Posição de início do ressalto hidráulico afogado

Wiest, Rafael André; Steinke Júnior, Renato; Teixeira, Eder Daniel; Prá, Maurício Dai; Saliba, Aloysio Portugal Maia; Marques, Marcelo Giulian

Rafael André Wiest

Companhia Estadual de Geração e Transmissão de Energia Elétrica, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-4687-2416

Renato Steinke Júnior

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-7311-3028

Eder Daniel Teixeira

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0001-7595-486X

Maurício Dai Prá

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-1858-1531

Aloysio Portugal Maia Saliba

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

https://orcid.org/0000-0002-0149-3295

Marcelo Giulian Marques

Universidade Federal do Rio Grande do Sul, Porto Alegre, RS, Brasil

https://orcid.org/0000-0002-9948-3094

E-mails: rafael.wiest@ceee.com.br (RAW), renato.steinkejunior@gmail.com (RSJ), eder.teixeira@ufrgs.br (EDT), mauricio.daipra@ufrgs.br (MDP), asaliba@ehr.ufmg.br (APMS), mmarques@iph.ufrgs.br (MGM)

Rafael André Wiest: Performed the methodology and obtained the results.

Renato Steinke Júnior: Wrote and formatted the text and revised the results.

Eder Daniel Teixeira: Revised the text and obtained the results.

Mauricio Dai Prá: Contributed with technical notes and revised the text.

Aloysio Portugal Maia Saliba: Contributed with technical notes and revised the text.

Marcelo Giulian Marques: Defined the objectives, contributed with technical notes and revised the text.

Equation	Authors (year)
$\frac{T_{w}}{Y_{1} \cdot \cos (α)} = 23.5 \cdot {(1 + \frac{3}{2} E)}^{- 2} + \frac{\sqrt{2} (F r_{1} - 3)}{\tanh (\frac{5}{2} E)}$	Hager (1988)Hager, W. H. (1988). B-jump in sloping channel. Journal of Hydraulic Research, 26(5), 539-558. http://dx.doi.org/10.1080/00221688809499192. http://dx.doi.org/10.1080/00221688809499...
$\frac{x_{s j}}{Y_{2}} = [\frac{2.3}{{(\tan α)}^{0.73}} - 0.8] {(\frac{T_{w}}{Y_{2}} - 1)}^{0.75}$	Ohtsu & Yasuda (1991)Ohtsu, I., & Yasuda, Y. (1991). Hydraulic jump in sloping channels. Journal of Hydraulic Engineering, 117(7), 905-921. http://dx.doi.org/10.1061/(ASCE)0733-9429(1991)117:7(905). http://dx.doi.org/10.1061/(ASCE)0733-942...
$\frac{T_{w}}{Y_{1} \cdot \cos (α)} = \sqrt{2} e x p (- \frac{\tan α}{8.42}) E^{- [0.181 / {(\tan α)}^{0.663}]} {(F r_{1} - 1)}^{0.963} + \frac{1}{E}$	Carollo et al. (2011)Carollo, F. G., Ferro, V., & Pampalone, V. (2011). Sequent depth ratio of a B-jump. Journal of Hydraulic Engineering, 137(6), 651-658. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000342. http://dx.doi.org/10.1061/(ASCE)HY.1943-...
$\frac{T_{w}}{Y_{1} \cdot \cos (α)} = [7.9 - 10.82 \frac{k_{s}}{h_{c}}] \cdot M^{[0.73 + 1.86 \frac{k_{s}}{h_{c}}]} \cdot N^{2.37} + M$	Bejestan & Shokrian (2015)Bejestan, M. S., & Shokrian, M. (2015). Mathematical expression for the B-jump sequent depth ratio on sloping bed. KSCE Journal of Civil Engineering, 19(3), 790-795. http://dx.doi.org/10.1007/s12205-013-0434-6. http://dx.doi.org/10.1007/s12205-013-043...

