---
title: "Plant Gas Exchange and Sap Transport"
book: "University Biology — Year 1"
subject: biology
language: en
chapter: 24
exercises: 12
source: https://one-course.com/books/biology/3/en/chapter/24-plant-gas-exchange-and-sap-transport
---

# Chapter 24 — Plant Gas Exchange and Sap Transport

At the top of a sequoia a hundred metres above the ground, water is being pulled out of the soil by the evaporation from [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), up a column of dead [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) no wider than a hair, under a tension that would snap a steel wire of the same cross-section. There is no pump; the water is hauled by the same [hydrogen bonds](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-water) that make it cling to itself. Meanwhile, in a second set of tubes beside the first, the sugar those [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) made is flowing the other way, pushed by pressure the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) themselves generate. A plant’s two plumbing systems, the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) and the [phloem](#def-b1-plant-transport-phloem), are driven by physics that the plant sets up and then [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to run. This chapter describes the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) through which a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) trades water for carbon dioxide, the cohesion–tension mechanism that lifts sap, the vessels that carry it, the [pressure-flow mechanism](#thm-b1-plant-transport-pressureflow) that moves sugar, and the compromise between drinking and eating that governs the whole.

## 24.1 Stomata: the gate

**Definition 24.1 (Stoma, guard cells).**

A *stoma* is a pore in the epidermis of a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) (or a green stem) bounded by two *guard [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)*, kidney-shaped [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) whose walls are thickened on the side facing the pore and whose [cellulose](https://one-course.com/books/biology/3/en/chapter/10-carbohydrates#def-b1-carbohydrates-polysaccharide) microfibrils run around them like hoops. When the guard [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) take up water and swell, the hoops prevent them from widening and force them to bow apart: the pore opens. When they lose water, it closes. A [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) carries a few hundred [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) per square millimetre, mostly on its lower surface; open, their pores are one or two percent of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s area and nearly all of its gas exchange passes through them.

![A stoma seen from outside: two guard cells around the pore, set in a waxed epidermis. The pore opens when the guard cells swell.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/fig-1a37efdd6b19.svg)

*A [stoma](#def-b1-plant-transport-stoma) seen from outside: two [guard cells](#def-b1-plant-transport-stoma) around the pore, set in a waxed epidermis. The pore opens when the [guard cells](#def-b1-plant-transport-stoma) swell.*

**Proposition 24.2 (How a stoma opens, and when).**

The [guard cells](#def-b1-plant-transport-stoma) open the pore by pumping protons out ([Chapter 23](https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition#ch-b1-plant-water-minerals)), which drives potassium and chloride in and makes malate inside; the solutes lower their [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis), water follows from the neighbouring [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), and their [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) rises by a megapascal. Reversing the ion fluxes closes the pore in minutes. The signals: *light* (blue light directly on the [guard cells](#def-b1-plant-transport-stoma), and the fall of internal $\mathrm{CO_2}$ as photosynthesis starts) opens; *high internal $\mathrm{CO_2}$* closes; *water stress* closes, through the hormone *[abscisic acid](#prop-b1-plant-transport-opening)*, made in wilting [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), which triggers ion loss from the [guard cells](#def-b1-plant-transport-stoma) within minutes; dry air closes. The [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) opens its gate when carbon is worth the water and shuts it when water is scarce — and most plants do so in a daily rhythm, opening at dawn and closing at dusk, that persists for days in constant light.

![A summer day for a leaf. The stomata open at dawn, transpiration rises with the sun and the dryness of the air, and the leaf’s water potential falls as the column is put under tension; at midday, in dry air, the stomata partly close and the leaf recovers a little before the afternoon.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/fig-29d1ca42e619.svg)

*A summer day for a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs). The [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) open at dawn, transpiration rises with the sun and the dryness of the air, and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) falls as the column is put under tension; at midday, in dry air, the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) partly close and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) recovers a little before the afternoon.*

