An Official Journal of the American Society of Thermal and Fluids Engineers

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Hydraulic Properties of Branching Pipelines with Permeable Walls

ABSTRACT

Stationary motion of a viscous incompressible liquid through a cylindrical tube with rigid permeable wall as applied to sap flow through the conducting system of plant leaves is investigated. As the liquid moves it percolates through the wall into the surrounding medium where the hydrostatic pressure is kept at a constant level. The outflow consists of two components; one depends on the pressure p inside the tube and the other is independent of p (passive and active components of the water transport, respectively). The analysis of the total hydraulic resistance of the system and distribution heterogeneity of the liquid inside the medium is carried out. For some outflow conditions the parameters of an optimal tube that provides liquid delivery at minimal total energy expenditures are investigated. It is shown that solutions of the optimization problem for the tubes both with permeable and impermeable walls lead to similar geometrical relations. In that way various hydromechanical factors can underlie similarities in construction of the long-range water transport systems in plant and animal tissues.