análisis por el método gumbel tingomayo

INTENSIDADES MÁXIMAS PARA DISTINTOS PERÍODOS DE DURACIÓN

ESTACIÓN : AUGUSTO WEBERBAUER LATITUD : 07° 10' DEPARTAMENTO : CAJAMARCAINFORMACIÓN : INTENSIDADES MÁXIMAS LONGITUD : 78° 30' PROVINCIA : CAJAMARCA

RED HIDROMETEOROLÓGICA : UNC ALTITUD: 2690 msnm DISTRITO : CAJAMARCA

INTENSIDADES MÁXIMAS EN mm/horaAÑO 5 min 10 min 30 min 60 min 120 min.

1° 2° 3° 1° 2° 3° 1° 2° 3° 1° 2° 3° 1° 2° 3°1973 101.00 56.00 52.00 71.00 44.00 35.00 24.00 20.00 18.00 14.00 12.00 10.00 11.00 6.00 6.501974 73.00 71.00 54.00 58.00 54.00 38.00 34.00 30.00 22.00 18.00 17.00 13.00 19.00 8.00 8.701975 90.00 60.00 54.00 50.00 49.00 44.00 24.00 21.00 20.00 16.00 13.00 13.12 10.00 8.00 8.701976 68.00 65.00 43.00 63.00 57.00 38.00 37.00 24.00 18.00 19.00 12.00 12.11 9.00 8.00 6.001977 65.00 48.00 46.00 53.00 44.00 32.00 37.00 18.00 17.00 21.00 14.00 11.00 11.00 10.00 7.001978 26.00 25.00 24.00 24.00 20.00 20.00 21.00 19.00 11.00 12.00 10.20 7.00 6.00 5.00 4.001979 60.00 50.00 46.00 60.00 45.00 39.00 38.00 33.00 26.00 23.00 20.00 15.00 14.00 10.00 8.001980 73.02 69.00 56.40 60.10 51.80 46.50 33.80 31.33 21.60 21.08 18.46 12.40 9.28 9.45 7.421981 67.20 58.80 54.00 54.80 43.80 42.60 29.13 26.62 25.00 15.54 15.30 15.20 13.02 8.87 7.601982 88.29 59.04 55.60 75.15 55.65 43.08 37.20 34.00 25.70 23.10 18.33 14.27 13.27 9.35 7.831983 75.30 73.20 53.80 50.40 49.46 48.60 31.40 28.90 28.68 23.71 20.34 15.44 13.99 12.41 9.051984 112.80 71.20 66.60 71.80 54.60 46.06 27.60 25.60 23.75 15.63 15.60 14.30 9.80 8.59 7.701985 59.30 40.80 38.40 54.40 28.80 22.63 25.52 16.25 11.60 14.70 9.50 8.30 8.05 5.15 5.101986 84.60 63.80 57.00 65.40 45.00 37.20 30.11 22.22 21.40 15.60 13.90 13.74 8.23 7.80 7.751987 76.00 52.00 52.00 49.20 45.40 44.40 21.60 19.00 18.96 13.20 12.86 12.40 7.95 7.88 7.001988 70.40 67.20 44.40 52.80 42.80 39.00 23.00 30.40 19.40 13.79 11.59 10.61 7.85 7.33 6.451989 73.60 61.20 57.60 47.80 46.20 42.60 28.04 22.55 22.40 16.48 13.18 12.90 9.64 9.50 8.151990 111.60 91.54 59.55 75.00 64.63 37.65 37.94 34.00 17.58 23.00 17.90 9.50 11.53 8.95 4.751991 83.00 62.00 53.00 73.00 81.00 36.00 41.00 39.00 21.00 26.00 20.00 14.00 14.00 13.00 10.001992 56.00 55.00 48.00 39.00 35.00 30.00 19.00 18.00 14.00 10.00 10.00 8.00 5.00 5.00 5.001993 58.00 56.00 50.00 51.00 47.00 42.00 28.00 26.00 24.00 18.00 13.00 13.00 10.00 10.00 6.00

CÁLCULO DE CAUDALES PARA MÁXIMAS AVENIDAS

ANÁLISIS POR EL MÉTODO GUMBEL PARA LA QUEBRADA TINGOMAYO

a. TRASLADO DE LAS INTENSIDADES DE WEBERBAUER A QUEBRADATINGOMAYO

Para el traslado de intensidades partiremos de un Análisis Regional por tratarse de una microcuenca y una estación que forman parte de la misma cuenca