## 24.2 Lifting water: cohesion and tension

**Theorem 24.3 (The cohesion–tension mechanism).**

Water rises in the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) because it is *pulled* from above, not pushed from below. Evaporation from the wet walls of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s mesophyll [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) into the air spaces (*transpiration*) draws the water in the wall’s fine pores into curved menisci, whose surface tension puts the water behind them under tension; the tension is transmitted, through the continuous columns of water in the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) held together by cohesion (the [hydrogen bonds](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-water) of [Chapter 8](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#ch-b1-water-small-molecules)), down the stem and into the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), and lifts water from the soil. To hold a column of height $h$ against gravity requires a tension $\rho g h$ — $1\,\mathrm{MPa}$ per hundred metres — plus what is needed to overcome the friction of flow, about as much again; the columns of a tall tree are at $-2\text{ to }-3\,\mathrm{MPa}$, well within the tensile strength of water in a fine tube.

**Evidence.** Dixon and Joly (1894) showed that water in a sealed glass tube withstands tensions of many megapascals without breaking, and that a transpiring leafy branch, sealed to a tube of water dipping into mercury, lifts the mercury higher than atmospheric pressure could. Scholander’s *pressure chamber* (1965) measures the tension directly: a cut [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) is sealed into a chamber with its stalk protruding, and the gas pressure that just forces sap back to the cut surface equals the tension the sap was under — $0.5\text{ to }1\,\mathrm{MPa}$ in a well-watered crop at noon, $2\text{ to }4\,\mathrm{MPa}$ in a desert shrub or the crown of a tall tree. A dendrometer shows the trunk of a tree shrinking by day, as the tension squeezes the vessels, and swelling by night; a thermometer in the wood shows sap flowing fastest when transpiration is highest, and stopping at night. No living [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) is required: a stem killed with poison or heat still conducts. ∎

![Cohesion–tension. Evaporation at the leaf lowers the water potential there; the tension is transmitted down unbroken columns of water in the xylem and draws water from the soil. The tree does no work: the sun does.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/fig-88db1f945efd.svg)

*Cohesion–tension. Evaporation at the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) lowers the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) there; the tension is transmitted down unbroken columns of water in the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) and draws water from the soil. The tree does no work: the sun does.*

**Definition 24.4 (Xylem conduits, cavitation).**

Water travels in the *[tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)* and *vessels* of the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ([Chapter 3](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#ch-b1-flowering-plant-organization)): dead [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) emptied of their contents, their lignified walls thickened in rings and spirals that keep them from collapsing under the tension inside, joined end to end through perforations (vessels) or through pits in their side walls ([tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)). A vessel may be $20\text{ to }300\,\text{µ}\mathrm{m}$ wide and centimetres to metres long: wide tubes carry far more (flow through a tube rises as the fourth power of its radius) but are more vulnerable to *cavitation* — the sudden formation of a gas bubble in water under tension, which empties the conduit and puts it out of service. Pits between conduits stop bubbles spreading; freezing and drought both cause cavitation, and a tree’s vessels are partly refilled by [root pressure](https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition#prop-b1-plant-water-minerals-rootpressure) in spring or replaced by new wood each year.

![Xylem vessels in longitudinal section: hollow tubes whose walls are reinforced with rings and spirals of lignin against the tension of the sap they carry.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/img-170ce3f545d0.jpg)

*[Xylem vessels](#def-b1-plant-transport-xylem) in longitudinal section: hollow tubes whose walls are reinforced with rings and spirals of lignin against the tension of the sap they carry.*

![Giant sequoias. Sap reaches their crowns a hundred metres up, pulled by evaporation from the leaves through columns of water under a tension of two megapascals or more.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/img-71fc1a49ecce.jpg)

*Giant sequoias. Sap reaches their crowns a hundred metres up, pulled by evaporation from the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) through columns of water under a tension of two megapascals or more.*

**Example 24.5 (The top of the tree).**

At $100\,\mathrm{m}$ the column’s weight alone demands $1\,\mathrm{MPa}$ of tension; friction in the vessels adds as much again by day, so the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at the crown is near $-2\,\mathrm{MPa}$ and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), to draw water from it, lower than that: their [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) must close earlier in the day and their photosynthesis is slower than a low branch’s, and the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) at the top are small and thick. The height of the tallest trees, some $120\,\mathrm{m}$, is probably set by this: above it, the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cannot keep the tension without cavitating on a dry afternoon.

