Rigid-Column Model for Rapid Filling in a Partially Filled Horizontal Pipe

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Abstract
Uncontrolled filling is often seen in storm sewers under wet weather conditions. This study develops a rigid-column model for rapid filling in a partially filled horizontal pipe with entrapped air. Numerical solutions compare very well with experimental measurements from earlier studies. Parametric analysis is conducted by nondimensionalizing the governing equations, and two typical scenarios are numerically investigated in detail: one with a fixed air pocket length and the other with a fixed air pocket volume under different tailwater depths. For the cases with a fixed air pocket length, the peak pressure becomes greater as the tailwater depth increases when the length ratio of the water column and the air pocket is large, whereas the trend is reversed when the length ratio is small. And the critical length ratio is system-dependent. In cases with a fixed air volume, the peak pressure is monotonically reduced with the increase in the tailwater depth. The proposed model can also be adapted for rapid filling with ventilation and surges in closed-conduit flows.

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