Poseemos la siguiente información:

H = altura, dimensionalmente [L]tc, tlluvia = tiempos de concentracón y de lluvia respectivamente, dimensionalmente [T]

0 = a + b .......(1)

0 = -a + c ...... (2)

RESOLVIENDO EL SISTEMA:

a = c = -b, para a = 1, c = 1, y b = -1

PARA EL TRASLADO DE LAS INTENSIDADES PROCEDEREMOS DE LA SIGUIENTE MANERA:

PARTIREMOS DE LA SIGUENTE RELACIÓN:

DONDE:

13.43 minutos ====> Utilizaremos 14 minutos

DE LA RELACIÓN ANTERIOR OBTENEMOS:

DATOS A UTILIZAR:

ALTITUD ESTACIÓN AUGUSTO WEBERBAUER = 2690 m.s.m.n

ALTITUD MEDIA DE LA MICROCUENCA TINGOMAYO = 2680 m.s.m.n

Iw, It = Intensidades, dimensionalmente [LT-1]

LUEGO, NUESTRO NÚMERO P = [LT-1]a [L]b [T]c

ENTONCES P = LaT-a Lb Tc

ENTONCES L0 T0 = La+b T-a+c

ENTONCES P = LT-1 L-1 T

ITINGOMAYO ===> INTENSIDAD AJUSTADA PARA LA MICROCUENCA TINGOMAYO

IWEBERBAUER ===> INTENSIDAD MÁXIMA MEDIDA DE LA ESTACIÓN AUGUSTO WEBERBAUER

HTINGOMAYO ===> ALTITUD DEL EMISOR LA MICROCUENCA TINGOMAYO

HWEBERBAUER ===> ALTITUD DE LA ESTACIÓN AUGUSTO WEBERBAUER

tlluviaWEBERBAUER ====> TIEMPO DE LA LLUVIA (5',10',30',60' Y 120')

TCONCENTRACIÓN =

I tingomayo=IweberbauerH tingomayoH weberbauer

tc tingomayotlluviaweberbauer

I tingomayoI weberbauer

=H tingomayoH weberbauer

tctingomayotlluviaweberbauer

CUADRO DE DATOS A OBTENER:INTENSIDADES BASE

INTENSIDADES PARA LA INTENSIDADES WEBERBAUER MICROCUENCA TINGOMAYO

INTENSIDADES MÁXIMAS EN mm/hora INTENSIDADES MÁXIMAS EN mm/horaAÑO 5 min 10 min 30 min 60 min 120 min. AÑO 5 min 10 min 30 min 60 min 120 min.

1° 1° 1° 1° 1° 1° 1° 1° 1° 1°1973 101.00 71.00 24.00 14.00 11.00 1973 281.75 99.03 11.16 3.25 1.281974 73.00 58.00 34.00 18.00 19.00 1974 203.64 57.78 15.81 4.18 2.211975 90.00 50.00 24.00 16.00 10.00 1975 251.06 49.81 11.16 3.72 1.161976 68.00 63.00 37.00 19.00 9.00 1976 189.69 62.77 17.20 4.42 1.051977 65.00 53.00 37.00 21.00 11.00 1977 181.32 52.80 17.20 4.88 1.281978 26.00 24.00 21.00 12.00 6.00 1978 72.53 23.91 9.76 2.79 0.701979 60.00 60.00 38.00 23.00 14.00 1979 167.38 59.78 17.67 5.35 1.631980 73.02 60.10 33.80 21.08 9.28 1980 203.70 59.88 15.71 4.90 1.081981 67.20 54.80 29.13 15.54 13.02 1981 187.46 54.60 13.54 3.61 1.511982 88.29 75.15 37.20 23.10 13.27 1982 246.29 74.87 17.30 5.37 1.541983 75.30 50.40 31.40 23.71 13.99 1983 210.06 50.21 14.60 5.51 1.631984 112.80 71.80 27.60 15.63 9.80 1984 314.67 71.53 12.83 3.63 1.141985 59.30 54.40 25.52 14.70 8.05 1985 165.42 54.20 11.87 3.42 0.941986 84.60 65.40 30.11 15.60 8.23 1986 236.00 65.16 14.00 3.63 0.961987 76.00 49.20 21.60 13.20 7.95 1987 212.01 49.02 10.04 3.07 0.921988 70.40 52.80 23.00 13.79 7.85 1988 196.39 52.60 10.69 3.21 0.911989 73.60 47.80 28.04 16.48 9.64 1989 205.31 47.62 13.04 3.83 1.121990 111.60 75.00 37.94 23.00 11.53 1990 311.32 74.72 17.64 5.35 1.341991 83.00 73.00 41.00 26.00 14.00 1991 231.54 72.73 19.06 6.04 1.631992 56.00 39.00 19.00 10.00 5.00 1992 156.22 38.86 8.83 2.32 0.581993 58.00 51.00 28.00 18.00 10.00 1993 161.80 50.81 13.02 4.18 1.161994 91.49 64.18 36.22 19.04 12.91 1994 255.22 63.94 16.84 4.43 1.501995 71.11 56.25 28.66 16.72 9.32 1995 198.37 56.04 13.32 3.89 1.081996 81.30 60.21 32.44 17.88 11.12 1996 226.79 59.99 15.08 4.16 1.291997 82.20 68.10 35.04 17.86 8.94 1997 229.30 67.85 16.29 4.15 1.041998 92.00 66.34 40.60 27.10 13.50 1998 256.64 66.10 18.88 6.30 1.57

