DISEO DE RAPIDACALCULO DE UNA RAPIDA1.- DISEO DEL CANAL AGUAS ARRIBATenemos los siguientes datos, para el canal.Z =2.00C.R aguas arriba =84.7m.s.n.mb =0.9n =0.014S =0.001Q =7.14 m/sQ x n / (s 1/2) = A x (R2/3) = [A5/3] / [P2/3]Si se sabe que:A =(b x Yn) + (Z x Yn)P =b + [2 x Yn x (1 + Z)1/2]Q x n / (s1/2) = A x ( R2/3)3.160= (A5/3) / (P2/3)Iterando tenemos :Yn =0.97Yn =1.3619766827Con este tirante remplazamos en las formulas y obtenemos:Area =4.936 mPerimetro=6.9909448927Radio H. =0.7060190087Espejo =6.3479067309V =1.446 m/shv =0.1065981183E=Yn+hv=1.4685748011Calculo de borde Libre .BL=0.3*Yn=0.4539922276(max.)Usaremos :BL =0.5Resultados:T =6.3479067309BL=0.5Yn=1.3619766827b =0.92.- DISEO DE LA TRANSICION ENTRE CANAL Y RAPIDA =12.5Longitud de Transicin de entrada :tan =0.222Tc =Tr =LT =( TC - TR)*Cot /20.9LT =14.26555570033.- DISEO HIDRAULICO DE LA RAPIDACaractersticas de la RpidaCon la ayuda del perfil del terreno se definieron las siguientes carctersticas:Pendiente S1=0.115Pendiente S2=0.080Tramo L =69.290mTramo inf. L2=0.000mLong. Total =69.290n =0.000(revestido con concreto)b =0.014mz =0.000(seccin de la rpida rectangular)entonces:Tirante Crtico para canal trapezoidal:Q^2/g=((b*Yc+Z*Yc^2))^3b + 2ZYciterando Yc=0.8355.2 =0.0entonces:Yc =0.835Ac =0.012 mVc =610.607 m/shvc=19022.518Ec =19023.3525548292T =0.014Clculo de los tirantes de Escurrimiento en la RpidaA la longitud horizontal69.29se le ha dividido en20tramos, cada una de3.4645Las longitudes inclinadas sern:a) Para pendientes S1=0.115L =(h1^2+L^2)h =0.115h1 =0.398L =3.48733376013.4645b) Para pendientes S2=0.080L =(h2^2+L^2)h =0.080h2 =0.277L =3.47554110773.4645Se aplica el teorema de Bernoulli, mediante el mtodo de incrementos finitos:Confeccionamos la tabla 1.0, teniendo en cuenta que:h1 + Y1 + V1^2/2g = Y2 + V2^2/2g + (Vn/R^(2/3))^2*L..(A)El valor de la energa es :E = Y +V^2/2gPor lo tanto el Bernoulli debe cumplirse para la igualdad:h1 + E1 = E2 + hf(1-2)AC DEelev. =84.7s1=0.1150s2=0.0799elev. =77.26elev. =77.26KM2.936KM3+01269.290.00AC DETABLA 1.0 Teorema de Bernoulli por tramos finitos para S1 =0.079912345678910YAPRR^(2/3)VV^2/2gEhf1E + hf10.1000.0010.2140.0070.0355098.5711326297.4801326297.5800.0001326297.5800.1100.0020.2340.0070.0354635.0651096113.6201096113.7300.0001096113.7300.1200.0020.2540.0070.0354248.810921039.917921040.0370.000921040.0370.1300.0020.2740.0070.0353921.978784791.408784791.5380.000784791.5380.1400.0020.2940.0070.0353641.837676682.388676682.5280.000676682.5280.1500.0020.3140.0070.0353399.048589465.547589465.6970.000589465.6970.1600.0020.3340.0070.0363186.607518084.953518085.1130.000518085.1130.1700.0020.3540.0070.0362999.160458926.464458926.6340.000458926.6340.1800.0030.3740.0070.0362832.540409351.074409351.2540.000409351.2540.1900.0030.3940.0070.0362683.459367395.424367395.6140.000367395.6140.2000.0030.4140.0070.0362549.286331574.370331574.5700.000331574.5700.2100.0030.4340.0070