## Mathematical Analysis Of Pore Volume

A pore volume Vo is the volume of the porous medium in question occupied by fluid and may be defined by (Kirkham and Powers, 1972, p. 401) where V is the bulk volume of the porous medium and a is the water-filled porosity, and we note that the right-hand side of Equation 12.2 yields one pore volume. The number of pore volumes p of fluid passed through a medium in time t is equal to the volume Qt of fluid moved through the medium divided by its pore volume, that is, which, on dividing the...

## Comparison Of Measurements Made With The Pressure Chamber And The Thermocouple Psychrometer

For accurate measurements, one should compare measurements made with a thermocouple psychrometer with those made with a pressure chamber before assuming that the pressure chamber is giving valid measurements of water potential. Because the thermocouple-psychrometer method is based on sound physics using the Kelvin equation (Rawlins, 1972), measurements FIG. 17.1 Pressure chamber for measurement of sap presure in the xylem of a twig. Left direct observation right stepwise sap extrusion and...

## Leaf Area Index

FIG. 26.2 Relationship between leaf area index and evapotranspiration. (From Chang, J.H., Climate and Agriculture An Ecological Survey, Fig. 71, p. 130, 1968. Aldine Publishing Co Chicago. Reproduced by permission of Dr. Jen-Hu Chang.) FIG. 26.3 The plant evaporation, Ep, relative to the potential evaporation, Eo, as influenced by leaf area index, when the soil water is not limited. (From Ritchie, J.T., Model for predicting evaporation from a row crop with incomplete cover. Water Resources...

## Evapotranspiration

The term potential evapotranspiration must be defined when we talk of vapotranspiration. The concept of potential evapotranspiration was put forth by Thornthwaite (1948) and Penman (1948). We will use the definition of Rosenberg (1974, p. 172), noting that his definition is similar to that of Penman. (For a biography of Penman, see the Appendix, Section V.) I. DEFINITION OF POTENTIAL EVAPOTRANSPIRATION Rosenberg says that potential evapotranspiration (abbreviated as ETP by him, but as PET by...

## Air

FIG. 19.1 Water relations of a mangrove growing with its roots immersed in sea water. The diagram indicates the essential parts of the mangrove tree from the standpoint of water relations, particularly the membranes of the endodermis and of the leaf cells. It is important to note that if leaf membranes should suddenly cease to be differentially permeable, salt and subsequently water would move from leaf cells into the pathway due to the high tension of water there, and thus the leaf cells would...

## Osmometer

We have mentioned that osmotic potential can be determined with an osmometer. The osmometer measures osmolality, not osmotic pressure, so we must learn how we can relate osmolality to osmotic pressure (or its negative value, osmotic potential). Osmolality expresses the total concentration of dissolved particles in a solution without regard for the particle size, density, configuration, or electrical charge (Wescor, 1989). All these items listed are particle characters. A colligative property...

## Relationship Between Vapor Pressure And Temperature

As stated earlier, we obtain water potential by observations of vapor pressure. The changes in temperature measured are actually minute. The relation between vapor pressure and temperature is as follows where e partial pressure of water vapor in air eu saturated vapor pressure at the wet-bulb temperature Ta dry-bulb temperature (air temperature) Tw wet-bulb temperature g psychrometric constant, taken to be 0.658 C at 20 C and 1000 mb pressure (Monteith, 1973, p. 221). (gis 0.655 at 15 C 0.662...

## Structure Of Secondary Xylem

In Chapter 14, Section IV, we considered secondary xylem when making calculations of Poiseuille-law flow through wood. Here we look at the structure of secondary xylem. A study of a block of wood reveals the presence of two distinct systems of cells (Fig. 18.3) (Esau, 1977, p. 101) the axial (longitudinal or vertical) and the radial (transverse or horizontal) or ray system. The axial system contains files of cells with their long axes oriented vertically in the stem or the root, that is,...

## Leaf Anatomy

Plants are usually classified according to their water relations, as follows xerophytes, mesophytes, and hydrophytes (Esau, 1977, p. 351). The xero-phytes are adapted to dry habitats. Mesophytes require abundant available soil water and a relatively humid atmosphere. Hydrophytes (or hygro-phytes) depend on a large supply of moisture or grow partly or completely submerged in water. The structural features typical of plants of the different habitats are referred to as xeromorphic, mesomorphic, or...

