A Mathematical Description of Water Flow through Plant Tissues

Non-steady-state flow of water through plant tissues is a complex process to study because of the number of hydraulic parameters involved and the geometric intricacy of the tissues. The importance of understanding water flow through plants together with the increasing power of computers and numerical solution methods have suggested revisiting earlier mathematical approaches to the transport process. In this paper, equations are derived for a one-dimensional case including terms for resistance and capacitance with particular consideration of an inductance term for kinetic energy used in the acceleration of water. Calculations of power into each component for several test cases suggest that the inductance term is not likely to be very important for flow in plant tissues. Lastly, equations for a three-dimensional case are derived and expressed for rectangular, cylindrical, and spherical coordinate systems.