.0362427.891300747.728300747.9380.000300747.9380.2200.0030.4540.0070.0362317.532274028.405274028.6250.000274028.6250.2300.0030.4740.0070.0362216.770250717.860250718.0900.000250718.0900.2400.0030.4940.0070.0362124.405230259.979230260.2190.000230260.2190.2500.0040.5140.0070.0362039.429212207.597212207.8470.000212207.8470.2600.0040.5340.0070.0361960.989196197.852196198.1120.000196198.1120.2700.0040.5540.0070.0361888.360181933.811181934.0810.000181934.0810.2800.0040.5740.0070.0361820.918169170.597169170.8770.000169170.8770.2900.0040.5940.0070.0361758.128157704.813157705.1030.000157705.1030.3000.0040.6140.0070.0361699.524147366.387147366.6870.000147366.6870.3500.0050.7140.0070.0361456.735108269.182108269.5320.000108269.5320.4000.0060.8140.0070.0361274.64382893.59382893.9930.00082893.9930.5000.0071.0140.0070.0361019.71453051.89953052.3990.00053052.3990.6000.0081.2140.0070.036849.76236841.59736842.1970.00036842.1970.7000.0101.4140.0070.036728.36727067.29627067.9960.00027067.9960.8000.0111.6140.0070.036637.32120723.39820724.1980.00020724.1980.9000.0131.8140.0070.036566.50816374.04316374.9430.00016374.9431.0000.0142.0140.0070.036509.85713262.97513263.9750.00013263.975Tirante en el tramo de 75 m, de s1= 0.067Entonces obtendremos 9 tirantes:Y1 =1.85Y2 =1.815Yc =0.835y =1.85Y3 =1.795h1 =0.3984175b =0.01Y4 =1.78L =3.4645z =1.5Y5 =1.765Q =7Y6 =1.76A =5.15965Y7 =1.755V =1.357Y8 =1.7470.035hf =0.0939Y9 =1.7390.02P=6.68430.015R =0.772comprobamos segn ecuacin A:0.0150.0050.40 +0.835 +19022.518 =1.850 +3875.230 +0.0000.0051.93=3877.080.0080.008TABLA 1.1 Teorema de Bernoulli por tramos finitos para S2 =0.05812345678910YAPRR^(2/3)VV^2/2gEhf2E + hf20.1000.0010.2140.0070.0355098.5711326297.4801326297.5800.0001326297.5800.1100.0020.2340.0070.0354635.0651096113.6201096113.7300.0001096113.7300.1200.0020.2540.0070.0354248.810921039.917921040.0370.000921040.0370.1300.0020.2740.0070.0353921.978784791.408784791.5380.000784791.5380.1400.0020.2940.0070.0353641.837676682.388676682.5280.000676682.5280.1500.0020.3140.0070.0353399.048589465.547589465.6970.000589465.6970.1600.0020.3340.0070.0363186.607518084.953518085.1130.000518085.1130.1700.0020.3540.0070.0362999.160458926.464458926.6340.000458926.6340.1800.0030.3740.0070.0362832.540409351.074409351.2540.000409351.2540.1900.0030.3940.0070.0362683.459367395.424367395.6140.000367395.6140.2000.0030.4140.0070.0362549.286331574.370331574.5700.000331574.5700.2100.0030.4340.0070.0362427.891300747.728300747.9380.000300747.9380.2200.0030.4540.0070.0362317.532274028.405274028.6250.000274028.6250.2300.0030.4740.0070.0362216.770250717.860250718.0900.000250718.0900.2400.0030.4940.0070.0362124.405230259.979230260.2190.000230260.2190.2500.0040.5140.0070.0362039.429212207.597212207.8470.000212207.8470.2600.0040.5340.0070.0361960.989196197.852196198.1120.000196198.1120.2700.0040.5540.0070.0361888.360181933.811181934.0810.000181934.0810.2800.0040.5740.0070.0361820.