b. ANÁLISIS POR EL MÉTODO GUMBEL PARA 5 min.

INTENSIDADES # DE ORDEN

P(x) = m/(n+1) - P(x)

Tr (Años)

F(X)DELTA

MÁXIMAS (m) 1/P(x)X = mm/hora

314.6658736059 1 0.04 0.96 27.00 0.96 0.01311.3183643123 2 0.07 0.93 13.50 0.95 0.03281.7486988848 3 0.11 0.89 9.00 0.90 0.01256.6423791822 4 0.15 0.85 6.75 0.83 0.02255.2196877323 5 0.19 0.81 5.40 0.82 0.01251.063197026 6 0.22 0.78 4.50 0.80 0.03

246.2929962825 7 0.26 0.74 3.86 0.78 0.04235.9994052045 8 0.30 0.70 3.38 0.73 0.02231.5360594796 9 0.33 0.67 3.00 0.70 0.03229.3043866171 10 0.37 0.63 2.70 0.69 0.06226.7937546468 11 0.41 0.59 2.45 0.67 0.08212.0089219331 12 0.44 0.56 2.25 0.56 0.00210.0562081784 13 0.48 0.52 2.08 0.54 0.02205.3139033457 14 0.52 0.48 1.93 0.50 0.02203.6959405204 15 0.56 0.44 1.80 0.49 0.04203.6401486989 16 0.59 0.41 1.69 0.49 0.08198.3678215613 17 0.63 0.37 1.59 0.44 0.07196.3872118959 18 0.67 0.33 1.50 0.42 0.09189.6921933086 19 0.70 0.30 1.42 0.36 0.06187.4605204461 20 0.74 0.26 1.35 0.34 0.08181.3234200743 21 0.78 0.22 1.29 0.28 0.06167.375464684 22 0.81 0.19 1.23 0.17 0.02

165.4227509294 23 0.85 0.15 1.17 0.15 0.00161.7962825279 24 0.89 0.11 1.13 0.13 0.02156.2171003717 25 0.93 0.07 1.08 0.09 0.0272.52936802974 26 0.96 0.04 1.04 0.00 0.04

media 213.53 0.09devestan. 51.05 0.27 O.K.!

a 0.03b 190.56

VERIFICACIÓN DEL AJUSTE GUMBEL POR LA PRUEBA DE KOLMOGOROVSEGÚN KOLMOGOROV, EL MÁXIMO VALOR ABSOLUTO RESULTANTE DE LA DIFERENCIA ENTRE LA FUNCIÓN DE PROBABILIDADESTIMADA Y OBSERVADA DEBERÁ SER MENOR DE UN VALOR CRÍTICOQUE DEPENDE DEL NÚMERO DE DATOS Y EL NIVEL DE SIGNIFICANCIASELECCIONADOS, PARA NUESTRO CASO DICHO VALOR CRÍTICO ESPARA UN NIVEL DE SIGNIFICACIÓN DE 0,05 ESTÁ DADO POR:

DONDE:

n = NRO DE DATOS

LUEGO PARA n = 26

0.26671794

D =| F(X) - P(X)|

D MÁX =D 0 =

Do = 1.36/(n)1/2

D = VALOR CRÍTICO

D o =

c. ANÁLISIS POR EL MÉTODO GUMBEL PARA 10 min.

