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A Simpler Iterative Steady State Solution of Münch Pressure-Flow Systems Applied to Long and Short Translocation Paths

^a Department of Botany, University of Toronto, Toronto, Canada M5S 1A1

A simple steady state iterative solution of Münch pressure-flow in unbranched sieve tubes containing only water and sucrose is derived. The iterative equations can be solved on a programmable desk calculator. Solutions are presented for steady state transport with specific mass transfer rates up to 1.5 x 10^–5 mole second^–1 centimeters^–2 (= 18.5 grams hour^–1 centimeters^–2) over distances in excess of 50 meters. The calculations clearly indicate that a Münch pressure-flow system can operate over long distances provided (a) the sieve tube is surrounded by a semipermeable membrane; (b) sugars are actively loaded in one region and unloaded at another; (c) the sieve pores are unblocked so that the sieve tube hydraulic conductivity is high (around 4 centimeters² second^–1 bar^–1); (d) the sugar concentration is kept high (around one molar in the source region); and (e) the average sap velocity is kept low (around 20-50 centimeters hour^–1). The dimensions of sieve cells in several species of plants are reviewed and sieve tube hydraulic conductivities are calculated; the values range from 0.2 to 20 centimeters² second^–1 bar^–1. For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 x 10^–7 centimeters second^–1 bar^–1 or greater.

² Present address: Department of Physics, Ohio State University, Columbus, Ohio.

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