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Sedimentation and detrital gold 213

4.9 Depth±velocity relationships for four regimes of channel flow (after
Robertson and Rouse, 1941).

Since open channel flow is inherently turbulent, the only practical regimes of
flow in natural stream channels are sub-critical turbulent and super-critical
turbulent in that order of importance. Sub-critical laminar and super-critical
laminar regimes of flow may occur only where there is a very thin depth of fluid.
The rate of momentum transfer (shear stress ) is proportional to the viscosity
and to the velocity gradient; such conditions are of particular significance in the
operation of gravity concentration devices such as shaking tables, vanners and
other thin film separating plant (see Chapter 8). Depth±velocity relationships
covering the fundamental regimes of flow are illustrated in Fig. 4.9.

Boundary layer concept
The discovery that `momentum is transferred from a flowing stream to a solid
surface through a surrounding thin layer of water' was probably recognised first
by Prandtl (1942) in 1931 from articles on the motion of fluids and gases by
Gustav Fischer published in 1913. Prandtl found that within this narrow region
of stress, the velocity is zero at the interface and increases parabolically to reach
its maximum value at some distance into the stream where it approaches stream
velocity. The zone in which this vertical velocity gradient exists is called the