Aula 12_20142_Exemplo 6_3_Porto_2006 MODIF

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Exemplo 6.3_Porto
	e [m]	n [m²/s]	g [m/s²]	n
alasimoes: Expoente de Q na equação de resistência.				Prof. André Luiz Andrade Simões
	0.0000015	1.0E-06	9.8	2
					1	2	3	4	5	6	7	8	9	10	11	12
								1									2									3									4									5									6									7									8									9
	Nó	Cotas	Qnó		Anel 1			ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO									ITERAÇÃO
		[m]	[L/s]		Trecho	D	L	Qa	Qa	V	Re	e/D	f
alasimoes: alasimoes:
Equação de Swamee (1993)	
alasimoes: Expoente de Q na equação de resistência.										hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ
	Reservatório	470.8				[m]	[m]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]
	1	463.2	0		1	0.15	1850	25	0.025	1.41	2.1E+05	1.00E-05	0.0154	19.45	778.0084625338	-0.007296553	17.70	0.02	1.00	1.5E+05	1.00E-05	0.0165	10.42	588.8283169509	-0.003938212	13.77	0.01	0.78	1.2E+05	1.00E-05	0.0174	6.63	481.4217876253	0.0005587454	14.32	0.01	0.81	1.2E+05	1.00E-05	0.0172	7.12	496.9514259981	-0.0002960943	14.03	0.01	0.79	1.2E+05	1.00E-05	0.0173	6.86	488.7351388433	-0.0000022665	14.03	0.01	0.79	1.2E+05	1.00E-05	0.0173	6.85	488.6721309318	-0.0000321048	13.99	0.01	0.79	1.2E+05	1.00E-05	0.0173	6.83	487.7794464149	-0.0000071191	13.99	0.01	0.79	1.2E+05	1.00E-05	0.0173	6.82	487.581450106	-0.0000049624	13.98	0.01	0.79	1.2E+05	1.00E-05	0.0173	6.82	487.4434253061	-0.0000018272
	2	460.2	10		6
alasimoes: Este trecho é compartilhado pelos anéis.	0.1	850	10	0.01	1.27	1.3E+05	1.50E-05	0.0171	12.02	1201.7623610157	-0.01115	-1.15	-0.00	-0.15	1.5E+04	1.50E-05	0.0280	-0.26	225.8507385029	-0.0046274064	-5.77	-0.01	-0.74	7.4E+04	1.50E-05	0.0191	-4.49	776.9953579752	0.0013443981	-4.43	-0.00	-0.56	5.6E+04	1.50E-05	0.0203	-2.80	631.254560045	-0.0003520993	-4.78	-0.00	-0.61	6.1E+04	1.50E-05	0.0199	-3.20	670.1232446749	0.000067652	-4.71	-0.00	-0.60	6.0E+04	1.50E-05	0.0200	-3.12	662.6972073943	-0.0000237677	-4.74	-0.00	-0.60	6.0E+04	1.50E-05	0.0200	-3.15	665.3083585315	0.0000021589	-4.74	-0.00	-0.60	6.0E+04	1.50E-05	0.0200	-3.15	665.0712781882	-0.0000020846	-4.74	-0.00	-0.60	6.0E+04	1.50E-05	0.0200	-3.15	665.3001969799	-0.0000002158
	3	458.9	8		7	0.2	650	-10	-0.01	-0.32	6.4E+04	7.50E-06	0.0197	-0.33	33.1039161654	-0.007296553	-17.30	-0.02	-0.55	1.1E+05	7.50E-06	0.0176	-0.88	51.0018061007	-0.003938212	-21.23	-0.02	-0.68	1.4E+05	7.50E-06	0.0168	-1.28	60.0688826097	0.0005587454	-20.68	-0.02	-0.66	1.3E+05	7.50E-06	0.0169	-1.22	58.8014986845	-0.0002960943	-20.97	-0.02	-0.67	1.3E+05	7.50E-06	0.0169	-1.25	59.4738433438	-0.0000022665	-20.97	-0.02	-0.67	1.3E+05	7.50E-06	0.0169	-1.25	59.4789836205	-0.0000321048	-21.01	-0.02	-0.67	1.3E+05	7.50E-06	0.0169	-1.25	59.5517844512	-0.0000071191	-21.01	-0.02	-0.67	1.3E+05	7.50E-06	0.0169	-1.25	59.5679250881	-0.0000049624	-21.02	-0.02	-0.67	1.3E+05	7.50E-06	0.0169	-1.25	59.5791754592	-0.0000018272