## Nonlimiting Water Range

In 1985, John Letey, a soil physicist at the University of California in Riverside, developed a concept called the non-limiting water range (NLWR), which acknowledges that water may not be equally available to plants between field capacity and the permanent wilting point. The interaction between water and other physical factors that affect plant growth must be considered. Bulk density and pore size distribution affect the relationship between water and both aeration and mechanical resistance....

## Relation Between Water Potential And Relative Humidity

The use of thermocouple psychrometers to measure water potential is based on a sound physical-chemical foundation. A definite, quantitative relation exists between water potential of a sample and the relative vapor pressure above it (Barrs, 1968, p. 281 Rawlins, 1972 Savage and Cass, 1984), as follows y (RT) Vw )j ln (e e ), (16.1) where y water potential, R ideal gas constant, T absolute temperature ( K), Vw molar volume of pure water, e partial pressure of water vapor in air, e saturated...

## Leaf Resistances

The resistances to water-vapor transport in a leaf are the epidermal resistance, made up of the stomatal resistance and the cuticular resistance, and the boundary-layer resistance. The resistances to carbon dioxide transport in a leaf are the same as for water vapor (stomatal, cuticular, and boundary-layer resistances), plus a fourth resistance called the mesophyll resistance, discussed later in this section. Water vapor diffuses through two of the resistances in a leaf acting in series the...

## References

Nature 124 103. Askenasy, E. (1895). Ueber sic das Saftsteigen. Botanisches Centralblatt 62 237-238. Baker, D.A. (1984). Water relations. In Advanced Plant Physiology (Wilkins, M.B., Ed.), pp. 297-318. Pitman London. Bernstein, L. (1961). Osmotic adjustment of plants to saline media. I. Steady state. Amer J Bot 48 909-918. Bernstein, L. (1963). Osmotic adjustment of plants to saline media. II. Dynamic phase. Amer J Bot 50 360-370. Blum, A., Munns, R.,...

## Calculation Of A Pore Volume

To learn how to calculate pore volumes, let us use an example from the experiment by Vogeler et al. (2001). They studied phytoremediation of soil contaminated with copper using poplar. The lysimeter with the poplar is shown on the cover of the book edited by Iskandar and Kirkham (2001). FIG. 12.11 Tritium breakthrough curve for Yolo loamy sand at two different water contents. The bicolored circle shows where 0.5 pore volume would occur. (From Advanced Soil Physics by Kirkham, D., and Powers,...

The Scholander pressure chamber is commercially available (Figs. 17.7 and 17.8), and it is widely used (Cochard et al., 2001) because of its many advantages. They include simplicity, comparative speed of measurement, and fair portability (Oosterhuis et al., 1983). Even though thermocouple psychrometers appear to provide more accurate measurements than pressure chambers (Millar, 1982) and are based on sound theory, they are not FIG. 17.7 A commercially available pressure chamber. The pressure...

## Available Water

Plant available water, AW, may be defined as the difference between field capacity, FC, and wilting point, WP. The formula is The field capacity might be measured as 5 of water per unit volume of bulk soil for a sand, which we shall label A, and might be measured as 50 per unit volume of bulk soil for a heavy clay, which we shall call B. The wilting point might be 2 water per unit volume for the sand A, and it might be 20 per unit volume for the heavy clay B. Using the numerical values of FC...

## Days After Irrigation

FIG. 8.1 Diagram showing field capacity as a range of values of soil water contents. (From Taylor, S.A., and Ashcroft, G.L., Physical Edaphology The Physics of Irrigated and Nonirrigated Soils, p. 301, 1972 by W.H. Freeman and Company. Used with permission.) 1. Previous soil water history A wetting soil and a drying soil hold different amounts of water. A soil that is saturated and then dries has a higher field capacity than a soil that is being wetted. This is due to hysteresis (see Chapter...

## Field Capacity

To define field capacity we consider the following. In many soils, after a rain or irrigation, the soil immediately starts draining to the deeper depths. After one or two days the water content in the soil will reach, with time, for many soils, a nearly constant value for a particular depth in question. This somewhat arbitrary value of water content, expressed as a percent, is called the field capacity. It is not known who first used the term field capacity. The term was not used by Briggs and...

