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The predicted pressure evolutions at T1 for Case 1 (V₀ = 0.0278 m/s) by the three elastic models and by the three viscoelastic models shown in Figures 18 and 19, respectively, and the corresponding experimental data are similar to those for Case 2, but the corresponding pressure amplitudes decrease because the initial velocity decreases; the predicted pressure transients at T1 for Case 3 (V₀ = 0.9946 m/s) by the three elastic models and by the three viscoelastic models shown in Figures 20 and 21, respectively, and the corresponding experimentals are also similar to those for Case 2, but the corresponding amplitudes increase due to higher initial velocity. Similarly, the comparisons show that the SF, the CB-UF and the MIAB-UF cannot capture the pressure transient, whereas the SF-VE, the CB-UF-VE and the MIAB-UF-VE can do so accurately. The phase relations between the pressure head, the retarded strain and the velocity changes at T1 predicted by the three viscoelastic models in Figures 22(a), 23(a), 24(a), 25(a), 26(a) and 27(a), and the phase synchronization of the pressure head and the elastic strain in Figures 22(b), 23(b), 24(b), 25(b), 26(b) and 27(b) are similar to those for Case 2. Figures 28 and 29 show that the periodic decay evolutions of the predicted total strain for Cases 1 and 3 are similar to those for Case 2, but the maximum strains shown in Table 3 are correspondingly much smaller due to lower initial velocity for Case 1, and much larger due to higher initial velocity for Case 3.

Table 3

Maximum total strains at T1 by the three viscoelastic models for Cases 1–3

Case no.	Maximum total strains predicted by the three viscoelastic models (–)
Case no.	SF-VE	CB-UF-VE	MIAB-UF-VE
1	4.05E-5	4.21E-5	4.04E-5
2	7.57E-4	7.84E-4	7.56E-4
3	1.63E-3	1.68E-3	1.62E-3

Case no.	Maximum total strains predicted by the three viscoelastic models (–)
Case no.	SF-VE	CB-UF-VE	MIAB-UF-VE
1	4.05E-5	4.21E-5	4.04E-5
2	7.57E-4	7.84E-4	7.56E-4
3	1.63E-3	1.68E-3	1.62E-3

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Figure 18

(a) Pressure head changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the elastic models. (b) The corresponding enlarged views of the areas labeled by circle.

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(a) Pressure head changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the elastic models. (b) The corresponding enlarged views of the areas labeled by circle.

Figure 19

(a) Pressure head changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the viscoelastic models. (b) The corresponding enlarged views of the areas labeled by circle.

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(a) Pressure head changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the viscoelastic models. (b) The corresponding enlarged views of the areas labeled by circle.

Figure 20

(a) Pressure head changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the elastic models. (b) The corresponding enlarged views of the areas labeled by circle.

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(a) Pressure head changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the elastic models. (b) The corresponding enlarged views of the areas labeled by circle.

Figure 21

(a) Pressure head changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the viscoelastic models. (b) The corresponding enlarged views of the areas labeled by circle.

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(a) Pressure head changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the viscoelastic models. (b) The corresponding enlarged views of the areas labeled by circle.

Figure 22

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the SF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the SF-VE. (b) Pressure head and elastic strain changes.

Figure 23

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the CB-UF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the CB-UF-VE. (b) Pressure head and elastic strain changes.

Figure 24

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the MIAB-UF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the MIAB-UF-VE. (b) Pressure head and elastic strain changes.

Figure 25

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the SF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the SF-VE. (b) Pressure head and elastic strain changes.

Figure 26

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the CB-UF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the CB-UF-VE. (b) Pressure head and elastic strain changes.

Figure 27

(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the MIAB-UF-VE. (b) Pressure head and elastic strain changes.

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(a) Pressure head, retarded strain and velocity changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the MIAB-UF-VE. (b) Pressure head and elastic strain changes.

Figure 28

Total strain changes upstream the valve (T1) for Case 1 (V0 = 0.0278 m/s) by the viscoelastic models.

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Total strain changes upstream the valve (T1) for Case 1 (V₀ = 0.0278 m/s) by the viscoelastic models.

Figure 29

Total strain changes upstream the valve (T1) for Case 3 (V0 = 0.9946 m/s) by the viscoelastic models.

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Total strain changes upstream the valve (T1) for Case 3 (V₀ = 0.9946 m/s) by the viscoelastic models.

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