	4	461.2	5		8	0.2	850	-15	-0.015	-0.48	9.5E+04	7.50E-06	0.0181	-0.89	59.5645960304	-0.007296553	-22.30	-0.02	-0.71	1.4E+05	7.50E-06	0.0167	-1.82	81.6806941028	-0.003938212	-26.23	-0.03	-0.84	1.7E+05	7.50E-06	0.0161	-2.44	93.076162058	0.0005587454	-25.68	-0.03	-0.82	1.6E+05	7.50E-06	0.0162	-2.35	91.4780174447	-0.0002960943	-25.97	-0.03	-0.83	1.7E+05	7.50E-06	0.0162	-2.40	92.3256370378	-0.0000022665	-25.97	-0.03	-0.83	1.7E+05	7.50E-06	0.0162	-2.40	92.3321190354	-0.0000321048	-26.01	-0.03	-0.83	1.7E+05	7.50E-06	0.0162	-2.40	92.4239251514	-0.0000071191	-26.01	-0.03	-0.83	1.7E+05	7.50E-06	0.0162	-2.40	92.4442801312	-0.0000049624	-26.02	-0.03	-0.83	1.7E+05	7.50E-06	0.0162	-2.41	92.4584681379	-0.0000018272
	5	457.7	10										Soma	30.2433270714	2072.4393357453							Soma	7.46	947.3615556573							Soma	-1.5774076939	1411.5621902682							Soma	0.7571044798	1278.4855021723							Soma	0.01	1310.6578638998							Soma	0.0836766405	1303.180440982							Soma	0.0185816985	1305.063514549							Soma	0.012948528	1304.6649335135							Soma	0.0047680989	1304.7812658831
	6	463.2	5
	7	459.2	2
					Anel 2
	Resumo				Trecho	D	L	Qa	Qa	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ	Qa-nova	Qa-nova	V	Re	e/D	f	hf	hf/Qa	DQ
	Trecho	Q [L/s]	Q-Epanet
alasimoes: alasimoes:
upcoming...			[m]	[m]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]
	1	13.98	13.98		2	0.125	790	5	0.005	0.41	5.1E+04	1.20E-05	0.0207	1.11	221.7927010515	0.0038507364	8.85	0.01	0.72	9.0E+04	1.20E-05	0.0183	3.07	347.1481306991	0.0006891944	9.54	0.01	0.78	9.7E+04	1.20E-05	0.0180	3.51	368.4076477129	-0.0007856527	8.75	0.01	0.71	8.9E+04	1.20E-05	0.0184	3.01	344.1497955243	0.000056005	8.81	0.01	0.72	9.0E+04	1.20E-05	0.0183	3.05	345.8913769243	-0.0000699186	8.74	0.01	0.71	8.9E+04	1.20E-05	0.0184	3.00	343.7168210313	-0.0000083371	8.73	0.01	0.71	8.9E+04	1.20E-05	0.0184	3.00	343.4573205103	-0.000009278	8.72	0.01	0.71	8.9E+04	1.20E-05	0.0184	2.99	343.1684833878	-0.0000028778	8.72	0.01	0.71	8.9E+04	1.20E-05	0.0184	2.99	343.0788815511	-0.0000016114