INTENSIDADES # DE ORDEN P(x) = m/(n+1) - P(x) Tr (Años) DELTA

MÁXIMAS (m) 1/P(x) F(X)X = mm/hora

99.03048327138 1 0.04 0.96 27.00 0.99 0.0274.87063197026 2 0.07 0.93 13.50 0.88 0.0574.72118959108 3 0.11 0.89 9.00 0.87 0.0172.72862453532 4 0.15 0.85 6.75 0.85 0.0071.53308550186 5 0.19 0.81 5.40 0.84 0.0267.8468401487 6 0.22 0.78 4.50 0.78 0.00

66.09637174721 7 0.26 0.74 3.86 0.74 0.0065.15687732342 8 0.30 0.70 3.38 0.72 0.0263.94141263941 9 0.33 0.67 3.00 0.70 0.0362.76579925651 10 0.37 0.63 2.70 0.67 0.0459.98617100372 11 0.41 0.59 2.45 0.60 0.0059.87657992565 12 0.44 0.56 2.25 0.59 0.0459.77695167286 13 0.48 0.52 2.08 0.59 0.0757.7843866171 14 0.52 0.48 1.93 0.53 0.05

56.04089219331 15 0.56 0.44 1.80 0.48 0.0354.59628252788 16 0.59 0.41 1.69 0.43 0.0254.19776951673 17 0.63 0.37 1.59 0.41 0.0452.8029739777 18 0.67 0.33 1.50 0.37 0.03

52.60371747212 19 0.70 0.30 1.42 0.36 0.0650.81040892193 20 0.74 0.26 1.35 0.30 0.0450.2126394052 21 0.78 0.22 1.29 0.28 0.06

49.81412639405 22 0.81 0.19 1.23 0.27 0.0849.01710037175 23 0.85 0.15 1.17 0.24 0.0947.62230483271 24 0.89 0.11 1.13 0.20 0.0938.85501858736 25 0.93 0.07 1.08 0.03 0.0523.91078066914 26 0.96 0.04 1.04 0.00 0.04


a 0.09b 52.81


DONDE:

n = NRO DE DATOS

LUEGO PARA n = 26

0.27

D =| F(X) - P(X)|

D MÁX =D 0 =

Do = 1.36/(n)1/2

D = VALOR CRÍTICO

D o =

99.030483374.870632

74.721189672.728624571.533085567.846840166.096371765.156877363.941412662.765799359.986171

59.876579959.776951757.784386656.040892254.596282554.197769552.802974

52.603717550.810408950.212639449.814126449.017100447.622304838.855018623.9107807

d. ANÁLISIS POR EL MÉTODO GUMBEL PARA 30 MIN.



19.06220570012 1 0.04 0.96 27.00 0.89 0.0718.87623296159 2 0.07 0.93 13.50 0.88 0.0417.66741016109 3 0.11 0.89 9.00 0.81 0.0717.63951425031 4 0.15 0.85 6.75 0.81 0.0417.29546468401 5 0.19 0.81 5.40 0.79 0.0317.20247831475 6 0.22 0.78 4.50 0.78 0.0017.20247831475 7 0.26 0.74 3.86 0.78 0.0416.8398314746 8 0.30 0.70 3.38 0.75 0.04

16.29121189591 9 0.33 0.67 3.00 0.69 0.0215.80768277571 10 0.37 0.63 2.70 0.63 0.0015.71469640644 11 0.41 0.59 2.45 0.62 0.0315.08238909542 12 0.44 0.56 2.25 0.53 0.0214.59885997522 13 0.48 0.52 2.08 0.46 0.0613.99909789343 14 0.52 0.48 1.93 0.37 0.1113.54346468401 15 0.56 0.44 1.80 0.30 0.1513.32494671623 16 0.59 0.41 1.69 0.26 0.1413.0366889715 17 0.63 0.37 1.59 0.22 0.15

