Page 236 - Handbook of Gold Exploration and Evaluation

Sedimentation and detrital gold 207

point along a stream line:

2
Energy E† ˆ 0:5 pv ‡ P ‡ pgZ ˆ a constant 4.5
where Z is the elevation of a point relative to some arbitrary datum, e.g. sea
level; pgZ is the energy of position, i.e. potential energy; P is the pressure at that
2
point; and 0.5 pv the energy of motion, i.e. kinetic energy.
The proportionality constant (often referred to as C or K) expresses the
frictional and other losses in the system due to the boundaries over which flow is
taking place and the physical nature of the flow. An example is Darcy's law:
K D ˆ K l
= † 4.6
where K D is the hydraulic proportionality constant LT ÿ1 †, which is a system
2
parameter that depends upon the intrinsic permeability K l of the medium L †,
ÿ2
ÿ3
and on the weight density
FL †, and dynamic viscosity FTL † of the
water. Note that a rapid decrease in dynamic viscosity takes place with increas-
ing temperature. The steep gradient of the curve between 0 ëC and 20 ëC (Fig.
4.7) suggests that some aspects of solids-fluid flow in sub-arctic conditions may
be significantly different from those in the tropics. Table 4.3 lists the various
values of water properties as functions of temperature.

Diffusion equations

Diffusion equations describe the movement of matter, momentum and energy
through a medium in response to a gradient of matter, momentum and energy
respectively (see `Geochemical dispersion', Chapter 5). The general dimensions
2 1
of diffusion are L T †. Since flow is always away from a region of high
concentration to one of lower concentration:
4.7
Q S ˆ ÿD S ds =dx

4.7 Plot of dynamic viscosity vs. temperature ëC.