Analytical Model of Capillary Suction Velocity of a Pipe with Multiple Sizes

Abstract

Absorption of water in concrete is often described by simple linear water uptake vs. square-root-of-time law. This model based on the classical capillary model derived from the Hagen-Poiseuille’ flow which travel on a single pipe dimension. However, in cement-like material concrete, the pore structure is complex, including for example, variable pore radius and complicated topological changes. In this work, an analytical velocity model of Hagen Poiseuille’s flow on a pipe with multiply sizes is constructed. This model takes the pipe geometry as described by two sets of parameters α_i and β_i;i=1,2…,N into account. In addition, a numerical study of other flow models using Navier Stokes and Stokes models has been conducted. The analytical model is in good agreement with the numerical models at a series of different pipe geometry sizes.