Page 243 - Handbook of Gold Exploration and Evaluation
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214 Handbook of gold exploration and evaluation
4.10 Development of boundary layer in open channel with ideal entrance
conditions (Dingman, 1984, modified from Chow, 1959).
boundary layer. Within the boundary layer, flow possesses a velocity gradient
that enables it to transmit stress. Viscous forces are negligible in flow outside of
the boundary layer and hence cannot exert stress on that boundary.
A simplified two-dimensional profile of a boundary layer with accompanying
downward transfer of momentum across a wide open channel section is
demonstrated in Fig. 4.10. The absence of a vertical velocity gradient denotes
the absence of friction in the flow entering the horizontal boundary which thus
has a common velocity of v V 0 . Friction at the boundary retards the flow
inducing a downward transfer of momentum and creating a boundary layer of
thickness . A laminar boundary layer is developed between 0 and x 1 where
turbulence arises. Thickness of the boundary layer increases and turbulent flow
is fully developed at x 2 with a thin zone of laminar flow near the bottom. This
condition is typical of most streams.
Significance of Reynolds number
The parameter known as the Reynolds number `Re' provides a relationship
between inertial forces and viscous forces for all types of fluid motion. Re has
the dimensions:
2 ÿ1
2 ÿ1
Re = VL=v L T =L T 0 4.13
In open channel (stream) flow the characteristic length is taken as the hydraulic
radius R A=P, where A is the cross-section of flow and P is the wetted
perimeter. Equation 4.13 can be re-written:
Re = vR= 4.14