	2	8.72	8.72		3	0.100	700	-3	-0.003	-0.38	3.8E+04	1.50E-05	0.0221	-1.15	384.2976287281	0.0038507364	0.85	0.00	0.11	1.1E+04	1.50E-05	0.0303	0.13	149.3314809067	0.0006891944	1.54	0.00	0.20	2.0E+04	1.50E-05	0.0260	0.36	231.5560754335	-0.0007856527	0.75	0.00	0.10	9.6E+03	1.50E-05	0.0313	0.10	136.82747203	0.000056005	0.81	0.00	0.10	1.0E+04	1.50E-05	0.0307	0.12	144.1283353077	-0.0000699186	0.74	0.00	0.09	9.4E+03	1.50E-05	0.0315	0.10	134.9949430397	-0.0000083371	0.73	0.00	0.09	9.3E+03	1.50E-05	0.0316	0.10	133.893121914	-0.000009278	0.72	0.00	0.09	9.2E+03	1.50E-05	0.0317	0.10	132.6635818181	-0.0000028778	0.72	0.00	0.09	9.2E+03	1.50E-05	0.0317	0.10	132.2814732755	-0.0000016114
	3	0.72	0.72		4	0.100	600	-5	-0.005	-0.64	6.4E+04	1.50E-05	0.0197	-2.45	489.7976782314	0.0038507364	-1.15	-0.00	-0.15	1.5E+04	1.50E-05	0.0280	-0.18	159.6268527577	0.0006891944	-0.46	-0.00	-0.06	5.9E+03	1.50E-05	0.0360	-0.04	82.2473488115	-0.0007856527	-1.25	-0.00	-0.16	1.6E+04	1.50E-05	0.0274	-0.21	169.4481974952	0.000056005	-1.19	-0.00	-0.15	1.5E+04	1.50E-05	0.0277	-0.19	163.7663566903	-0.0000699186	-1.26	-0.00	-0.16	1.6E+04	1.50E-05	0.0273	-0.22	170.8512809435	-0.0000083371	-1.27	-0.00	-0.16	1.6E+04	1.50E-05	0.0273	-0.22	171.6904475484	-0.000009278	-1.28	-0.00	-0.16	1.6E+04	1.50E-05	0.0272	-0.22	172.6229445224	-0.0000028778	-1.28	-0.00	-0.16	1.6E+04	1.50E-05	0.0272	-0.22	172.9118927763	-0.0000016114
	4	-1.28	-1.28		5	0.100	980	-10	-0.01	-1.27	1.3E+05	1.50E-05	0.0171	-13.86	1385.5613103475	0.0038507364	-6.15	-0.01	-0.78	7.8E+04	1.50E-05	0.0189	-5.79	941.3160373111	0.0006891944	-5.46	-0.01	-0.70	7.0E+04	1.50E-05	0.0194	-4.68	857.2117687782	-0.0007856527	-6.25	-0.01	-0.80	8.0E+04	1.50E-05	0.0188	-5.95	952.9482670743	0.000056005	-6.19	-0.01	-0.79	7.9E+04	1.50E-05	0.0189	-5.86	946.1983772028	-0.0000699186	-6.26	-0.01	-0.80	8.0E+04	1.50E-05	0.0188	-5.98	954.6234943809-0.0000083371	-6.27	-0.01	-0.80	8.0E+04	1.50E-05	0.0188	-5.99	955.6269866382	-0.000009278	-6.28	-0.01	-0.80	8.0E+04	1.50E-05	0.0188	-6.01	956.7434445489	-0.0000028778	-6.28	-0.01	-0.80	8.0E+04	1.50E-05	0.0188	-6.01	957.0896848678	-0.0000016114
	5	-6.28	-6.28		6
alasimoes: Este trecho é compartilhado pelos anéis.	0.100	850	-10	-0.01	-1.27	1.3E+05	1.50E-05	0.0171	-12.02	1201.7623610157	0.0111472894	1.15	0.00	0.15	1.5E+04	1.50E-05	0.0280	0.26	225.8507385029	0.0046274064	5.77	0.01	0.74	7.4E+04	1.50E-05	0.0191	4.49	776.9953579752	-0.0013443981	4.43	0.00	0.56	5.6E+04	1.50E-05	0.0203	2.80	631.254560045	0.0003520993	4.78	0.00	0.61	6.1E+04	1.50E-05	0.0199	3.20	670.1232446749	-0.000067652	4.71	0.00	0.60	6.0E+04	1.50E-05	0.0200	3.12	662.6972073943	0.0000237677	4.74	0.00	0.60	6.0E+04	1.50E-05	0.0200	3.15	665.3083585315	-0.0000021589	4.74	0.00	0.60	6.0E+04	1.50E-05	0.0200	3.15	665.0712781882	0.0000020846	4.74	0.00	0.60	6.0E+04	1.50E-05	0.0200	3.15	665.3001969799	0.0000002158
	6	-4.74
alasimoes: Ponto de vista do anel 1			
alasimoes: Este trecho é compartilhado pelos anéis.	
