### Abstract

The emptying efficiency/depletion ratio firstly proposed by Hanin (1999) [7] has proven analytically that tanks with cross-sectional area expressed in the form of a higher-order polynomial of the liquid head (denoted as higher-order tank in this paper) are effective in reducing the efflux time. In this study, a Lagrangian particle method (moving particle semi-implicit (MPS) method) is used to simulate the draining process of water particles in tanks of various geometries (n-order tank), mainly to improve the physical understanding on why higher-order tanks are more effective in draining water particles. Analytically, it is shown that the reduction in efflux time is associated with the decrease of J-factor introduced in this paper. It can be proven that there exists a theoretical minimum of the J-factor (hence the efflux time) as the order (n) approaches infinity. In cases where the deformation of the free surface is mild while draining, the predicted time evolution of the water head agrees quite well with that of Torricelli's law. Generally, the simulated averaged discharge coefficient increases with the order of the shape function used to describe the cross-sectional area of the tank, which may explain the effectiveness of higher-order tanks. From the Lagrangian particle simulation, the use of the flow sequence technique has revealed that water particles with identical range of drainage time form an inverted U-band (draining layer) in lower-order tanks. Interestingly, as the order (n) increases, flattening of such draining layers is observed and this has led to a reduction of efflux time of water particles especially for those near the side-walls.

Original language | English |
---|---|

Pages (from-to) | 1437-1451 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 66 |

Issue number | 8 |

DOIs | |

Publication status | Published - 01 Nov 2013 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*66*(8), 1437-1451. https://doi.org/10.1016/j.camwa.2013.08.018