## 24.3 Moving sugar: pressure flow

**Definition 24.6 (Phloem, sieve tubes, source and sink).**

Sugar travels in the *phloem*, in *[sieve tubes](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)*: files of living [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) that have lost their nuclei and most [organelles](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-prokeuk) but keep their membranes, joined end to end through perforated *sieve plates*, each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) nursed by a *companion [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)* that supplies its [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) and [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp). The sap is $10\text{ to }30\,\%$ sucrose, with [amino acids](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid), ions and signalling molecules, and it flows from *sources* — photosynthesising [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), or storage [organs](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ) being emptied — to *sinks* — growing tips, [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), fruits, seeds, storage [organs](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ) being filled — at $0.5\text{ to }1\,\mathrm{m}/\mathrm{h}$, in any direction, and in different directions in different tubes.

**Theorem 24.7 (Pressure flow).**

[Phloem](#def-b1-plant-transport-phloem) sap moves by bulk flow driven by a difference of hydrostatic pressure between source and sink (Münch, 1930). At the source, companion [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) *load* sucrose into the [sieve tubes](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) against its gradient (by proton symport, from the [apoplast](https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition#def-b1-plant-water-minerals-pathways), or through [plasmodesmata](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell)); the tube’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) falls, water enters from the neighbouring [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), and the [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) rises to $1\,\mathrm{MPa}$ or more. At the sink, sucrose is *unloaded* and consumed or stored, the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) rises, water [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), and the [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) is low. Between them the sap flows down the pressure gradient through the sieve plates, carrying whatever is dissolved in it. The plant spends energy only at the two ends; the flow itself is passive.

**Evidence.** An aphid feeding on a stem inserts its stylet into a single [sieve tube](#def-b1-plant-transport-phloem); cut the aphid away and the stylet, left in place, exudes sap for hours under the tube’s own pressure — pure [phloem](#def-b1-plant-transport-phloem) sap, whose sucrose concentration and rate of flow can be measured, and whose pressure, measured with a manometer on the stylet, is about $1\,\mathrm{MPa}$ near a source and lower toward the sink. Labelled $\mathrm{^{14}CO_2}$ fed to a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) appears in the stem’s [phloem](#def-b1-plant-transport-phloem) within minutes and moves at the speed the stylet flow predicts; chilling a length of stem, which slows the living [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) but barely affects a pressure-driven flow, slows transport only slightly; poisoning the source [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s loading stops it. ∎

![Pressure flow. Loading sucrose at the source draws water in from the xylem and raises the pressure; unloading at the sink lets water out and lowers it; the sap flows between them, and the water returns by the xylem.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/fig-748969955273.svg)

*Pressure flow. Loading sucrose at the source draws water in from the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) and raises the pressure; unloading at the sink lets water out and lowers it; the sap flows between them, and the water returns by the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues).*

![An aphid feeding on a stem: its stylet, finer than a hair, is inside one sieve tube, and the pressure of the phloem drives sap into the insect — so much that the surplus leaves it as honeydew. Cut away, the stylet becomes the plant physiologist’s tap.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-transport/img-42bd4deef62e.jpg)

*An aphid feeding on a stem: its stylet, finer than a hair, is inside one [sieve tube](#def-b1-plant-transport-phloem), and the pressure of the [phloem](#def-b1-plant-transport-phloem) drives sap into the insect — so much that the surplus [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) it as honeydew. Cut away, the stylet becomes the plant physiologist’s tap.*

**Method 24.8 (Reading a translocation experiment).**

1. Feed a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) labelled $\mathrm{CO_2}$ ; sample the stem above and below at intervals: the label’s position against time gives the direction and speed of flow.
2. Girdle the stem (remove a ring of bark, which carries the [phloem](#def-b1-plant-transport-phloem) , leaving the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ): sugar accumulates above the ring and the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) starve below — the [phloem](#def-b1-plant-transport-phloem) , not the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) , carries it; the tree dies in a season.
3. Collect sap from severed aphid stylets at two heights: the drop in sucrose and in pressure between them is the gradient that drives the flow.
4. Change the sinks: remove the fruits, and the label goes to the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ; shade the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) , and it becomes a sink itself. The pattern of flow is the pattern of demand.

