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

Melvin T. Tyree, A. Lawrence Christy and Jack M. Ferrier
Plant Physiology
Vol. 54, No. 4, Fiftieth Anniversary Issue, 1924-1974 (Oct., 1974), pp. 589-600
Stable URL: http://www.jstor.org/stable/4263776
Page Count: 12
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## Abstract

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 × 10-5 mole $\text{second}^{-1}\text{centimeters}^{-2}$ (= 18.5 grams $\text{hour}^{-1}\text{centimeters}^{-2}$) 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 $\text{centimeters}^{2}\text{second}^{-1}\text{bar}^{-1}$); (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 $\text{hour}^{-1}$). 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 $\text{centimeters}^{2}\text{second}^{-1}\text{bar}^{-1}$. For long distance pressure-flow to occur, the hydraulic conductivity of the sieve cell membranes must be about 5 × 10-7 centimeters $\text{second}^{-1}\text{bar}^{-1}$ or greater.

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