Fistoem Rr

7/30/2019 Fistoem Rr

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Dynamic responses


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Analogi Aliran Air dan Listrik


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Volume flowrate

in liters/min,

cm3/sec, m3/sec,

etc

Electric current

flow in

coulombs/sec =

amperes.


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Hysteresis


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Low pass filter

C= =Wmax =WmaxCr

d/d can be called a

relative capacitance (Cr )


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Sigmoid curve


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Jp=(s-l)/Rp (4.27)

The rate of change of leaf water content (d Wl/dt) is given by the difference

between the flow of water into the leaf and that lost by evaporation, so

(4.28)

substituting from equation 4.27 gives

(4.29)

If one now assumes a constant capacitance one can write (from equation 4.26)

(4.30)

This is a first-order dilferential equation of the type commonly encountered in the

analysis of electrical circuits. It can be solved using standard mathematical techniques

to give the time dependence oflafter a step change in E (Fig. 4.13):


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The value (= RC) is called the time

constant , time to get 63 % total

change

So to get the time to achieve 50%

total change is x (-In 0.5) = 0.693

= +

=


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The capacitance (C) of any part of the system may be

defined as the ratio of the change in tissue water content

(W) to the change in water potential

C= =Wmax =WmaxCr(4.26)

Where Wmax is the maximum (turgid) tissue water

content and is the relative water content. The term

d/d can be called a relative capacitance (Cr) Forinclusion in flow models, the basis for C must be the same

as that used for E.


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A consequence this is that, since the voltage

drop across the voltage source is pi, and the

voltage drop between the nodes (o) and

ground is , then the voltage drop across the

capacitor represents the turgor pressure (p).


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Liquid phase transport processes

The movement of solutes from tissue or over shorterdistances from cell to cell within plants is essential fornormal growth and development. For example,minerals from the soil must reach the leaves and other

aerial tissues while carbohydrates from the leaves mustbe transported downwards to build new roots. Detailsof the various transport processes can be found inNobel (1991), Zimmermann & Milburn (1975), Lttge &Pitman (1976) or Moorby (1981), as well as other texts

on transport mechanisms. Here, only a brief outlinewill be presented to place different processes inperspective


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In Chapter 3 (p. 57) it was stated that, when a

finite quantity of material released in a plane,

the concentration profile is the shape of theGaussian curve, and the distance from the origin

(x) at which the concentration falls to 37% of

that at the origin is given by x = (4Dt) (4.33)


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Diffusion is much slower in solution and effectiveonly over short distances For example. solvingequation 4.33 for a typical solute D of 1 x 10-9 m2

s

-1

, gives the time to diffuse 100 m as 2.5 s (i.e.(100 >< 10-6)2/(4x10-9)s), 2.5 x I04 s (6.9 h) todiffuse 1 cm and 2.5 X108 s ( 8 years) to diffuse 1m. Clearly, therefore simple diffusion cannot be

an important mechanism for long distancetransport in plants, though it is important for cell-to-cell or within-cell transport.


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The long-distance movement of solutes isprimarily in the bulk flow of water in thexylem or in the other specialised conducting

tissue, the phloem. However, because transpiration is

unidirectional, it cannot be involved inbasipetal transport so that another pathway isrequired for redistribution of solutes,particularly in a downward direction.


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This alternative long-distance transport Pathway, which isparticularly important for carbohydrate movement tomeristematic or storage tissues, is in the specialised (living)sieve tubes of the phloem.

The mechanism of phloem transport is still incompletelyunderstood but it is thought that this also involves massflow, though in this case the pressure gradient that drivesthe flow may be generated by active (energy-requiring)membrane transport pumps that concentrate the solutes inthe phloem sieve tubes of the source tissues.

The high solute concentrations lower the water potential sothat water follows through the semi-permeable sieve-tubemembrane, thus raising the hydrostatic pressure andcausing flow out of the source tissue.


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For both xylem and phloem, therefore, the

flux of the ith solute (Ji, kg m-2 s-1) across a plane

is given by the product of concentration andvelocity

Ji = ciJv (4.34)


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Typical concentrations of different solutes in phloem andxylem sap are presented in Table 4.3. This table shows thatby far the major component of the phloem is sugar whilethere is none in the xylem. Although this is true for manyplants, some trees such as sugar maple do have significant

amounts of sugar in the xylem, particularly in spring. The concentrations of almost all substances, with the

notable exception of calcium, are markedly higher in thephloem.

Therefore, a given Jv

in the phloem will transport moresolute than an equivalent velocity in the xylem, thoughtransport in the phloem does require expenditure of energyby the plant while the much greater bulk flow in the xylemis driven by energy from elsewhere.


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Calcium is somewhat exceptional in that mostworkers have found fairly similar concentrationsof calcium in the two types of sap, or else calciumis more concentrated in the xylem (e.g. Table

4.3). A consequence of the rather low calciumconcentration in the phloem appears to be thatIow transpiring tissues, such as apple fruits or theenclosed leaves of lettuce, can suffer severe

calcium deficiency, which gives rise to disorderssuch bitterpit and breakdown in apple andtipburn in lettuce (see e. g. Bangerth 1979)

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