**Example 24.9 (A potato in two seasons).**

In summer the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) are sources and the tubers underground the sinks: sucrose flows down, is unloaded, converted to [starch](https://one-course.com/books/biology/3/en/chapter/10-carbohydrates#def-b1-carbohydrates-polysaccharide), and the tubers swell. In spring the tuber sprouts: its [starch](https://one-course.com/books/biology/3/en/chapter/10-carbohydrates#def-b1-carbohydrates-polysaccharide) is turned back to sucrose, loaded into the [phloem](#def-b1-plant-transport-phloem), and flows up to the growing shoot — the same tube, the opposite direction, because the source and the sink have changed places.

## 24.4 The compromise

**Proposition 24.10 (Water-use efficiency).**

Every [stoma](#def-b1-plant-transport-stoma) that admits carbon dioxide loses water, and the exchange is unequal: the inside of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) is saturated with vapour and the air outside is dry, while $\mathrm{CO_2}$ is at $0.04\,\%$ outside and lower inside, so the outward gradient of water is hundreds of times the inward gradient of carbon dioxide. A C3 [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) loses $200\text{ to }500\,$ molecules of water per $\mathrm{CO_2}$ fixed; a C4 [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), concentrating $\mathrm{CO_2}$ and keeping its [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) narrower, $100\text{ to }200\,$; a [CAM plant](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-c4cam), opening only at night, $20\text{ to }50\,$ ([Chapter 14](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#ch-b1-photosynthesis)). The *[water-use efficiency](#prop-b1-plant-transport-wue)* is the carbon gained per water lost, and its improvement — by closing at midday, by sunken [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) and thick [cuticles](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), by the C4 and CAM pathways — is the plant’s side of the bargain with a dry atmosphere.

**Example 24.11 (The bargain in numbers).**

A maize plant transpiring a litre and a half a day fixes some $10\,\mathrm{g}$ of carbon dioxide: $80\,\mathrm{mol}$ of water for $0.23\,\mathrm{mol}$ of $\mathrm{CO_2}$, three hundred and fifty to one. A wheat field in a season transpires five hundred tonnes of water per hectare to make eight tonnes of grain; the water is the price of the carbon, and in most of the world’s fields it is the price that limits the harvest.

## 24.5 Exercises

**Exercise 24.1 ★.**

Explain how the shape and walls of [guard cells](#def-b1-plant-transport-stoma) turn a rise of [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) into an open pore.

**Solution of Exercise 24.1.**

The wall facing the pore is thick and the microfibrils run around the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) like hoops, so a swelling [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) cannot widen but must lengthen; two such [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) joined at their ends bow outward like a pair of sausages, and the gap between them opens.

**Exercise 24.2 ★.**

State the cohesion–tension mechanism in three sentences: where the force comes from, what transmits it, what it does at the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs).

**Solution of Exercise 24.2.**

Evaporation from the wet [cell walls](https://one-course.com/books/biology/3/en/chapter/10-carbohydrates#prop-b1-carbohydrates-wall) of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) into the air spaces creates the force, as surface tension in the walls’ fine pores puts the water under tension. The cohesion of water — its [hydrogen bonds](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-water) — transmits that tension down the unbroken columns in the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues). At the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) the tension lowers the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) below the soil’s and draws water in.

**Exercise 24.3 ★.**

From the daily figure, at what hour is transpiration highest, when does the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) reach its minimum, and why do the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) partly close at midday?

**Solution of Exercise 24.3.**

About noon; about 13:00; because the dry midday air raises transpiration faster than the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) can supply water, the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s potential falls and [abscisic acid](#prop-b1-plant-transport-opening) and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s own water stress close the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) partly.

**Exercise 24.4 ★.**

Define source and sink, and say what happens at each in the [pressure-flow mechanism](#thm-b1-plant-transport-pressureflow).

**Solution of Exercise 24.4.**

Source: an [organ](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ) exporting sugar (a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), a sprouting tuber), where sucrose is loaded into the [sieve tubes](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), water follows and the [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) rises. Sink: an [organ](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ) importing it ([root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), fruit, growing tip, filling tuber), where sucrose is unloaded, water [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and the [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) falls.

