Since the pipeline in this case rises uniformly in profile, was adopted to calculate the analytical size of the air vessel, and Table 2 shows the corresponding size parameters of the vessel. In addition, in Figures 4 and 5, the theoretical result for the amplitudes of the bottom pressure of the vessel and amplitudes of the water depth of the vessel are given. In the numerical computation, the analytical size of the air vessel is adopted, and the area of the impedance orifice is 0.5 m, as large as 20% of the pipeline's (Gong *et al.* 2013), and the orifice-metering coefficient is 0.6. Pipe friction and throttling were considered during the numerical computation, and the numerical result is shown in Figures 4 and 5.

Table 2

Total volume (m^{3})
. | Water volume (m^{3})
. | Gas volume (m^{3})
. | Cross-sectional area (m^{2})
. | Water height (m) . | Gas height (m) . | Water–gas ratio . |
---|---|---|---|---|---|---|

89 | 16 | 73 | 14.6 | 1.1 | 5.0 | 0.22 |

Total volume (m^{3})
. | Water volume (m^{3})
. | Gas volume (m^{3})
. | Cross-sectional area (m^{2})
. | Water height (m) . | Gas height (m) . | Water–gas ratio . |
---|---|---|---|---|---|---|

89 | 16 | 73 | 14.6 | 1.1 | 5.0 | 0.22 |

Table 3

Results . | Initial pressure (m) . | Maximum pressure (m) . | Minimum pressure (m) . | Initial water depth (m) . | Maximum water depth (m) . | Minimum water depth (m) . |
---|---|---|---|---|---|---|

Theoretical | 70.0 | 90.0 | 50.0 | 1.1 | 2.1 | 0.1 |

Numerical | 70.0 | 83.6 | 54.2 | 1.1 | 1.7 | 0.2 |

Results . | Initial pressure (m) . | Maximum pressure (m) . | Minimum pressure (m) . | Initial water depth (m) . | Maximum water depth (m) . | Minimum water depth (m) . |
---|---|---|---|---|---|---|

Theoretical | 70.0 | 90.0 | 50.0 | 1.1 | 2.1 | 0.1 |

Numerical | 70.0 | 83.6 | 54.2 | 1.1 | 1.7 | 0.2 |

Figure 4

Figure 5

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