13.01809169765 18 0.67 0.33 1.50 0.22 0.1212.83211895911 19 0.70 0.30 1.42 0.19 0.1011.86506071871 20 0.74 0.26 1.35 0.08 0.1811.15836431227 21 0.78 0.22 1.29 0.03 0.1911.15836431227 22 0.81 0.19 1.23 0.03 0.1510.69343246592 23 0.85 0.15 1.17 0.02 0.1310.04252788104 24 0.89 0.11 1.13 0.00 0.119.763568773234 25 0.93 0.07 1.08 0.00 0.078.833705080545 26 0.96 0.04 1.04 0.00 0.04


a 0.43b 14.00


DONDE:

n = NRO DE DATOS

LUEGO PARA n = 26

0.26671794

D =| F(X) - P(X)|

D MÁX =D 0 =

Do = 1.36/(n)1/2

D = VALOR CRÍTICO

D o =

19.062205718.876233

17.667410217.639514317.295464717.202478317.202478316.839831516.291211915.807682815.714696415.0823891

14.5988613.999097913.543464713.324946713.036689

13.018091712.832119

11.865060711.158364311.158364310.693432510.04252799.763568778.83370508

e. ANÁLISIS POR EL MÉTODO GUMBEL PARA 60 min.



6.299826517968 1 0.04 0.96 27.00 0.96 0.006.044114002478 2 0.07 0.93 13.50 0.95 0.025.511767038414 3 0.11 0.89 9.00 0.90 0.015.369962825279 4 0.15 0.85 6.75 0.88 0.035.346716232962 5 0.19 0.81 5.40 0.88 0.065.346716232962 6 0.22 0.78 4.50 0.88 0.104.900381660471 7 0.26 0.74 3.86 0.79 0.054.881784386617 8 0.30 0.70 3.38 0.79 0.08

4.4261511772 9 0.33 0.67 3.00 0.65 0.024.416852540273 10 0.37 0.63 2.70 0.65 0.02

4.1843866171 11 0.41 0.59 2.45 0.56 0.034.1843866171 12 0.44 0.56 2.25 0.56 0.00

4.15649070632 13 0.48 0.52 2.08 0.55 0.034.151841387856 14 0.52 0.48 1.93 0.54 0.063.88683023544 15 0.56 0.44 1.80 0.43 0.02

3.831038413879 16 0.59 0.41 1.69 0.40 0.013.719454770756 17 0.63 0.37 1.59 0.35 0.023.633442379182 18 0.67 0.33 1.50 0.31 0.033.626468401487 19 0.70 0.30 1.42 0.30 0.013.612520446097 20 0.74 0.26 1.35 0.30 0.043.417249070632 21 0.78 0.22 1.29 0.21 0.013.254522924411 22 0.81 0.19 1.23 0.15 0.043.205705080545 23 0.85 0.15 1.17 0.13 0.023.068550185874 24 0.89 0.11 1.13 0.09 0.022.789591078067 25 0.93 0.07 1.08 0.03 0.042.324659231722 26 0.96 0.04 1.04 0.00 0.04


a 1.27b 3.76


DONDE:

n = NRO DE DATOS

LUEGO PARA n = 26

0.26671794

D =| F(X) - P(X)|

D MÁX =D 0 =

Do = 1.36/(n)1/2

D = VALOR CRÍTICO

D o =

6.299826526.044114

5.511767045.369962835.346716235.346716234.900381664.881784394.426151184.416852544.184386624.184386624.156490714.151841393.886830243.831038413.719454773.633442383.6264684

3.612520453.417249073.254522923.205705083.068550192.789591082.32465923

f. ANÁLISIS POR EL MÉTODO GUMBEL PARA 120 min.