**Exercise 24.5 ★★.**

Compute the tension needed to hold a column of water $30\,\mathrm{m}$ high ($\rho g h$), and the total if friction doubles it. What must the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) of the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) at that height be at least?

**Solution of Exercise 24.5.**

$1000\times 9.8\times 30 = 0.29\,\mathrm{MPa}$; with friction $0.6\,\mathrm{MPa}$: the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at $-0.6\,\mathrm{MPa}$, and the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) below that, about $-1\,\mathrm{MPa}$.

**Exercise 24.6 ★★.**

Flow through a tube scales as $r^4$. Compare the flow through one vessel of $100\,\text{µ}\mathrm{m}$ radius with that through the number of $10\,\text{µ}\mathrm{m}$ [tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) of the same total cross-section. Why do plants keep the narrow ones?

**Solution of Exercise 24.6.**

Same cross-section: 100 [tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues). Flow per tube $\propto r^4$: one vessel $10^4$ units, each [tracheid](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) 1 unit, a hundred of them 100: the vessel carries a hundred times more. [Tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) cavitate less readily and a bubble in one puts only a tiny conduit out of use; conifers, all [tracheids](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), survive freezing winters that empty a vessel-bearing tree’s wood.

**Exercise 24.7 ★★.**

[Phloem](#def-b1-plant-transport-phloem) sap at $20\,\%$ sucrose ($0.6\,\mathrm{mol}/\mathrm{L}$) has a [solute potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) of about $-1.5\,\mathrm{MPa}$. Beside a [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at $-0.5\,\mathrm{MPa}$, what [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) does the [sieve tube](#def-b1-plant-transport-phloem) reach at equilibrium? At a sink where the sap is $5\,\%$ sucrose ($\Psi_s = -0.4\,\mathrm{MPa}$) beside the same [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), what [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell)? What pressure difference drives the flow?

**Solution of Exercise 24.7.**

$\Psi_p = \Psi_{\text{xylem}} - \Psi_s = -0.5 + 1.5 = 1.0\,\mathrm{MPa}$ at the source; at the sink $-0.5 + 0.4 = -0.1\,\mathrm{MPa}$ in principle (the tube would need a slight tension, i.e. in practice about zero [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell)); the difference of about $1\,\mathrm{MPa}$ drives the flow.

**Exercise 24.8 ★★.**

An aphid stylet exudes $1\,\text{µ}\mathrm{L}$ per hour of sap at $20\,\%$ sucrose. If the [sieve tube](#def-b1-plant-transport-phloem) has a radius of $10\,\text{µ}\mathrm{m}$, compute the speed of the sap and the sugar delivered per hour.

**Solution of Exercise 24.8.**

Cross-section $\pi\times 10^{-10} = 3.1 \times 10^{-10}\,\mathrm{m}^{2}$; $1\,\text{µ}\mathrm{L}$ $= 1 \times 10^{-9}\,\mathrm{m}^{3}$ per hour: speed $3.2\,\mathrm{m/h}$ — on the high side, since the stylet’s flow is faster than the undisturbed tube’s. Sugar: $0.2\,\mathrm{mg}$ per hour.

**Exercise 24.9 ★★.**

Explain why girdling a tree kills it in a season, yet its [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) stay green for weeks after the ring is cut.

**Solution of Exercise 24.9.**

The ring removes the [phloem](#def-b1-plant-transport-phloem), so sugar can no longer reach the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), which starve and die over months, after which water uptake fails and the crown dies. The [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) in the wood is untouched, so water still reaches the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), which go on photosynthesising for weeks — and sugar accumulates above the ring, swelling the bark there.

**Exercise 24.10 ★★★.**

A [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s air spaces are saturated at $25\,{}^{\circ}\mathrm{C}$ ($23\,\mathrm{g}/\mathrm{m}^{3}$ of vapour); the outside air holds $9\,\mathrm{g}/\mathrm{m}^{3}$. $\mathrm{CO_2}$ is $0.72\,\mathrm{g}/\mathrm{m}^{3}$ outside and $0.45\,\mathrm{g}/\mathrm{m}^{3}$ inside. The two gases diffuse through the same pores, with water diffusing 1.6 times faster than $\mathrm{CO_2}$. Compute the ratio of water lost to $\mathrm{CO_2}$ gained, by mass and by molecule.

