612072.66295.171964.67335.471881.094536337.88
13.502122.7787.502097.22152.542072.65292.001964.67333.181881.097584335.84
13.602122.7685.832097.21150.482072.63286.911964.66330.911881.097584333.74
13.702122.7484.162097.19148.442072.62282.231964.66328.621881.097584331.65
13.802122.7282.492097.18146.452072.61279.521964.65326.321881.097584329.55
13.902122.7080.842097.17144.422072.60273.201964.65324.061881.100632327.46
14.002122.6879.172097.16142.352072.58270.571964.64321.761881.100632325.36
14.102122.6677.502097.15140.282072.57265.221964.64319.501881.100632323.27
14.202122.6475.832097.14138.212072.56261.561964.63317.211881.100632321.17
14.302122.6274.162097.13136.182072.55257.801964.63314.911881.100632319.07
14.402122.6072.492097.12134.112072.53254.401964.62312.651881.097584316.98
14.502122.5870.822097.10132.042072.52250.521964.62310.351881.097584314.88
14.602122.5669.182097.09130.002072.51247.261964.61308.061881.097584312.79
14.702122.5467.512097.08127.942072.49245.171964.61305.791881.094536310.69
14.802122.5265.842097.07125.902072.48240.441964.60303.501881.094536308.60
14.902122.5064.172097.05123.832072.47237.661964.59301.231881.091488306.50
15.002122.4862.502097.04121.792072.46234.801964.59298.941881.091488304.41
15.102122.4761.962097.03119.722072.45231.891964.59296.651881.091488302.28
15.202122.4661.392097.02117.682072.44229.001964.58294.381881.08844300.16
15.302122.4560.822097.01115.652072.43226.111964.58292.091881.085392298.06
15.402122.4560.292096.99113.612072.42223.221964.57289.791881.085392295.94
15.502122.4459.722096.98111.602072.41220.361964.56287.531881.082344293.82
15.602122.4359.152096.97109.592072.40217.501964.56285.241881.082344291.72
15.702122.4258.622096.95107.602072.38214.611964.55282.941881.079296289.60
15.802122.4258.052096.94105.592072.37211.751964.55280.681881.076248287.50
15.902122.4157.512096.93103.612072.36208.871964.54278.381881.0732285.41
16.002122.4056.952096.91101.632072.35205.981964.54276.121881.0732283.28
16.102122.3956.382096.9099.652072.34203.151964.53273.821881.067104280.96
16.202122.3955.842096.8897.662072.33200.451964.52271.531881.061008278.67
16.302122.3855.272096.8795.682072.31197.881964.52269.261881.054912276.34
16.402122.3754.712096.8693.642072.30195.071964.52266.971881.048816274.02
16.502122.3654.172096.8491.632072.29192.301964.51264.681881.04272271.73
16.602122.3553.602096.8389.592072.27189.521964.50262.411881.033576269.29
16.702122.3553.072096.8187.582072.26186.721964.50260.121881.02748266.89
16.802122.3452.502096.7985.602072.25183.921964.49257.851881.018336264.48
16.902122.3351.932096.7883.622072.23181.091964.48255.561881.009192262.04
17.002122.3251.402096.7681.642072.22178.281964.48253.271881.003096259.64
17.102122.3150.832096.7479.682072.20175.481964.47250.691880.993952257.20
17.202122.3150.292096.7377.792072.19172.791964.47248.111880.98176254.80
17.302122.3049.722096.7175.892072.18170.181964.46245.511880.972616252.36
17.402122.2949.162096.6974.022072.16167.641964.45242.931880.963472249.92
17.502122.2848.622096.6872.122072.15165.091964.45240.351880.954328247.52
17.602122.2748.052096.6670.252072.13162.451964.44237.751880.942136245.11
17.702122.2647.492096.6468.412072.12159.741964.43235.141880.929944242.70