## Linear Flow Laws

It is linear because the v, the Darcy velocity, of v -Ki, varies linearly with the hydraulic gradient i (Kirkham and Powers, 1972, p. 74). Ohm's law is one of the most common linear flow laws and is used in problems concerning the flow of electricity. In Ohm's law, the current transported is linearly related to the difference in the driving potential across the system. We shall return to Ohm's law when we study electrical analogues (Chapter 20). Gauss's law,...

## Hydraulic Conductivity

The hydraulic conductivity should not be confused with the intrinsic permeability, sometimes just called the permeability, of the flow medium. The intrinsic permeability, symbolized by k by M. Muskat in his classic treatise (1946) (Muskat was a petroleum engineer in the United States well known for his studies in the 1930s and 1940s of fluid flow through porous media), is equal to Kh pg, where K is the Darcy hydraulic conductivity, h is the fluid viscosity, p is the fluid density, and g is the...

## Temperature Effects On Tensiometers

Temperature affects readings with tensiometers in two ways 1. Effects of temperature on water in soil, and 2. Effects of temperature on the instrument. Temperature affects the physical properties of water, including density and surface tension (Table 3.1). Therefore, the matric potential (tension) of water in the soil is affected by temperature changes. The major effect of temperature occurs at the soil surface, where temperature changes are greatest. Temperature effects on soil tension account...

## Endpenetrometer

FIG. 9.3 The cone penetrometer. (From SoilTest, 1978b Reprinted by permission of ELE International, Loveland, Colorado.) a gravitational field, w mg (weight mass times acceleration due to gravity). So each gram has an earth-pull on it of 980 dynes and each kilogram has an earth-pull on it of 9.8 newtons. In the cgs system of units, we make the following calculations (remember 1 x 106 dynes cm2 1 bar). To convert from the English system to the cgs system 1 psi 1 lb in2 (454 x 980) dynes (2.54...

## Biographies Of Briggs And Shantz

Lyman James Briggs, a physicist, was born May 7, 1874, in Assyria, Michigan, the son of Chauncey L. and Isabella (McKelvey) Briggs. He got his B.S. degree at Michigan State College in 1893, his M.S. degree at the University of Michigan in 1895, and his Ph.D. at Johns Hopkins in 1901 (Cattell, 1944). He received a Doctor of Science (Sc.D.) degree from Michigan State in 1932 a Doctor of Engineering degree from the South Dakota School of Mines in 1935 a Doctor of Laws (LL.D.) degree from the...

## How To Analyze A Pressurevolume Curve

Now let us return to the actual measurement of osmotic potential using a pressure-volume curve. Pressure is applied incrementally to a plant sample. After each increase in pressure, the volume of exudate from the cut end of the plant (e.g., stem, petiole) is collected and measured, and a curve of the reciprocal of pressure versus cumulative volume exuded is plotted (Figs. 18.10, 18.11). From this pressure-volume curve, the osmotic potential at full turgor and the osmotic potential at zero...

## Measurement Of Soil Water Content Using

Now let us look at the procedure, when we use TDR (Topp, 1993, pp. 544-549). First, we need the TDR equipment proper (Fig. 13.6). This includes the pulser of voltage a sampling receiver that receives both the pulse and the reflected pulse from the soil a timing device that synchronizes the timing for pulser, receiver, and data display and a data display that shows the time and voltage magnitude. (As noted above, commercial cable testers display an apparent length rather than a time.) The TDR...

## Rise And Fall Of Water In Soil Pores

Water is attracted into soil pores predominantly because of the attraction of water to other surfaces (adhesion) and because of capillarity. Surface tension controls the rise or fall of a liquid in a capillary tube. We have discussed surface tension and the equation to determine the height of rise in capillary tubes. We now discuss the rise and fall of water in soil pores (capillary tubes) and how the rise and fall determine the soil moisture characteristic curve. We follow the analysis of...