**Solution of Exercise 24.10.**

Gradients: water $23 - 9 = 14\,\mathrm{g}/\mathrm{m}^{3}$, $\mathrm{CO_2}$ $0.72 -
0.45 = 0.27\,\mathrm{g}/\mathrm{m}^{3}$; ratio of fluxes $1.6\times 14/0.27 = 83$ by mass; by molecule $83\times 44/18 = 200$ water molecules per $\mathrm{CO_2}$.

**Exercise 24.11 ★★★.**

On a hot dry afternoon a vessel cavitates. Describe what happens to the water column, to the tension in the neighbouring vessels, and to the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) it supplied; explain how pits limit the damage and how the plant recovers in the night or the spring.

**Solution of Exercise 24.11.**

The column snaps: a bubble expands to fill the vessel, the water above it is no longer pulled and the vessel stops conducting; the flow shifts to neighbouring vessels, raising their tension and their risk; the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) it supplied wilts partly. Pits between conduits are too fine for the bubble’s meniscus to pass, so the bubble stays in one conduit. At night, with tension gone, the bubble may dissolve under [root pressure](https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition#prop-b1-plant-water-minerals-rootpressure); in spring the tree grows a ring of new vessels and abandons the old.

**Exercise 24.12 ★★★.**

“A tree is a wick between the soil and the sky, with a sugar pipe running the other way.” Discuss in a paragraph: what each system carries, what drives it, where the plant spends energy, and where it spends none.

**Solution of Exercise 24.12.**

The [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) carries water and minerals upward, driven by evaporation at the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) — the sun’s energy, none of the plant’s; the [phloem](#def-b1-plant-transport-phloem) carries sugar (and signals) from sources to sinks, driven by a pressure difference the plant creates by spending [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) to load and unload sucrose at the two ends, with the flow in between free. The plant spends its energy only at the interfaces: the [proton pumps](https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition#prop-b1-plant-water-minerals-uptake) of the [guard cells](#def-b1-plant-transport-stoma) and the [phloem](#def-b1-plant-transport-phloem) loaders, and the wood it must build to hold the tension. Everything in between — the metres of pipe — runs on physics.

## 24.6 Problem: The Sequoia

**Problem 24.1.**

Weekend problem — a hundred-metre tree on a summer day: the tension at its crown, the sap’s speed, the water it moves, the sugar it sends down and the carbon it buys, ending on the xylem tension at the crown

A sequoia is $100\,\mathrm{m}$ tall with a crown of $2000\,\mathrm{m}^{2}$ of [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs). On a summer day it transpires $600\,\mathrm{L}$ of water in $12\,\mathrm{h}$ through sapwood of cross-section $0.5\,\mathrm{m}^{2}$, of which $20\,\%$ is conducting lumen. Water: $\rho = 1000\,\mathrm{kg}/\mathrm{m}^{3}$, $g =
9.8\,\mathrm{m}/\mathrm{s}^{2}$, $18\,\mathrm{g}/\mathrm{mol}$. Friction along the trunk costs as much tension as gravity. Soil [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) $-0.1\,\mathrm{MPa}$. The crown fixes $4\,\text{µ}\mathrm{mol}$ of $\mathrm{CO_2}$ per square metre of [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) per second for $12\,\mathrm{h}$; sucrose is $342\,\mathrm{g}/\mathrm{mol}$ and carries twelve carbons; [phloem](#def-b1-plant-transport-phloem) sap is $15\,\%$ sucrose by mass (density $1.06\,\mathrm{g}/\mathrm{mL}$) and flows at $0.6\,\mathrm{m}/\mathrm{h}$.

