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Table 5

Simulation results for the case of a stub diameter of D₃ = 15 mm for various stub lengths (L₃) and a valve closure time of t_c = 0.003 s

f	Without stub H_WS-Bmax (m)	With stub				Err_C-B(ws) (%)
f	Without stub H_WS-Bmax (m)	L₃ (m)	H_Cmax (m)	t_Cmax (s)	Formula for t_Cmax	Err_C-B(ws) (%)
Col. (1)	Col. (2)	Col. (3)	Col. (4)	Col. (5)	Col. (6)	Col. (7)
Frictionless f₁ = f₂ = f₃ = 0	212.03	0.02	225.64	0.01302	t_c + L₂/a₂ + L₃/a₃	6.42
		0.05	245.73	0.01305	t_c + L₂/a₂ + L₃/a₃	15.89
		0.10	278.14	0.01310	t_c + L₂/a₂ + L₃/a₃	31.18
		0.20	330.01	0.01320	t_c + L₂/a₂ + L₃/a₃	55.64
		0.30	362.21	0.01330	t_c + L₂/a₂ + L₃/a₃	70.83
		0.40	379.93	0.01340	t_c + L₂/a₂ + L₃/a₃	79.19
		0.50	391.51	0.01350	t_c + L₂/a₂ + L₃/a₃	84.65
		0.60	397.47	0.01360	t_c + L₂/a₂ + L₃/a₃	87.46
		0.70	401.41	0.01370	t_c + L₂/a₂ + L₃/a₃	89.32
		0.80	404.60	0.01380	t_c + L₂/a₂ + L₃/a₃	90.82
		0.90	407.28	0.01390	t_c + L₂/a₂ + L₃/a₃	92.09
		1.00	409.23	0.01400	t_c + L₂/a₂ + L₃/a₃	93.01
With friction f₁ = 0.018 f₂ = 0.018 f₃ = 0.073	196.03	0.02	208.81	0.01302	t_c + L₂/a₂ + L₃/a₃	6.52
		0.05	228.07	0.01305	t_c + L₂/a₂ + L₃/a₃	16.34
		0.10	258.97	0.01310	t_c + L₂/a₂ + L₃/a₃	32.11
		0.20	307.44	0.01320	t_c + L₂/a₂ + L₃/a₃	56.83
		0.30	336.52	0.01330	t_c + L₂/a₂ + L₃/a₃	71.67
		0.40	352.16	0.01340	t_c + L₂/a₂ + L₃/a₃	79.65
		0.50	362.18	0.01350	t_c + L₂/a₂ + L₃/a₃	84.76
		0.60	367.28	0.01360	t_c + L₂/a₂ + L₃/a₃	87.36
		0.70	370.60	0.01370	t_c + L₂/a₂ + L₃/a₃	89.05
		0.80	373.26	0.01380	t_c + L₂/a₂ + L₃/a₃	90.41
		0.90	375.45	0.01390	t_c + L₂/a₂ + L₃/a₃	91.53
		1.00	377.04	0.01400	t_c + L₂/a₂ + L₃/a₃	92.34

f	Without stub H_WS-Bmax (m)	With stub				Err_C-B(ws) (%)
f	Without stub H_WS-Bmax (m)	L₃ (m)	H_Cmax (m)	t_Cmax (s)	Formula for t_Cmax	Err_C-B(ws) (%)
Col. (1)	Col. (2)	Col. (3)	Col. (4)	Col. (5)	Col. (6)	Col. (7)
Frictionless f₁ = f₂ = f₃ = 0	212.03	0.02	225.64	0.01302	t_c + L₂/a₂ + L₃/a₃	6.42
		0.05	245.73	0.01305	t_c + L₂/a₂ + L₃/a₃	15.89
		0.10	278.14	0.01310	t_c + L₂/a₂ + L₃/a₃	31.18
		0.20	330.01	0.01320	t_c + L₂/a₂ + L₃/a₃	55.64
		0.30	362.21	0.01330	t_c + L₂/a₂ + L₃/a₃	70.83
		0.40	379.93	0.01340	t_c + L₂/a₂ + L₃/a₃	79.19
		0.50	391.51	0.01350	t_c + L₂/a₂ + L₃/a₃	84.65
		0.60	397.47	0.01360	t_c + L₂/a₂ + L₃/a₃	87.46
		0.70	401.41	0.01370	t_c + L₂/a₂ + L₃/a₃	89.32
		0.80	404.60	0.01380	t_c + L₂/a₂ + L₃/a₃	90.82
		0.90	407.28	0.01390	t_c + L₂/a₂ + L₃/a₃	92.09
		1.00	409.23	0.01400	t_c + L₂/a₂ + L₃/a₃	93.01
With friction f₁ = 0.018 f₂ = 0.018 f₃ = 0.073	196.03	0.02	208.81	0.01302	t_c + L₂/a₂ + L₃/a₃	6.52
		0.05	228.07	0.01305	t_c + L₂/a₂ + L₃/a₃	16.34
		0.10	258.97	0.01310	t_c + L₂/a₂ + L₃/a₃	32.11
		0.20	307.44	0.01320	t_c + L₂/a₂ + L₃/a₃	56.83
		0.30	336.52	0.01330	t_c + L₂/a₂ + L₃/a₃	71.67
		0.40	352.16	0.01340	t_c + L₂/a₂ + L₃/a₃	79.65
		0.50	362.18	0.01350	t_c + L₂/a₂ + L₃/a₃	84.76
		0.60	367.28	0.01360	t_c + L₂/a₂ + L₃/a₃	87.36
		0.70	370.60	0.01370	t_c + L₂/a₂ + L₃/a₃	89.05
		0.80	373.26	0.01380	t_c + L₂/a₂ + L₃/a₃	90.41
		0.90	375.45	0.01390	t_c + L₂/a₂ + L₃/a₃	91.53
		1.00	377.04	0.01400	t_c + L₂/a₂ + L₃/a₃	92.34

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