## Water Potential

The second expression utilizes the potential energy status of a small parcel of water (say a milligram) in the soil. The expression applies also to a small parcel of water in a plant. All water in the soil (or plant) is subjected to force fields originating from four main factors the presence of the solid phase (the matrix) the gravitational field any dissolved salts and the action of external gas or water pressure. If the force fields in the soil are compared to a reference point, then they...

## Wilting Point

The wilting point, also called the permanent wilting point, may be defined as the amount of water per unit weight or per unit soil bulk volume in the soil, expressed in percent, that is held so tightly by the soil matrix that roots cannot absorb this water and a plant will wilt. Unlike field capacity, the term wilting point is associated with known scientists, Briggs and Shantz (1912). They defined the wilting coefficient (wilting point) as the moisture content of the soil (expressed as a...

## Applications Of Tensiometers

Tensiometers have five applications (Richards, 1965). 1. They are used to determine rooting depth. One can follow readings with time, and the rate of increase in soil tension at any given depth can be related to the density of the active roots. 2. They are used for timing of field irrigations. It is time to irrigate when ten-siometer readings reach a prescribed value for a soil depth where feeder root concentration is greatest. The duration of an irrigation is judged with tensiometers measuring...

## Appendix Biography Of Isaac Newton

The following biographical material on Newton comes from Tannenbaum and Stillman (1959). Newton was born on December 25, 1642, in Woolsthorpe, Lincolnshire, England. He was premature, and the midwife thought he would not live the night. He did not have the advantage of a happy, loving family. His father was said to be extravagant and wild, but he had no influence on Isaac, because he died more than two months before Isaac was born. His mother, Hannah, remarried to a Reverend Mr. Smith to avoid...

## Water Movement in Saturated Soil

Understanding movement of water in saturated soil is important in drainage and groundwater studies. The French hydraulic engineer, Henry Darcy (1803-1858) determined experimentally the law that governs the flow of water through saturated soil (1856), which is called Darcy's law. (See the Appendix, Section VII, for a biography of Darcy.) To illustrate Darcy's law, let us consider Fig. 7.1, which shows water flowing through a soil column of length L and cross-sectional area, A (Kirkham and...

Infrared thermometers have three advantages. First, they are easy to use. The infrared thermometer is pointed at the canopy and a readout on the back of the instrument, facing the viewer, immediately displays the temperature. The instruments can give either the temperature of the canopy or the difference in temperature between the air and the canopy. The latter temperature usually is preferred, because it indicates how stressed a crop is. Canopies with temperatures below ambient temperature are...

## Relationship Between Yield And Transpiration And Yield And Evapotranspiration

Let us look at figures showing the relationship between yield and transpiration and yield and evapotranspiration. Figures 27.1 and 27.2 show the relationship between yield and transpiration as determined by Arkley (1963), who used data from Briggs and Shantz (1913a). The classical work by Briggs and Shantz demonstrated a close relation between transpiration and dry matter production. That is, dry matter is decreased by water deficits. In their experiments, the linear relationship held for...

## Example Of An Electrical Analogue Applied To Soil With Wormholes

The same container cited in the preceding example (24 cm long and 5 cm wide) was used to determine, in an electrical-analogue study, the water and air conductance in soil with earthworms (Kirkham, 1982). The objective was to quantify the relationship between conductance and wormholes of different sizes oriented in the horizontal and vertical directions, which simulated wormholes oriented horizontally to the soil surface or perpendicularly to the soil surface. Copper pipes of different...

## Thermoelectric Effects

Before discussing thermocouple psychrometers used in plant-water measurements, let us review the thermoelectric effects on which they are based. Figure 16.1 shows an electric circuit of two metals formed into two junctions. If a temperature difference exists between the two junctions, an electric current will flow between them (Barrs, 1968, p. 287). This is the Seebeck effect, named after Johann Seebeck in Berlin, who discovered it in 1821 (Shortley and Williams, 1971, p. 578). Holding the two...

## Measurement Of Mobility With The Tension Infiltrometer

Many water flow processes of interest such as groundwater recharge are concerned only with area-averaged water input. Therefore, preferential flow of water through structural voids does not necessarily invalidate equations that assume homogeneous flow, like Darcy's law. However, preferential flow is of critical importance in solute transport, because it enhances chemical mobility and can increase pollution hazards. Many times we need to monitor chemical mobility along with hydraulic properties....