**Part I — Tension.**

1. Compute the tension needed to support the column against gravity.
2. Add the friction: what is the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) tension at the crown?
3. Compute the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) at the crown, taking $\Psi_s = 0$ for the sap.
4. What must the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’ [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) be at the crown for water to enter them? If their $\Psi_s = -2.5\,\mathrm{MPa}$ , what [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) do they have?
5. Compare with a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) at $10\,\mathrm{m}$ on the same tree ( $\Psi_s =  -1.5\,\mathrm{MPa}$ ).
6. Water in fine tubes withstands about $-30\,\mathrm{MPa}$ ; why does the tree not simply grow to $1000\,\mathrm{m}$ ?

**Part II — Flow.**

7. Compute the transpiration rate in litres per hour and in cubic metres per second.
8. Compute the conducting cross-section of the sapwood.
9. Compute the mean speed of the sap.
10. Compute the mass of water held in the conducting lumen of the trunk ( $100\,\mathrm{m}$ of it).
11. How long does a water molecule take to travel from [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to crown at that speed?
12. Compute the transpiration per square metre of [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) per hour, in grams, and per second in millimoles.
13. The sap flows down a potential gradient from $-0.1\,$ at the soil to the crown’s value of question 3 over $100\,\mathrm{m}$ . What is the gradient in megapascals per metre? How does it compare with the gravitational part alone?

**Part III — Sugar.**

14. Compute the $\mathrm{CO_2}$ fixed by the crown per day, in moles.
15. Compute the sucrose it corresponds to, in moles and in kilograms.
16. Half is respired in the crown; the rest is sent down the [phloem](#def-b1-plant-transport-phloem) . Compute the mass of sucrose translocated per day and the mass of sap that carries it.
17. Compute the volume of sap and, at $0.6\,\mathrm{m}/\mathrm{h}$ , the cross-section of [sieve tubes](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) needed to carry it in $24\,\mathrm{h}$ .
18. Compute the time for sucrose to travel from crown to [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) .
19. Compute the water-use ratio: moles of water transpired per mole of $\mathrm{CO_2}$ fixed.

**Part IV — Compromises.**

20. The [phloem](#def-b1-plant-transport-phloem) sap’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) at the crown, with $\Psi_s = -1.2\,\mathrm{MPa}$ and [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) $1.0\,\mathrm{MPa}$ : compute it and compare with the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ’s there. Which way does water move between the two, and is that consistent with loading?
21. At the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) the [phloem](#def-b1-plant-transport-phloem) sap is $5\,\%$ sucrose ( $\Psi_s =  -0.4\,\mathrm{MPa}$ ) and the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at $-0.3\,\mathrm{MPa}$ . What [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) makes the [phloem](#def-b1-plant-transport-phloem) ’s $\Psi$ equal to the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ’s? What pressure difference between crown and [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) drives the flow?
22. The [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) close at midday and transpiration halves. Recompute the friction tension and the crown [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) potential. What does the tree gain and lose?
23. In a dry year the soil falls to $-1.0\,\mathrm{MPa}$ . Recompute the crown potential with full transpiration. Can the crown [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ( $\Psi_s = -2.5\,\mathrm{MPa}$ ) keep any [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) ? What must the tree do?
24. Explain why the tallest [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) are the smallest and thickest.
25. State the result: the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) tension at the crown of a $100\,\mathrm{m}$ tree on a summer day, and the sap speed that goes with it.