alasimoes: Este trecho é compartilhado pelos anéis.	4.74										Soma	-28.37	3683.21							Soma	-2.51	1823.27							Soma	3.64	2316.42							Soma	-0.25	2234.63							Soma	0.32	2270.11							Soma	0.04	2266.88							Soma	0.04	2269.98							Soma	0.0131	2270.27							Soma	0.0073	2270.66
	7	-21.02	-21.02
	8	-26.02	-26.02
								max(p/g)	min(p/g)		Trecho 1
								24.51	15.00		p/g [m]
			Dados								22.68
		Trecho	Cota do terreno [m]		Cota piezométrica [m]		hf	Carga de pressão [mH2O]
		Nº	Montante	Jusante	Montante	Jusante	[m]	Montante	Jusante
		0	470.8	463.2	486.97	485.88	1.09	16.17	22.68
		1	463.2	460.2	485.88	479.06	6.82	22.68	18.86
		2	460.2	458.9	479.06	476.07	2.99	18.86	17.17																				Implementação por André Luiz Andrade Simões
		3	458.9	459.2	476.07	475.98	0.10	17.17	16.78																				Universidade Federal da Bahia
		4	461.2	459.2	476.20	475.98	0.22	15.00	16.78																				Revisado em 2014
		5	457.7	461.2	482.21	476.20	6.01	24.51	15.00
		6	457.7	460.2	482.21	479.06	3.15	24.51	18.86
		7	463.2	457.7	483.46	482.21	1.25	20.26	24.51
		8	463.2	463.2	485.9	483.46	2.41	22.67	20.26
		Trecho	D [m]	Q [m³/s]	V [m/s]	Re	e/D	f	L [m]	hf [m]	J [m/m]
		0	0.25	0.04	0.815	2.0E+05	0.000006	0.0155	520	1.1	0.0021040913
	Implementação por André Luiz Andrade Simões
	Universidade Federal da Bahia
	Revisado em 2014
Exemplo 6.3_Porto_Solver
	e [m]	n [m²/s]	g [m/s²]	n
alasimoes: Expoente de Q na equação de resistência.				Prof. André Luiz Andrade Simões
	0.0000015	1.0E-06	9.8	2
	Nó	Cotas	Qnó
		[m]	[L/s]		Trecho	D	L	Qa	Qa	V	Re	e/D	f
alasimoes: alasimoes:
Equação de Swamee (1993)	
alasimoes: Expoente de Q na equação de resistência.										hf	hf/Qa	DQ	NÓ	Soma
	Reservatório	470.8	40			[m]	[m]	[L/s]	[m³/s]	[m/s]	[-]	[-]	[-]	[m]	[s/m²]	[m³/s]		Q
	1	463.2	0		1	0.15	1850	10.00	0.01	0.57	8.5E+04	1.00E-05	0.0185	3.74	373.5778440194	-0.005	1	20.00
	2	460.2	10		6
alasimoes: Este trecho é compartilhado pelos anéis.	0.1	850	10.00	0.01	1.27	1.3E+05	1.50E-05	0.0171	12.02	1201.7623610157	0.00000	2	-20.00
	3	458.9	8		7	0.2	650	10.00	0.01	0.32	6.4E+04	7.50E-06	0.0197	0.33	33.1039161654	-0.005	3	-8.00
	4	461.2	5		8	0.2	850	10.00	0.01	0.32	6.4E+04	7.50E-06	0.0197	0.43	43.289736524	-0.005	4	-5.00
	5	457.7	10		2	0.125	790	10.00	0.01	0.81	1.0E+05	1.20E-05	0.0179	3.82	382.4485674658	-0.005	5	-20.00
	6	463.2	5		3	0.100	700	10.00	0.01	1.27	1.3E+05	1.50E-05	0.0171	9.90	989.6866502482	-0.005	6	-5.00
	7	459.2	2		4	0.100	600	10.00	0.01	1.27	1.3E+05	1.50E-05	0.0171	8.48	848.3028430699	-0.005	7	-2.00