## Examples Of Surface Tension

The importance of surface tension can be illustrated in five ways. 1. A water beetle or other small aquatic organisms can float on water because of surface tension (Porter, 1971, p. 442). The fact that small insects can float on water shows the close relationship between the way they have evolved and water. (We remember from Chapter 2 that another example of the relationship between animal evolution and properties of water is the fact that water has a minimum specific heat at 35 C.) One can...

## Appendix Biography Of Wilhelm Pfeffer

Wilhelm Friedrich Philipp Pfeffer (1845-1920) was a German physiological botanist. He was born in Grebenstein, where his father owned a chemist's shop (pharmacy) (Frommhold, 1996), on March 9, 1845 (McIlrath, 1971). There he learned fundamental knowledge and manual skills for his later profession. After earning a degree in botany and chemistry from G ttingen University in 1865, he spent the next several years studying botany and pharmacy at Marburg University. He continued his botanical studies...

## Description Of A Tensiometer

A tensiometer is a device for measuring, when the soil is not too dry, the soil matric potential. In old terminology, the matric potential was called the soil moisture tension (see Chapter 5 for terminology used in soil-water relations). Because the instrument measures tension, it was called a tensiometer. For a review of the early literature on tensiometers, see Richards (1949). However, the instrument could have been called an ergmeter (Don Kirkham, Departments of Physics and Agronomy, Iowa...

## Ellipsoidal Description Of Water Flow Into Soil From A Surface Disc

The disc permeameter is being widely used to characterize the hydraulic properties of the surface of the soil. It is important to describe the multidimensional flow of water away from the circular source. Little work has been done to analyze precisely the flow of water away from a circular source of water applied at a constant negative potential, yo. The Wooding equation (1968 his Equation 64) does describe the steady rate of three-dimensional infiltration from a circular pond. His equation...

## Conductivity And Sorptivity With The Tension Infiltrometer

Even though the minidisk infiltrometer can be used to get hydraulic conductivity, the tension infiltrometer (Fig. 11.4) is more widely used. Two methods can be used to get unsaturated hydraulic conductivity with the tension infiltrometer the method of Smettem and Clothier (1989) and the method of Ankeny et al. (1991). In the Smettem and Clothier method, two tension infiltrometers with different radii are used to get both unsaturated hydraulic conductivity and sorptivity. In their method, two...

## Y ye ee eoeo yje214

Equation 21.4 gives us a relation between the water potential and the relative water content of the cell. ym(e) represents the relation between the water content and the matric potential. Growth can be expected to cause some departure from the expression used in deriving Equation 21.4, but to the extent that the assumptions are valid, Equation 21.4 gives a unique relation between the total water potential and the relative water content of the leaf. In...

## Water Potential References

Baker, J.M., and Allmaras, R.R. (1990). System for automating and multiplexing soil moisture measurement by time-domain reflectometry. Soil Sci Soc Amer J 54 1-6. Bishop, J.E. (1995). Link between EMF, brain cancer is suggested in major new study. However, no added risk of leukemia is found, unlike previous work. Wall Street Journal Wednesday, January 11, 1995 p. B4. Buchwald, J.Z. (1994). The Creation of Scientific Effects Heinrich Hertz and Electric Waves. University of Chicago Press Chicago,...

## Pore Volumes Based On Length Units

Jury et al. (1991, pp. 224-225) calculate pore volumes by multiplying the length of a column by the water content. They give the formula where dwb is the drainage water (cm) evolved at the breakthrough time dwb Jw b, Jw is the soil water flux (cm sec), tb is the breakthrough time (sec), L is the length of the soil column (cm), and V is the solute velocity (cm sec) (Figs. 12.12 and 12.13). (We will assume this velocity is the average pore velocity that Kirkham and Powers define the definition is...

## Hydraulic Press

The hydraulic press operates on the same principle as the pressure chamber, yet overcomes some of the pressure chamber's limitations (Campbell and Brewster, 1975) (Fig. 17.9). The press consists of a commercial 1.5 ton (1360 kg) hydraulic automobile jack modified to apply pressure through a thin rubber membrane to a leaf sample, which is observed through a 1.27-cm thick Plexiglas plate (Fig. 17.10) (Campbell and Brewster, 1975 Jones and Carabaly, 1980). The instrument applies pressure to the...

