Rapid filling in horizontal partially filled pipes with entrapped air may result in extreme pressure transients. This study advanced the current understanding of dynamic behavior of entrapped air above tailwater (the initial water column with a free surface in a partially filled pipe) through rigid-column modeling and sensitivity analysis of system parameters. Water and air were considered as incompressible fluid and ideal gas, respectively, and the continuity and momentum equations for water and a thermodynamic equation for air were solved by using the fourth order Runge-Kutta method. The effects of system parameters were examined in detail, including tailwater depth, entrapped air volume, driving head, pipe friction, and relative length of entrapped air and pipe. The results indicate that the presence of tailwater can mitigate the peak pressure when with identical initial volumes of entrapped air, as it can be considered to reflect a certain amount of loss of the net driving head. However, the peak pressure can increase as much as about 45% for the cases with fixed pipe length, due to the reduction in the initial entrapped air volume. The rise time for the first peak pressure was closely related to pipe friction, whereas the oscillation period (defined as the time duration between the first and second peaks) was virtually irrelevant. The applicability of the rigid-column model was discussed, and a time scale relevant indicator was proposed. When the indicator is larger than 20, the relative difference between the peak pressure estimation and experimental measurements is generally below 5%.


  • The effects of system parameters were examined in detail under four typical scenarios with tailwater.

  • The difference between the rise time for the first peak and the period of pressure oscillation was clarified, and friction loss should be always considered.

  • A dimensionless parameter λt is proposed, which can be used to determine the applicability of rigid-column methods.

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