An experimental investigation on the speed of sand flow through a fixed porous bed

In this study, we document several experiments that investigate the speed of the flow of fine sand through a fixed porous bed of packed glass beads under various conditions, including the height of the sand column ( H ) and porous bed ( h ) and the diameter of the glass beads ( D ) and sand grains ( d ). The experiments are conducted with glass beads packed at a constant density and sand at a different dry bulk density. The results show that the height of the sand does not affect the speed of the sand flow. The speed of the sand flow ( v ) decreases with an increase in h until h approaches a certain value. An equation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{v}}={\boldsymbol{a}}\sqrt{{\bf{g}}{\boldsymbol{D}}}{\bf{l}}{\bf{n}}(\frac{{\boldsymbol{D}}}{{\boldsymbol{kd}}})$$\end{document} v = a g D l n ( D kd)is proposed, where a and k are the experimentally determined coefficients. Moreover, the flow of sand through a fixed porous bed could be regarded as parallel flow through multiple pipes, and therefore, the relationship between D and the number and diameter of pipes, N and D p , are discussed. Further investigations are needed for the result that the flow of sand through a porous bed or multiple parallel pipes cannot be simplified to flow through one orifice with a certain diameter.