Hoja1DISEO DE RAPIDASDisear una rapida para enlazar un desnivel de 22 metros en un canal cuyas caracteristicas son las siguientes:Z=22mAguas arriba:Aguas abajo:Q=2m^3/segQ=2m^3/segb=1mb=1mz=1.5z=1.5S=10/00S=10/00n=0.02n=0.02Y=0.88mY=0.88m

SOLUCIN1.-CARACTERISTICAS HIDRAULICAS DEL CANAL AGUAS ARRIBA Clculo del Area: A=2.0416m^2Clculo de la velocidad:V=0.980m/sClculo de la energia especifica:E=0.929mEl perfil del terreno presenta dos tramos de diferente pendiente: la superior de 0.25 y la inferior de 0.20en una longitud de proyeccion horizontal de 50m y 35m respectivamente, ver Fig.12.-CARACTERISTICAS DE LA RAPIDACon la ayuda del perfil del terreno se definen ciertas caracteristicas de la rapida:Pendiente S1=0.25Pendiente S2=0.2Tramo sup.L1=50mTramo inf.L2=35mLong. Total =85mn =0.015b =1.0mz =1.5Tirante crtico en la seccin de control A-ATabla de iteracion para calcular el tirante critico en canales de seccion trapezoidal

yc(asum.)4(2yc+b)/(5(2yc+b)+b)yc+g*(b+z*yc)yc/(b+2*z*yc)2*gyc0.60.730.80360.58928571430.58928571430.730.79290.58142857140.58142857140.730.78500.57566666670.57566666670.730.77920.57144126980.57144126980.730.77500.56834264550.56834264550.730.77190.5660703210.5660703210.730.76960.56440394970.56440394970.730.76800.5631819440.5631819440.730.76680.56228580660.56228580660.730.76590.56162863910.56162863910.730.76520.56114671630.56114671630.730.76470.56079330620.56079330620.730.76440.56053413890.56053413890.730.76410.56034408280.56034408280.730.76390.56020470830.56020470830.730.76380.56010250040.56010250040.730.76370.5600275479OKCaracteristicas hidraulicas de la seccion de control:T=2.1200550958myc=0.56mVc=1.942m/sEc=0.75m3.-CLCULO DE LOS TIRANTES DE ESCURRIMIENTO EN LA RAPIDALos 85m de longitud horizontal se han dividido en17 tramos, cada uno de 5mLas longitudes inclinadas seran:a)para pendiente S1=0.25L=5.153882032b)para pendiente S1=0.2L=5.0990195136Se aplica el teorema de bernoulli, mediante el metodo de incrementos finitos.TEORIA DE BERNOULLI POR TRAMOS FINITOS123456789101112yAPRR^2/3vv^2/2gEhf1E+hf1hf2E+hf20.10.1151.36055512750.08452432220.192599193717.391304347815.415773033615.51577303369.455235999424.9710090339.354586031924.87035906550.110.128151.39661064030.09175785740.203436484715.606710885712.41434376512.5243437656.824676605219.34902037026.752028658819.27637242380.120.14161.43266615310.09883670370.21376938214.124293785310.16797527710.2879752775.062435150215.35041042725.00854607415.29652135090.130.155351.46872166580.10577225330.223656317912.87415513368.44769981678.57769981673.842307569512.42000738613.801406619712.37910643640.140.16941.50477717860.11257480670.23314573411.80637544277.10451075927.24451075922.97368679710.21819755612.942032221710.18654298090.150.183751.54083269130.11925370030.242278332410.88435374156.03818330126.18818330122.34041641878.528599722.31550293838.50368623960.160.19841.57688820410.12581741650.251088704310.08064516135.17937853565.33937853561.86912908877.20850762431.84923241117.18861094670.170.213351.61294371680.13227367930.25960653639.37426763534.4789446334.6489446331.51203012266.16097475561.49593472516.1448793580.180.22861.64899922960.13862953720.26785752338.74890638673.90129270964.08129270961.23713425795.31842696751.22396509715.30525780680.190.244151.68505474230.14489143520.27586407228.19168543933.42016872253.61016872251.02252336424.63269208671.01163871