17.802122.2646.952096.6366.602072.10156.901964.42232.541880.917752240.33
17.902122.2546.382096.6164.652072.09153.931964.42229.931880.90556237.92
18.002122.2445.842096.5962.552072.07151.381964.41227.331880.893368235.51
18.102122.2345.282096.5760.602072.05148.041964.40224.721880.881176233.05
18.202122.2244.712096.5558.592072.03144.701964.40222.121880.868984230.58
18.302122.2144.172096.5256.632072.02141.811964.39219.511880.856792228.12
18.402122.2043.612096.5055.162072.00139.351964.38216.911880.8446225.66
18.502122.1943.042096.4953.922071.98136.571964.38214.301880.832408223.19
18.602122.1942.502096.4852.872071.97134.001964.37211.701880.817168220.76
18.702122.1841.942096.4752.052071.95131.931964.36209.091880.801928218.35
18.802122.1741.402096.4551.312071.94130.261964.35206.491880.786688215.94
18.902122.1640.832096.4550.662071.93127.941964.34203.881880.774496213.54
19.002122.1540.272096.4450.212071.91126.181964.34201.281880.759256211.10
19.102122.1439.732096.4449.722071.90124.421964.33198.671880.744016208.67
19.202122.1339.162096.4349.162071.89122.901964.32196.071880.725728206.26
19.302122.1238.622096.4248.682071.88120.711964.31193.461880.710488203.82
19.402122.1138.062096.4148.312071.87119.241964.30190.861880.695248201.39
19.502122.1037.492096.4147.802071.85117.091964.30188.251880.680008198.95
19.602122.0936.952096.4047.202071.84115.451964.29185.651880.658672196.55
19.702122.0836.392096.3946.692071.83113.811964.28183.041880.640384194.14
19.802122.0735.822096.3946.412071.82112.131964.27180.431880.622096191.73
19.902122.0635.282096.3845.872071.80110.521964.27177.831880.603808189.33
20.002122.0534.722096.3744.742071.79108.881964.26175.221880.58552186.92
20.102122.0434.182096.3543.752071.78107.351964.25172.851880.567232184.60
20.202122.0333.612096.3443.152071.77105.591964.24170.441880.545896182.28
20.302122.0233.052096.3342.652071.76104.091964.23168.061880.527608179.95
20.402122.0132.512096.3342.282071.74102.341964.23165.681880.50932177.63
20.502122.0031.942096.3241.712071.73100.841964.22163.271880.487984175.31
20.602121.9931.382096.3040.832071.7299.141964.21160.901880.4636173.07
20.702121.9730.842096.2940.072071.7197.611964.20158.551880.439216170.84
20.802121.9730.272096.2839.472071.7095.971964.20156.171880.41788168.60
20.902121.9529.732096.2738.852071.6894.441964.19153.791880.393496166.39
21.002121.9429.172096.2638.202071.6792.881964.18151.411880.369112164.15
21.102121.9328.602096.2437.602071.6691.381964.17149.031880.338632162.00
21.202121.9228.062096.2337.102071.6489.791964.16146.681880.308152159.85
21.302121.9127.502096.2236.612071.6388.211964.16144.301880.277672157.67
21.402121.9026.962096.2136.162071.6186.541964.15141.921880.247192155.52
21.502121.8826.392096.2035.712071.5984.071964.14139.551880.216712153.36
21.602121.8725.822096.1935.282071.5680.871964.13137.201880.183184151.10
21.702121.8625.292096.1834.892071.5478.181964.13134.821880.149656148.83
21.802121.8524.722096.1734.492071.5276.291964.12132.441880.116128146.57
21.902121.8324.152096.1634.122071.5074.471964.11130.061880.0826144.30
22.002121.8223.622096.1633.752071.4872.691964.10127.711880.049072142.04
22.102121.8123.052096.1433.362071.4670.991964.09125.331880.012496139.74