					5	0.100	980	10.00	0.01	1.27	1.3E+05	1.50E-05	0.0171	13.86	1385.5613103475	-0.005
	Resumo				6
alasimoes: Este trecho é compartilhado pelos anéis.	0.100	850	10.00	0.01	1.27	1.3E+05	1.50E-05	0.0171	12.02	1201.7623610157	0
	Trecho	Q [L/s]	Q-Epanet
alasimoes: alasimoes:
upcoming...		
alasimoes: Este trecho é compartilhado pelos anéis.							Anel 1	Soma	16.52	1651.7338577245
	1	10.00	13.98					20.00				Anel 2	Soma	48.08	4807.76
	2	10.00	8.72
	3	10.00	0.72
	4	10.00	-1.28
	5	10.00	-6.28
	6	10.00
alasimoes: Ponto de vista do anel 1			
alasimoes: Este trecho é compartilhado pelos anéis.	4.74
	7	10.00	-21.02
	8	10.00	-26.02
								max(p/g)	min(p/g)		Trecho 1
								25.00	-23.81		p/g [m]
			Dados								25.00
		Trecho	Cota do terreno [m]		Cota piezométrica [m]		hf	Carga de pressão [mH2O]
		Nº	Montante	Jusante	Montante	Jusante	[m]	Montante	Jusante
		0	470.8	463.2	489.29	488.20	1.09	18.49	25.00
		1	463.2	460.2	488.20	484.46	3.74	25.00	24.26
		2	460.2	458.9	484.46	480.64	3.82	24.26	21.74																				Implementação por André Luiz Andrade Simões
		3	458.9	459.2	480.64	470.74	9.90	21.74	11.54																				Universidade Federal da Bahia
		4	461.2	459.2	462.26	470.74	-8.48	1.06	11.54
		5	457.7	461.2	448.40	462.26	-13.86	-9.30	1.06																				Revisado em 2014
		6	457.7	460.2	448.40	436.39	12.02	-9.30	-23.81
		7	463.2	457.7	448.07	448.40	-0.33	-15.13	-9.30
		8	463.2	463.2	447.6	448.07	-0.43	-15.56	-15.13
		Trecho	D [m]	Q [m³/s]	V [m/s]	Re	e/D	f	L [m]	hf [m]	J [m/m]
		0	0.25	0.04	0.815	2.0E+05	0.000006	0.0155	520	1.1	0.0021040913
																																																																																																																												Implementação por André Luiz Andrade Simões
																																																																																																																												Universidade Federal da Bahia
																																																																																																																												Revisado em 2014
Anel 1
Anel 2
Use o solver. Se não convergir, clique em Opções (botão existente na janela do solver) e escolha "Usar escala automática".
Observem que esse cálculo também pode ser realizado com o solver.
Vmax
					D	Vmáx	Qmáx
					[mm]	[m/s]	[L/s]
					50	0.68	1.33
					60	0.69	1.95
					75	0.71	3.15
					100	0.75	5.89
					125	0.79	9.66
					150	0.83	14.58
					200	0.90	28.27
					250	0.98	47.86
					300	1.05	74.22
					350	1.13	108.24
					400	1.20	150.80
					500	1.35	265.07
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