**Solution of Problem 24.1.**

**1.** $1000\times 9.8\times 100 = 0.98\,\mathrm{MPa}$. **2.** About $2.0\,\mathrm{MPa}$ of tension. **3.** $\Psi = -0.1 - 2.0 = -2.1\,\mathrm{MPa}$ (soil plus the two tensions). **4.** Below $-2.1\,$: with $\Psi_s = -2.5$, [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) at most $-2.1 + 2.5 = 0.4\,\mathrm{MPa}$ — a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) near the edge of wilting all afternoon. **5.** At $10\,\mathrm{m}$: gravity $0.1\,$, friction $0.1\,$, [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) $-0.3\,\mathrm{MPa}$; [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) up to $-0.3 + 1.5 = 1.2\,\mathrm{MPa}$: comfortably turgid. **6.** At $1000\,\mathrm{m}$ the tension would be $20\,\mathrm{MPa}$ at the crown, and the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) would need $\Psi_s$ below that to draw water: impossible for living [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), and any vessel would cavitate on the first dry afternoon long before; the limit is set by [cavitation](#def-b1-plant-transport-xylem) and by the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), not by the strength of water. **7.** $50\,\mathrm{L}/\mathrm{h}$; $1.4 \times 10^{-5}\,\mathrm{m}^{3}/\mathrm{s}$. **8.** $0.2\times 0.5 = 0.1\,\mathrm{m}^{2}$. **9.** $1.4\times 10^{-5}/0.1 = 1.4 \times 10^{-4}\,\mathrm{m}/\mathrm{s}$, $0.5\,\mathrm{m}/\mathrm{h}$. **10.** $0.1\times 100 = 10\,\mathrm{m}^{3}$: ten tonnes of water hanging in the trunk. **11.** $100/0.5 = 200\,\mathrm{h}$, eight days. **12.** $50\,000/2000 = 25\,\mathrm{g}$ per square metre per hour; $25/18/3600 = 0.39\,\mathrm{mmol}$ per square metre per second. **13.** $(-2.1 + 0.1)/100 = -0.02\,\mathrm{MPa}/\mathrm{m}$, twice the gravitational gradient of $0.01\,\mathrm{MPa}/\mathrm{m}$. **14.** $2000\times 4\times 10^{-6}\times 43\,200 = 346\,\mathrm{mol}$. **15.** $346/12 = 28.8\,\mathrm{mol}$ of sucrose, $9.9\,\mathrm{kg}$. **16.** $4.9\,\mathrm{kg}$ of sucrose in $4.9/0.15 = 33\,\mathrm{kg}$ of sap. **17.** $31\,\mathrm{L}$; over $24\,\mathrm{h}$ at $0.6\,\mathrm{m}/\mathrm{h}$, flow $3.6 \times 10^{-7}\,\mathrm{m}^{3}/\mathrm{s}$ at $1.7 \times 10^{-4}\,\mathrm{m}/\mathrm{s}$: cross-section $2.2 \times 10^{-3}\,\mathrm{m}^{2}$, $22\,\mathrm{cm}^{2}$ of [sieve tubes](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) — a thin cylinder of bark. **18.** $100/0.6 = 170\,\mathrm{h}$, a week. **19.** $600\,000/18 = 33\,000\,\mathrm{mol}$ of water for $346\,\mathrm{mol}$ of $\mathrm{CO_2}$: about 96 to 1 — low for a C3 plant, because a sequoia’s crown lives in humid coastal air. **20.** $-1.2 + 1.0 = -0.2\,\mathrm{MPa}$ against the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)’s $-2.1\,$: water would move from [phloem](#def-b1-plant-transport-phloem) to [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), so the [phloem](#def-b1-plant-transport-phloem) cannot draw water from the crown’s [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at those values; loading at the crown of a tall tree must lower the [phloem](#def-b1-plant-transport-phloem)’s $\Psi_s$ further (more concentrated sap) or the crown’s [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) is less tense than the simple estimate — a real puzzle of tall-tree physiology. **21.** $-0.3 + 0.4 = 0.1\,\mathrm{MPa}$; difference $1.0 - 0.1 =
0.9\,\mathrm{MPa}$ over $100\,\mathrm{m}$. **22.** Friction halves to $0.5\,$: tension $1.5\,\mathrm{MPa}$, crown potential $-1.6\,\mathrm{MPa}$; the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) regain [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) ($0.9\,\mathrm{MPa}$) and the risk of [cavitation](#def-b1-plant-transport-xylem) falls, but carbon fixation halves for the hours the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) are closed. **23.** Crown $-1.0 - 2.0 = -3.0\,\mathrm{MPa}$: below the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’ $\Psi_s$, so no [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) is possible and the crown wilts; the tree must close its [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) (raising the crown to about $-2.5\,$, zero [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell)), shed [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) at the top, and wait for rain. **24.** Their [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) is the lowest in the tree: to keep [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) they carry more solutes and thicker walls, and to limit transpiration, smaller blades; they grow slowly, because their [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) close early. **25.** About $2\,\mathrm{MPa}$ of tension at the crown (a [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) near $-2.1\,\mathrm{MPa}$), with sap moving at about $0.5\,\mathrm{m}/\mathrm{h}$ through the sapwood.