Page 235 - Handbook of Gold Exploration and Evaluation

206 Handbook of gold exploration and evaluation

2
1. Geometric dimensions are described in terms of length (L), area (L ) and
3
volume (L ).
2. Kinematic dimensions are described as time (T), velocity (LT ÿ1 ),
3 ÿ1
acceleration (LT ÿ2 ) and discharge (L T ).
3. Dynamic dimensions are described as mass (M), force (MLT ÿ2 ), pressure
ÿ1 ÿ2
intensity (ML T ), impulse and momentum (MLT ÿ1 ), energy and work
2 ÿ3
2 ÿ2
(ML T ) and power (ML T ).
Thermodynamic measurements are expressed as some combination of length,
mass of (force), time and temperature. Important physical quantities in which the
dimensions cancel out are the dimensionless Froude number `F' and the
Reynolds' number `Re'.

4.2.2 Fundamentals of physical equations

To gain an understanding of hydrological and fluvial morphology it is necessary
to first understand the essential characteristics of equations that describe the
various parts of the hydrological cycle (Dingman, 1984). Some properties, such
as the physical characteristics of water, can be considered as constants in the
matters discussed in this chapter. Other properties of importance to hydrology
such as rates of flow in streams, water depths and precipitation, are extremely
variable in space and time.
It should be noted that most empirical formulae describe sedimentary
processes in terms of theoretical equations that are dimensionally homogeneous,
i.e., analytically correct, and descriptions of specific features of their particular
dimensional systems are provided in qualitative terms. This does not mean that
they are necessarily correct. Experimental results, although faithfully repro-
duced, are often derived from data that are either inadequate or incorrect. The
equations so modified may deviate materially from mathematical correctness
and lead to entirely wrong conclusions. For example, although Heywood's shape
factor (refer to Chapter 8, eqn 8.8) is dimensionally homogeneous, it will be
physically correct only if the correct value of the dimensionless coefficient k is
used. Approximate value becomes increasingly uncertain when applied to the
more extreme shapes of gold.

Conservation of energy
Conservation problems relate to the fundamental statements that matter, energy
and momentum cannot be created or destroyed in any normal physical process.
As an expression of the conservation of energy for a steady flow of fluid, eqn 4.5
defines the different forms of energy at every point in a stream. Since water is
virtually incompressible, fluid density remains constant throughout the region of
flow. The equation of motion (Bernoulli's theorem) is a constant represented by
the sum of the potential head, the pressure head and the velocity head at every