324.62180743570.20.261.72111025510.15106527850.28364585217.69230769233.01588163273.21588163270.8528593464.06874097860.84378075024.05966238290.210.276151.75716576780.15715648750.29122023127.24244070252.67344277932.88344277930.71720581693.60064859620.70957123833.59301401760.220.29261.79322128060.16317004660.29860262776.83526999322.38129030992.60129030990.60763263253.20892294240.60116444873.20245475850.230.309351.82927679340.16911054750.30580679446.46516890252.13039800912.36039800910.51830151912.87869952820.51278425542.87318226440.240.32641.86533230610.17498222650.31284505316.12745098041.91364197332.15364197330.44485461342.59849658670.4401191842.59376115730.250.343751.90138781890.18078899870.31972848745.81818181821.72534351021.97534351020.38399794782.3593414580.37991033112.35525384130.260.36141.93744333160.18653448810.32646710375.5340343111.56093454411.82093454410.33321292122.15414746530.32966590562.15060044970.270.379351.97349884440.19222205330.33306996755.27217609071.41670951741.68670951740.29055332991.97726284730.2874604211.97416993840.280.39762.00955435710.19785481220.3395453175.03018108651.28963923361.56963923360.25450055951.82413979310.25179142851.82143066210.290.416152.04560986990.20343566290.34590066134.80595938961.1772296461.4672296460.22385891811.69108856410.22147596411.68870561010.30.4352.08166538260.20896730260.35214286334.59770114941.07741365241.37741365240.19767906891.57509272120.19557479651.57298844890.350.533752.26194294640.23596970070.38185999373.74707259950.71562451921.06562451920.11165878171.17728330080.1104701861.17609470520.40.642.44222051020.26205659860.40950895183.1250.49773827730.89773827730.06752898710.96526726430.06681014830.96454842560.50.8752.80277563770.31219052580.46019985712.28571428570.26628388360.76628388360.02860671030.79489059390.0283021950.79458607860.61.143.16333076530.36037963920.50641531461.75438596490.15687411390.75687411390.01391725610.770791370.01376910840.77064322230.71.4353.52388589280.40722090430.54939753861.3937282230.09900501320.79900501320.00746276490.80646777820.00738332460.8063883378CURVASLos tirantes calculados por este metodo son:para S1=0.25para S2=0.20y1=26.85y10=18y2=22.7y11=18.3y3=20.7y12=18.52y4=19.7y13=18.68y5=19y14=18.79y6=18.6y15=18.85y7=18.35y16=18.9y8=18.2y17=18.93y9=18.1y10=183.-CALCULO DEL COLCHON AMORTIGUADORSe efectua utilizando el metodo grafico, que consiste en trazar las curvas Elevaciones vs tirantes, asi como tambien la curva elevaciones vs tirantes conjugadas menores en la poza de amortiguacion.A.-Calculo de las curvas elevaciones vs tirantesDonde se produce el tirante y17=0.1893mse tiene:y17=0.1893mEstacion=0+85A=0.24m^2v=8.23m/shv=3.45m

cota de fondo=1505.5msnmE=3.64mLa elevacion de la linea de energia en la estacion 0+085 sera:cota de fondo + Energia especifica=1505.5+3.64=1509.14Elevacion=1509.14-E123456y (m)A (m^2)v=Q/A (m/s)v^2/2*g (m)y+v^2/2*g (m)Elevacion0.130.155412.8748.4488.5781500.5630.140.169411.8067.1057.2451501.8960.150.1837510.8846.0386.1881502.9520.160.198410.0815.1795.3391503.8010.170.213359.3744.4794.6491504.4920.180.22868.7493.9014.0811505.0590.190.244158.1923.4203.6101505.530B.-Calculo de la curva elevaciones vs tirantes conjugados menoresSe elabora la tabla que sigue, usando las siguientes expresiones:TIRANTES-FUERZA ESPECCIFICA12345678Y (m)A (m^2)V=Q/A (m/s)Q*V (m^4/s^2)Q*V/g (m^3) (m)A* (m^3)M (m^3)

