Page 241 - Handbook of Gold Exploration and Evaluation
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212    Handbook of gold exploration and evaluation

















                     4.8 Shearing stress on element a travelling at mean velocity v in direction x. It
                     will be deformed at angular rate equal to dv/dy.

              simple terms the dynamic viscosity   of a fluid describes the relationship
              between the stress intensity and the accompanying rate of fluid deformation. The
              elementary form of a shear stress produced by the layers between adjacent
              elements of a fluid slipping over one another is illustrated in Fig. 4.8. This figure
              shows that when element a travels at a mean velocity v in the direction x it will
              be deformed at an angular rate of dv=dy and the intensity of shear along a-a will
              be as first expressed by Newton:
                       ˆ   dv=dy                                           4.11
              The shear stress   is related to the rate of angular deformation dv=dy through a
              proportionality factor   representing the viscosity of the fluid.
                 Kinematic viscosity is measured in `Stokes' as the absolute viscosity of a
              fluid divided by its density. Kinematics is that branch of mathematics, which
              treats of pure motion without reference to mass or cause.   is the ratio of
              dynamic viscosity   to mass density  :
                       ˆ  =                                                4.12

              The behaviour of a fluid in motion is governed basically by the effects of
              viscosity and gravity relative to the inertial forces of the flow (Chow, 1959).
              Depending upon the relationship of viscous to inertial effects, three intergrading
              flow lines are developed laminar, turbulent and transitional:

              1. Flow will be laminar if viscous forces are sufficiently dominant and stream-
                 lines remain virtually separate from one another over a defined length of
                 flow.
              2. Flow will be turbulent if inertial forces are dominant; particles will then
                 move in highly irregular paths and streamlines will become hopelessly
                 confused.
              3. A mixed or transitional state of flow exists between the laminar and
                 turbulent states.
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