22.202121.8022.512096.1332.852071.4569.321964.08122.951879.978968137.45
22.302121.7921.952096.0329.532071.4367.711964.07120.571879.942392135.16
22.402121.7721.382096.0129.112071.4166.091964.06118.221879.908864132.86
22.502121.7620.842095.9828.682071.3964.481964.06115.841879.872288130.57
22.602121.7420.272095.9528.292071.3862.891964.05113.471879.835712128.25
22.702121.7319.712095.9227.862071.3661.311964.04111.121879.799136125.95
22.802121.7219.172095.8827.552071.3459.721964.03108.741879.76256123.66
22.902121.7018.602095.8427.162071.3258.161964.02106.361879.725984121.37
23.002121.6918.072095.8026.822071.3056.611964.01103.981879.689408119.04
23.102121.6717.502095.7726.392071.2855.051964.00101.631879.649784116.75
23.202121.6616.932095.7225.912071.2653.491963.9999.251879.613208114.46
23.302121.6416.402095.6924.892071.2351.961963.9896.871879.573584112.16
23.402121.6315.832095.6723.872071.2150.461963.9794.521879.537008109.87
23.502121.6115.292095.6523.332071.1948.871879.497384107.55
23.602121.5914.722095.6322.602071.1747.371879.45776105.25
23.702121.5814.162095.6122.092071.1445.841879.418136102.96
23.802121.5613.622095.6021.492071.1244.341879.378512100.67
23.902121.5513.052095.5821.012071.0942.841879.33888898.34
Hoja2
Tiemposeccin 1Seccin 16Seccin 38Seccin 60
0.000.7612.492.4712.971.6313.000.2113.03
0.100.7612.492.4712.971.6513.000.2213.28
0.200.7612.492.4712.971.6713.000.2213.54
0.300.7612.492.4712.971.6913.000.2213.79
0.400.7612.492.4712.971.7113.000.2214.02
0.500.7612.492.4812.971.7413.000.2314.27
0.600.7612.492.4912.971.7913.050.2314.55
0.700.7612.492.5112.971.8313.420.2314.87
0.800.7612.492.5712.971.8713.680.2415.15
0.900.9619.792.6312.971.9214.020.2415.43
1.001.1327.072.7012.971.9714.330.2415.74
1.101.2734.382.7712.972.0114.720.2416.03
1.201.4041.652.8313.002.0615.060.2416.34
1.301.5148.962.8913.112.1115.430.2516.62
1.401.6256.242.9613.422.1615.800.2516.91
1.501.7263.543.0614.072.2016.170.2517.22
1.601.8170.823.1715.262.2516.540.2517.50
1.701.9078.133.2816.932.3016.910.2617.81
1.801.9885.403.3418.922.3417.270.2618.09
1.902.0692.713.4220.982.3917.700.2618.41
2.002.1399.993.4723.022.4318.090.2718.69
2.102.36124.993.5124.752.4818.380.2719.00
2.202.56149.993.5626.312.5218.750.2719.28
2.302.74175.003.6027.472.5719.110.2719.57
2.402.91200.003.6629.422.6119.510.2819.88
2.503.07225.013.7433.612.6519.880.2820.16
2.603.23250.013.8440.892.6920.270.2820.47
2.703.38275.013.9551.032.7320.640.2820.76
2.803.52299.994.0663.602.7721.010.2821.07
2.903.65324.994.1677.502.8121.350.2921.35
3.003.77350.004.2692.342.8521.690.2921.66
3.103.91379.674.36106.052.9022.000.2921.95
3.204.04409.324.44118.732.9522.480.2922.23
3.304.16439.004.52131.793.0223.360.3022.54
3.404.28468.674.60145.323.1224.750.3022.82
3.504.39498.324.67159.963.2626.620.3023.13
3.604.49528.004.73175.793.4128.660.3023.42
3.704.59557.674.79190.603.5831.180.3123.73
3.804.69587.324.85204.283.7234.010.3124.01
3.904.78617.004.91218.124.0436.590.3124.30
4.004.87646.674.96231.864.3038.880.3124.61
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nivelqnqnqnq
Hoja2
Seccin 1 (km 0.0)
Seccin 16 (km 6.36)
Seccin 38 (km 20.41)
Seccin 60 (km32.24)
Hoja3
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