## Types Of Thermocouple Psychrometers

Four types of instruments with thermocouples are in use to measure water potential of plants 1. Isopiestic thermocouple psychrometer (Boyer, 1972a, 1972b) (Fig. 16.3) in which solutions of varying concentrations are put manually on the wet junction of the thermocouple psychrometer. The isopiestic solution is the solution that has the same vapor pressure as that of the tissue and produces no thermocouple output (the null point). 2. The Peltier thermocouple psychrometer (Fig. 16.4, left) in which...

## Potentials In The Soilplantatmosphere Continuum

No matter how water gets to the top of tall trees, the gradient in water potential from the soil to the top of the tree is calculated to be large. Nobel (1974, p. 402 1983, p. 507 1991, p. 521) shows representative values for the water potential, y, and its components (ym, matric potential ys, solute potential yg, gravitational potential yp, turgor potential) in the soil-plant-atmosphere continuum. Let us choose three values of the water potential and its components that he gives one for the...

## Tension Infiltrometer Or Disc Permeameter

Recognition of the importance of macropores and preferential flow has led to the development of instruments that can be used in the field to control preferential water flow through macropores and soil cracks. Let us first define macropores and see their size in relation to other soil pores. Pores in the soil can be classified into five categores (Clothier, 2004) macropores, with diameters ranging from 75 to > 5000 m mesopores with diameters ranging from 30 to 75 im micropores with diameters...

## Limitations Of The Cohesion Theory

Even though most plant physiologists feel that the cohesion theory is probably the correct explanation for the rise of water in plants, the theory has FIG. 19.2 The cohesion theory of the ascent of sap summarized. (From Salisbury, F.B., and Ross, C.W., Plant Physiology, 2nd ed., p. 58, 1978. Wadsworth Publishing Company, Inc Belmont, California. Reprinted with permission of Brooks Cole, a division of Thomson Learning www.thomsonrights.com. Fax 800 730-2215.) FIG. 19.2 The cohesion theory of the...

## Description Of The Equation

In his paper, Gardner (1960) solved the flow equation to determine water movement to a plant root. The flow equation for a single root in an infinite, two-dimensional medium is de t (1 r)(3 3r) rD(3e 3r) (15.1) where e is the water content of the soil on a volumetric basis, D is the diffu-sivity, t is the time, and r is the radial distance from the axis of the root. The solution to Equation 15.1, subject to boundary conditions that Gardner (1960) defines, is given by Carslaw and Jaeger (1959)...

## Measurement Of The Components Of The Water Potential

Differences in total water potential, osmotic potential, pressure potential, matric potential, and gravitational potential can develop in the water of part of a plant, for example, a leaf. (We say potential, when we recognize that we mean potential energy. Potential is shorter than potential energy and saves spaces in printing.) As we saw in Chapter 5 (Equation 5.3), when we were focusing on soil water, these five potentials for water at a particular point in a plant or soil are related by the...

## Minidisk Infiltrometer

The minidisk infiltrometer is made by Decagon Devices (Pullman, Washington). It consists of a plastic tube, 22.5 cm long and 3.1 cm in outside diameter, marked with milliliter gradation (0 to 100 mL), a rubber stopper placed in the top, and a styrofoam-looking base that holds the tension. One-half centimeter above the base is an air-inlet tube. The original minidisk infiltrometer, first sold in 1997, infiltrates water at a set suction (tension) of 2.0 cm and has a radius of 1.59 cm. Decagon...

## Measurement Of Stomatal Aperture And Stomatal Resistance

Because water is lost mainly through the stomata on the surfaces of leaves, it is critical to know the extent of stomatal opening, to evaluate how much water a plant is losing. Slavik (1971), Kanemasu (1975a), Willmer (1983), and Weyers and Meidner (1990) enumerate different methods used to assess stomatal aperture. These methods include the following 1. Observation under a microscope (Hsiao and Fischer, 1975a Schoch and Silvy, 1978 Willmer and Beattie, 1978 Omasa et al., 1983 Martin et al.,...