Modeling of water rising in systems of cylindrical capillaries of different radii

Abstract

The promotion of water in the systems of cylindrical capillaries is studied in detail. A mathematical model of the water movement in both symmetric and asymmetric capillaries connected to a vertical capillary is built. In this case, the radii of both vertical and angled capillaries are considered identical. General properties of the water movement in branching capillaries are determined on the basis of the mathematical model. In particular, the greatest promotion of water occurs in the lower level of the capillaries. It is found that the shape of plants depends on the presence of capillary systems in them. However, the capillary systems of various parts of the plants differ in radii. For example, the diameter of the central capillary of a leaf is larger than that of the capillaries in the lamina. The patterns of water movement in the branching capillary systems with capillaries of different radii are considered. An expression for calculating the critical vertical capillary height at which water does not come from the vertical capillary to the inclined capillaries is obtained. It is shown that under certain conditions, the height of water in a vertical capillary can twofold exceed the height of water in a single vertical capillary of the same radius.