2.208426270136 1 0.04 0.96 27.00 0.98 0.021.627261462206 2 0.07 0.93 13.50 0.87 0.051.627261462206 3 0.11 0.89 9.00 0.87 0.011.62609913259 4 0.15 0.85 6.75 0.87 0.02

1.569144981413 5 0.19 0.81 5.40 0.85 0.031.542411400248 6 0.22 0.78 4.50 0.83 0.051.513353159851 7 0.26 0.74 3.86 0.81 0.071.500567534077 8 0.30 0.70 3.38 0.81 0.101.340166047088 9 0.33 0.67 3.00 0.68 0.011.292510532838 10 0.37 0.63 2.70 0.63 0.001.278562577447 11 0.41 0.59 2.45 0.61 0.021.278562577447 12 0.44 0.56 2.25 0.61 0.061.162329615861 13 0.48 0.52 2.08 0.47 0.051.162329615861 14 0.52 0.48 1.93 0.47 0.011.139083023544 15 0.56 0.44 1.80 0.44 0.001.12048574969 16 0.59 0.41 1.69 0.42 0.01

1.083291201983 17 0.63 0.37 1.59 0.37 0.001.078641883519 18 0.67 0.33 1.50 0.36 0.031.046096654275 19 0.70 0.30 1.42 0.32 0.021.03912267658 20 0.74 0.26 1.35 0.31 0.05

0.956597273854 21 0.78 0.22 1.29 0.20 0.020.935675340768 22 0.81 0.19 1.23 0.18 0.010.92405204461 23 0.85 0.15 1.17 0.16 0.02

0.912428748451 24 0.89 0.11 1.13 0.15 0.040.697397769517 25 0.93 0.07 1.08 0.02 0.060.581164807931 26 0.96 0.04 1.04 0.00 0.04


a 3.69b 1.08


DONDE:

n = NRO DE DATOS

LUEGO PARA n = 26

0.26671794

D =| F(X) - P(X)|

D MÁX =D 0 =

Do = 1.36/(n)1/2

D = VALOR CRÍTICO

D o =

2.208426271.627261461.627261461.626099131.569144981.5424114

1.513353161.500567531.340166051.292510531.278562581.278562581.162329621.162329621.139083021.120485751.0832912

1.078641881.046096651.039122680.956597270.935675340.924052040.912428750.697397770.58116481

g. CÁLCULO DEL COEFICIENTE "C"

ZONA SUPERFICIE COEFICIENTE C*A1 ROCOSO 0.125 0.3 0.03752 ROCOSO 0.734 0.3 0.22023 BOSQUE 0.92 0.15 0.13804 BOSQUE 0.072 0.15 0.01085 BOSQUE 0.13 0.15 0.01956 ALREDEDORES 2.419 0.4 0.9676

4.4 1.3936

0.32

Ai (Km2)

Atotal SC*Ai

COEFICIENTE "C" = SC*Ai/Atotal =

0 20 40 60 80 100 120 140

0

200

400

INTENSIDAD vs TIEMPO (PARA DISTINTOS TIEMPOS DE RETORNO)

5.00

TIEMPO (en minutos)

INT

EN

SID

AD

(e

n m

m)

h. ANÁLISIS POR EL MÉTODO GUMBEL

INTENSIDAD MÁXIMA EN (mm/h)Tr (años) 5 10 30 60 120 Vida Útil

5.00 250.261 69.153 17.478 4.939 1.490 5010.00 280.130 77.328 19.220 5.528 1.693 5015.00 296.981 81.941 20.203 5.860 1.808 5020.00 308.781 85.171 20.891 6.093 1.888 5030.00 325.263 89.682 21.852 6.418 2.001 50

CÁLCULO DEL CAUDAL

Utilizaremos la fórmula: Q = C*I*A/n

PARA LOS MUROS DE ENCAUZAMIENTO Y LIMITADOR DE GASTOTr = 30 años

donde: Q =C = coeficiente de escorrentía 0.32

A = 4.27I = Intensidad Máxima (mm/hora) 89.682 mm/hora

n = 1

Q = 34.04

caudal en m3/seg.

Área de la cuenca (Km2) Km2

m3/seg

i. CÁLCULO DEL CAUDAL EN BASE A LA HUELLA

Los datos fueron medidos en dos secciones distintas de la quebrada, también conociéndose la pendiente en dicho tramo y con el único objetivo de hacer una comparación con los datos obtenidos por el Método de Gumbel

DATOS DE LA SECCIÓN:

ÁREA PROMEDIO = 9.4512PERÍMETRO MOJADO = 18.2697 mRADIO HIDRÁULICO = 0.5173 m

PENDIENTE (%) = 3%n = 0.035

(PARA FLUJO NORMAL)

Q = 30.14

m2

Q =( A*S1/2*R2/3)/n

m3/seg

análisis por el método gumbel tingomayo

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