|
<br />100k
<br />
<br />'"
<br />E
<br /><.)
<br />~
<br />::l.
<br />>.
<br />-
<br />.00
<br />C
<br />lI.l
<br />"'C
<br />~
<br />lI.l
<br />~
<br />o
<br />a..
<br />
<br />
<br />10k
<br />
<br />0.1
<br />
<br />0.01
<br />0.1
<br />
<br />1 1 0 1 00 1 k
<br />Water conductivity, fJS/cm
<br />
<br />Fig. 6. Four-way logarithmic graph of relations among
<br />measures of electrical-field intensity (power density,
<br />current density, and voltage gradient) relative to water
<br />conductivity. Reproduced with permission from Fig. 7 in
<br />Kolz, 1989a; axis labels modified.)
<br />
<br />voltage gradient near and between electrodes is inde-
<br />pendent of (unaffected by) water conductivity if that water
<br />conductivity remains uniform (unstratified) in proximity
<br />to and between the electrodes and other parameters (e.g.,
<br />basin, electrodes, voltage differential between electrodes)
<br />are identical. Under such conditions, a map of voltage
<br />gradient would be the same whether water conductivity
<br />was 10 or 1,500 IlS/cm. However, this would not be true if
<br />water conductivity was stratified as in an estuary or at
<br />and just downstream of a tributary, spring, or industrial
<br />outflow of substantially different conductivity.
<br />Current density (1) is usually expressed as microam-
<br />peres or milliamperes per square centimeter, IlA/cm2 or
<br />mA/cm2, respectively (Il = 10-6, m = 10-3), and described
<br />as the amount of current passing through a unit area of
<br />isopotential surface (perpendicular to the lines of flux).
<br />Current is the quantity of electrical charge flowing per
<br />unit time, usually expressed as amperes (A, coulombs/
<br />sec). Since instruments have not yet been developed for
<br />
<br />SNYDER 13
<br />
<br />direct measurement of current density, it must be calcu-
<br />lated (J = cE)o
<br />Power density (D) is the amount of power dissipated
<br />per unit volume between two isopotential surfaces. Power,
<br />the mathematical product of voltage and current, is the
<br />amount of energy expended per unit time, usually ex-
<br />pressed as watts (W,joules/sec). Similarly, power density
<br />is the mathematical product of voltage gradient and cur-
<br />rent density, and it is usually expressed as microwatts per
<br />cubic centimeter, Il W/cm3. Because it is a function of cur-
<br />rent density, power density is also dependent on water
<br />conductivity. Like current density, instruments have not
<br />yet been developed for direct measurement of power den-
<br />sity, and it too must be calculated (D = JE = eEl =.P / c).
<br />Although reintroduced to electrofishing literature a de-
<br />cade ago by Kolz (1989a), the term "power density" was
<br />perhaps first introduced and used in North American lit-
<br />erature by Monan and Engstrom (1963). Power density,
<br />or the volumetric expression of power it represents, was
<br />also used or discussed by Adams et al. (1972) and Stern in
<br />et al. (1972, 1976).
<br />Kolz (1989a) and Kolz and Reynolds (1989b, 1990a)
<br />used a unique 4-way logarithmic graph of water conduc-
<br />tivity, voltage gradient, current density, and power den-
<br />sity (Fig. 6) to help explain their theory of power-density
<br />transfer (discussed below) and for overlaying graphs of
<br />in-water field-intensity thresholds for observed re-
<br />sponses offish to electric fields. Any point on the graph
<br />simultaneously represents the corresponding values for
<br />each quantity, and knowing any two quantities (e.g., con-
<br />ductivity and voltage gradient) provides a quick alterna-
<br />tive to calculation for approximating the remaining two
<br />quantities. Many interesting relations between these fac-
<br />tors are revealed by studying the graph. For example,
<br />when voltage gradient is held constant, both current den-
<br />sity and power density increase in direct proportion to
<br />water conductivity. At any point on the graph for which
<br />voltage gradient is 1 V /cm, the numeric values for both
<br />current density and power density are equal to water con-
<br />ductivity.
<br />The relation between voltage gradient and current
<br />density relative to water conductivity at a constant power
<br />density of 100 Il W /cm3 can be visually explored in Fig. 7.
<br />The upper and middle graphs are essentially the same
<br />except that the upper graph uses logarithmic scales for
<br />both axes, and the middle graph uses an arithmetic scale
<br />for the Y-axis. The range of conductivities of particular
<br />concern in fresh waters, about 10 to 1,500 IlS/cm, is
<br />bounded by dotted vertical lines in both of these graphs
<br />and represented exclusively in the bottom graph for which
<br />all axes are arithmetic with separate Y-axis scales for
<br />current density and voltage gradient. Because of the
<br />inverse relation between current density and voltage
<br />gradient relative to conductivity (c = J / E), the curve for
<br />
|