Q	EL_us	EL_ds	EL_sj	x_sj	Z	α	Y₁	Fr₁	Y₂	S
(m³/s)	(m)	(m)	(m)	(m)	(m)	(º)	(m)	(m)	-	-
997.64	465.78	442.92	441.94	12.91	7.73	45.00	0.29	10.50	4.21	2.12
1004.17	465.84	444.08	443.01	13.99	8.82	45.00	0.30	9.99	4.15	2.43
1005.80	465.80	447.79	445.97	16.57	11.28	41.61	0.35	8.43	4.05	3.40
2000.00	465.67	444.26	442.68	13.38	8.20	45.00	0.60	7.25	5.83	1.76
1995.57	465.65	444.96	443.66	14.37	9.19	45.00	0.62	6.91	5.72	1.92
1995.57	465.69	445.92	444.60	15.26	10.07	43.93	0.65	6.52	5.66	2.11
1995.57	465.70	450.09	446.75	17.41	12.00	40.11	0.75	5.57	5.54	2.91
3000.00	465.74	445.36	442.83	13.25	8.08	45.00	0.90	5.89	7.05	1.61
3005.05	465.71	445.77	443.92	14.05	8.87	45.00	0.93	5.58	6.91	1.70
2995.44	465.77	448.33	445.66	15.86	10.63	42.80	1.03	4.98	6.75	2.12
3005.05	465.76	450.06	446.74	16.97	11.63	40.91	1.11	4.59	6.68	2.41
4001.03	465.75	446.16	443.06	13.12	7.94	45.00	1.20	5.11	8.07	1.51
4006.36	465.77	446.34	443.76	13.47	8.29	45.00	1.23	4.94	7.97	1.55
4011.68	465.78	447.03	444.55	14.61	9.43	45.00	1.26	4.74	7.85	1.66
4019.68	465.77	450.05	446.72	16.57	11.28	41.61	1.45	4.07	7.66	2.10
5995.32	465.71	447.82	444.02	13.62	8.45	45.00	1.82	4.08	9.64	1.43
6007.67	465.72	449.67	446.78	16.26	11.00	42.41	2.10	3.44	9.23	1.70
6020.03	465.72	450.32	446.81	15.95	10.72	42.66	2.10	3.44	9.22	1.77
7998.56	465.73	449.55	444.68	13.68	8.50	45.00	2.43	3.53	10.97	1.42
8005.44	465.72	451.10	447.47	16.32	11.05	42.18	2.82	2.96	10.48	1.63

Q	Fr₁	S	Fr₁ . (S-1)	Equation 4	Hager (1988) Hager, W. H. (1988). B-jump in sloping channel. Journal of Hydraulic Research, 26(5), 539-558. http://dx.doi.org/10.1080/00221688809499192. http://dx.doi.org/10.1080/00221688809499...	Ohtsu & Yasuda (1991) Ohtsu, I., & Yasuda, Y. (1991). Hydraulic jump in sloping channels. Journal of Hydraulic Engineering, 117(7), 905-921. http://dx.doi.org/10.1061/(ASCE)0733-9429(1991)117:7(905). http://dx.doi.org/10.1061/(ASCE)0733-942...	Carollo et al. (2011) Carollo, F. G., Ferro, V., & Pampalone, V. (2011). Sequent depth ratio of a B-jump. Journal of Hydraulic Engineering, 137(6), 651-658. http://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0000342. http://dx.doi.org/10.1061/(ASCE)HY.1943-...	Bejestan & Shokrian (2015) Bejestan, M. S., & Shokrian, M. (2015). Mathematical expression for the B-jump sequent depth ratio on sloping bed. KSCE Journal of Civil Engineering, 19(3), 790-795. http://dx.doi.org/10.1007/s12205-013-0434-6. http://dx.doi.org/10.1007/s12205-013-043...
(m³/s)	-	-	-	(%)	(%)	(%)	(%)	(%)
997.64	10.50	2.12	11.76	3.79	-2.89	21.25	10.58	11.64
1004.17	9.99	2.43	14.29	2.99	-0.75	58.02	10.27	10.88
2000.00	7.25	1.76	5.51	-1.86	-4.36	-10.34	15.18	17.78
1995.57	6.91	1.92	6.36	-4.91	-5.90	11.08	10.63	12.49
1995.57	6.52	2.11	7.24	-6.16	-4.16	40.82	10.32	11.90
3000.00	5.89	1.61	3.59	0.77	-0.73	-18.29	25.31	29.38
3005.05	5.58	1.70	3.91	-3.34	-3.79	-5.50	19.01	22.14
4001.03	5.11	1.51	2.61	1.44	-0.53	-27.18	32.20	37.89
4006.36	4.94	1.55	2.72	0.02	-2.23	-20.24	28.81	33.87
4011.68	4.74	1.66	3.13	-3.95	-5.17	-3.16	21.10	24.69
5995.32	4.08	1.43	1.75	-0.95	-5.69	-30.15	34.66	41.67
6007.67	3.44	1.70	2.41	-9.10	-13.66	-12.34	18.28	23.12
7998.56	3.53	1.42	1.48	6.01	-2.34	-18.44	45.97	53.72
8005.44	2.96	1.63	1.86	-5.45	-16.18	29.28	23.06	28.77

Q	EL_us	EL_ds	EL_sj	x_sj	Z	S
(m³/s)	(m)	(m)	(m)	(m)	(m)	-
1005.80	465.80	447.79	445.63	16.57	11.28	3.40
1995.57	465.70	450.09	446.75	17.41	12.00	2.91
2995.44	465.77	448.33	445.66	15.86	10.63	2.12
3005.05	465.76	450.06	446.74	16.97	11.63	2.41
4019.68	465.77	450.05	446.72	16.57	11.28	2.10
6020.03	465.72	450.32	446.81	15.95	10.72	1.77

[1] E-mails: rafael.wiest@ceee.com.br (RAW), renato.steinkejunior@gmail.com (RSJ), eder.teixeira@ufrgs.br (EDT), mauricio.daipra@ufrgs.br (MDP), asaliba@ehr.ufmg.br (APMS), mmarques@iph.ufrgs.br (MGM)

Brasil

Brasil

Posição de início do ressalto hidráulico afogado

RESUMO