2.209.460.210.420.040.827.747.790.050.0537.2174.427.590.020.007.590.100.1217.3934.783.550.050.013.550.200.267.6915.381.570.090.021.590.300.444.609.200.940.130.061.000.400.643.136.250.640.180.110.750.500.882.294.570.470.210.190.650.601.141.753.510.360.250.290.650.701.441.392.790.280.290.420.700.801.761.142.270.230.330.580.810.902.120.951.890.190.360.770.961.002.500.801.600.160.401.001.161.102.920.691.370.140.441.271.411.203.360.601.190.120.471.581.711.303.840.521.040.110.511.942.051.404.340.460.920.090.542.352.451.605.440.370.740.070.613.333.401.806.660.300.600.060.684.544.602.008.000.250.500.050.756.006.05Elevacion de la linea de energia es:cota de fondo+y+v^2/2g=1503+0.88+0.048912479Elevacion de la linea de energia:1503.928912479mELEAVACION-TIRANTES CONJUGADOS MENORES1234567y1 (m)Y2 (m)A2 (m^2)V2=Q/A (m/s)V2^2/2g (m)Y2+V2^2/2g (m)Elev. Del fondo del tanque 1503.9289-(6)

0.11.645.67440.35250.00631.64631502.28260.21.163.17840.62920.02021.18021502.74870.30.92.11500.94560.04560.94561502.98330.40.751.59381.25490.08030.83031503.09860.50.661.31341.52280.11820.77821503.1507TIRANTES VS. ELEVACIONES FONDO TANQUE4.-COMPROBACION DEL FUNCIONAMIENTO DEL COLCHON:Se comprueban dos cosas.a)Se aplica la ecuacion de la cantidad de movimiento, debiendo cumplirse que:Para:y1=0.145A1=0.1765375V1=11.3290377399y2=1.373A2=4.2006935v2=0.4761118611Se obtiene:2.3352896276=5.86462b)Se debe cumplir tambien la siguiente relacion:y2+V2^2/2gAltura del colchon + yn+Vn^2/2gAltura del colchon=1503-1502.525=0.475my2=1.38455364451.403912479Se cumple la relacion, pero para dar mayor seguridad al funcionamiento hidraulico del colchon,consideraremos un 40% de ahogamiento por lo que se tendra que bajar el nivel del colchon.Vmax=1.5veces la velocidad media al principio de la trayectoria(estacion 0+085)tg()=pendiente del canal Sluego:En el problema se tiene:S=0.2v=8.2287g=9.81y17=0.1893Reemplazando valores se obtiene:y=0.20X+9.81*x^2*(1+0.04)/4.5*8.23^2y=-0.2x-0.0334832259X^2COORDENADAS DE LA TRAYECTORIA EN LA RAPIDA123456XX^20.2X0.0334832259X^2(3)-(4)ELEVACIN0000.000.001505.500.50.250.10.01-0.111505.39110.20.03-0.231505.271.52.250.30.08-0.381505.12390.60.30-0.901504.604.520.250.90.68-1.581503.926361.21.21-2.411503.097.556.251.51.88-3.381502.127.2953.14411.4581.78-3.241502.26

En la trayectooria se distinguen 2 puntos muy importantes:P.C=Punto de comienzo, que en este caso seria la cota de las estacion 0+085(1505.50)P.T=Punto terminal, como regla practica se recomienda que esta cota debe ser la misma que la de la superficie normal del agua en el canal aguas abajo o menor.La profundidad final del colchon ser:0.4E2=0.5538214578E2+0.4*E2=1.3845536445+0.5538214578=1.9383751022mCota del colchon:1503.9289-1.9383751022=1501.9905248978msnmProfundidad:1503-1501.9905248978=1.01mPORCENTAJE DE AHOGAMIENTO%Ahog.=1.9383751022-1.3845536445=0.4=40%1.3845536445por razones constructivas se adoptara la profundidad del colchon igual a 1.00m%Ahog.=1.9289-1.3845536445=0.3931565655=39%1.38455364455.-LONGITUD DEL SALTO HIDRAULICOPara un colchon sin obstaculos, comunmente se toma:Lr=6(Y2-Y1)Lr=7.368mTomamos Lr=7.5m6.- CALCULO DE LA TRAYECTORIAEsta dada por la formul:Altura de la trayectoria sera aproximadamentey=HH:diferencia de nivel entre el canal agua arriba y abajo y su longitud es:3X=2*Y0.666+S