918169170.597169170.8770.000169170.8770.2900.0040.5940.0070.0361758.128157704.813157705.1030.000157705.1030.3000.0040.6140.0070.0361699.524147366.387147366.6870.000147366.6870.3500.0050.7140.0070.0361456.735108269.182108269.5320.000108269.5320.4000.0060.8140.0070.0361274.64382893.59382893.9930.00082893.9930.5000.0071.0140.0070.0361019.71453051.89953052.3990.00053052.3990.6000.0081.2140.0070.036849.76236841.59736842.1970.00036842.1970.7000.0101.4140.0070.036728.36727067.29627067.9960.00027067.9960.8000.0111.6140.0070.036637.32120723.39820724.1980.00020724.1980.9000.0131.8140.0070.036566.50816374.04316374.9430.00016374.9431.0000.0142.0140.0070.036509.85713262.97513263.9750.00013263.975De esta tabla graficamos energia vs tirante, para hallar los tirantes del segundotramo.y =1.739b =0.01Tirante en el tramo de 90 m, de s2= 0.058z =1.5Entonces obtendremos0tirantesQ =7A =4.5605275Y10 =0.3825V =1.535Y11 =0.383Y9 =1.739hf =0.1202Y12 =0.383h2 =0.27681355P=6.2841Y13 =0.383L =3.4645R =0.726Y14 =0.383Y15 =0.383Y16 =0.383Y17 =0.383y =0.3825Y18 =0.383b =0.01Y19 =0.383z =1.5Y20 =0.383Q =7A =0.224814375comprobamos segn ecuacin A:V =31.1370.28 +1.739 +0.120 =0.383 +90652.141 +0.000hf =49.46432.14 =90652.52P=1.3931R =0.1614.- Clculo del colchn amortiguadorUsaremos el mtodo grfico el cual consiste en trazar las curvas elevaciones-tirantes entre las secciones D-D y E-E y elevaciones tirantes conjugadas menoresen el tanque amortiguador. EL punto de intercepcin dar la elevacin del tanque yel tirante menor, ver FIG.4a) Clculo de la curva I :Donde se produce el tirante Y20 =1.739,se tiene :Y20 =1.739Estacin =3+012A =0.024 mV =293.19 m/sV^2/2g =4385.729y =0.315cota de fondo =77.26b =2E =4387.468z =1.5Q =7La elevacin de la linea de energa en la estacin3+012ser:A =0.7788375V =8.988cota de fondo + Energa especficahf =4.121477.26 +4387.468 =4464.728P=3.1357R =0.248Asumiendo tirantes menores a Y20, calculamos a la energa especfica para los tirantesasumidos y luego sus respectivas elevaciones respecto a la linea de energa de la estacin3+012TABLA 2.0 ELEVACIONES - TIRANTES EN EL CANAL DE LA RAPIDA123456Y(m)A (m2)V (m/s)V^2/2g (m)Y+ V^2/2gelevacin0.6000.008849.76236841.59736842.197-32377.46880.5950.008856.90337463.38537463.980-32999.25190.5900.008864.16538101.04838101.638-33636.91010.5850.008871.55138755.13138755.716-34290.98840.5800.008879.06439426.20339426.783-34962.05550.5750.008886.70840114.85840115.433-35650.70470.5700.008894.48640821.71440822.284-36357.55590.5650.008902.40241547.41941547.984-37083.25600.5600.008910.45942292.64942293.209-37828.48140.5550.008918.66243058.11243058.667-38593.93860.5500.008927.01343844.54543845.095-39380.36690.5450.008935.51844652.72244653.267-40188.5393a) Clculo de la curva II :Elaboramos tabla 3.0 a partir de la ecuacin de la cantidad de movimiento.donde:QV/g + A = M = (Y/3)*((2b+T)/(b+T))TABLA 3.0 TIRANTES - FUERZA ESPECFICAYAV = Q/AQVQV/gTA*M(m)(m2)(m/s)(m4/s2)(m3)(m)(m)(m3)(m3)0.050.00110197.14372787.2067427.2660.010.02500.00007427.2660.100.0015098.57136393.6033713.6330.010.05000.00013713.6330.300.0041699.52412131.2011237.8780.010.15000.00061237.8780.400.0061274.6439098.401928.4080.010.20000.0011928.4090.500.0071019.7147278.721742.7270.010.25000.0018742.7280.600.008849.7626065.600618.9390.010.30000.0025618.9410.700.010728.3675199.086530.5190.010.35000.0034530.5220.800.011637.3214549.200464.2040.010.40000.0045464.2090.860.012591.4824221.996430.8160.010.43100.0052430.8210.900.013566.5084043.734412.6260.010.45000.0057412.6321.000.014509.8573639.360371.3630.010.50000.0070371.3701.200.017424.8813032.800309.4690.010.60000.0101309.4791.300.018392.1982799.508285.6640.010.65000.0118285.6761.400.020364.1842599.543265.2590.010.70000.0137265.2731.600.022318.6612274.600232.1020.010.80000.0179232.1201.800.025283.2542021.867206.3130.010.90000.0227206.3362.000.028254.9291819.680185.6820.011.00000.0280185.7102.200.031231.7531654.255168.8010.011.10000.0339168.8352.500.035203.9431455.744148.5450.011.25000.0438148.5892.800.039182.0921299.772132.6300.011.40000.0549132.6853.000.042169.9521213.120123.7880.011.50000.0630123.8513.400.048149.9581070.400109.2240.011.70000.0809109.305Nivel de energa en seccn E-E de fig. Acota de fondo :77.01V^2/2g =0.1065981183Y =1.3619766827Nivel de energa =78.4785748011TABLA 4 : ELEVACIN - TIRANTES CONJUGADOS MENORESY1Y2A2V2 = Q/AV2^2/2gY2+V2^2/2gElev. Del fondo del(m)(m)(m2)(m/s)(m)(m)tanque0.130.042169.95241473.66391476.6639-1398.18530.22.450.034208.10502209.57512212.0251-2133.54660.31.800.025283.25404093.51074095.3107-4016.83220.41.550.022328.94015520.48905522.0390-5443.56040.51.350.019377.67207277.35247278.7024-7200.22390.61.250.018407.88578488.30398489.5539-8411.07530.71.080.015472.089911370.863211371.9432-11293.4646Entonces de la fig 4 obtenemos :El tirante conjugado menor Y1 =0.275mElevacin del fondo de tanque =3.92msnm5.- Comprobacin del funcionamiento del colchn:a) Se aplica la ecuacin de la cantidad de movimiento, debiendose cumplirse que:Q^2/(g*A1) + A1*1 = Q/(g*A) + A22..()Para :Y1 =0.275A1 =0.004 mV 1 =1854.026 m/sT =0.014E1 =175378.4542021921 =0.138por tanteos:Y 2 =1.9A2 =0.027 mV 2 =268.346 m/sT =0.0142 =0.950entonces:Y2 = (K/(3b + 2ZY2)^(1/2)(seccin trapezoidal) ()donde:K = 6(Q/g (V1-V2)+P1)Empuje hidrostatico :P1 = bY1^2/2 + Y1^3/3P1 =0.0074616667Por lo tanto :K =6929.790En la ecuacin ()Y2 =406.1957789782En la ecuacin .()1350.413 =27.41Por ser de consideracin la diferencia entonces tomamos otro tirante Y2Si :Y 2 =2.7647A2 =0.039 mV 2 =184.417 m/sT =0.014E2 =1737.94624301272 =1.382En la ecuacin .()1350.413 =18.872OK !Por lo tanto los tirantes conjugados son :Y1 =0.275Y2 =2.7647b) Se debe cumplir tambien la siguiente relacin :Y2 + V2^2/2g Altura del colchn + Yn + Vn^2/2g.()Y2 =2.7647V 2 =184.41680575Altura del colchn =73.09Yn =1.3619766827Vn =1.45 m/sLuego :remplazando en la ecuacin ()1737.946