Sediment Movement in Alluvial Rivers - River Dynamics and Integrated River Management - page 262

A hydrograph is a graph of flow discharge versus time. It is typically a plot but can be a listing of flow
rate versus time for a specific river. Figure 5.3 shows the discharge hydrograph of a flood in 2005 at the
Longchuan Station on the East River, which shows the flood consisting of 3 parts: a rising limb, a crest
segment or peak discharge, and a recession curve or falling limb.

Fig. 5.3 Hydrograph of a flood in 2005 at the Longchuan Station on the East River, which shows a rising limb (from
June 10 to June 20), a crest segment (from June 20 to June 26), and a recession or falling limb (from June 20 to July 15)

5.1.2 Open Channel Flows
Laminar flow and turbulent flow— Open channel flows may be laminar or turbulent, subcritical or
supercritical, depending on the Reynolds number and Froude number. The phenomena of laminar flow and
turbulent flow can still be best illustrated by the classical experiment of Reynolds, as shown in Fig. 5.4.
At the beginning of the experiment, the tank is full of clear water that had been allowed to stand completely
still for some time; the valve is then opened slightly and water begins to flow through the tube. At the
same time a dye solution is injected at the entrance to reveal the pattern of flow. At low velocities the dye
solution follows a distinct straight line as it passes through the pipe. It does not mix with surrounding
flow layers (a). This is laminar flow. At a higher velocity, the line of dye begins to waver (b). With still
further increasing velocity, the line breaks up and the dye solution diffuses over the entire cross section
of the tube, completely losing its original appearance (c). This is called turbulent flow.

Fig. 5.4 Experiment of Reynolds. (a) Laminar flow; (b) Transitional flow; and (c) Turbulent flow

For laminar flow the following relation between shear stress, W and velocity gradient, d
d

u
y

is well

known.

d u d u

WP U v (5.1)

d y d y

in which P and Q are the coefficients of dynamic viscosity and kinematical viscosity for the fluid,
respectively, U is the density of the fluid, u is the velocity in the x -direction and y is the direction normal
to the flow boundary. This is Newton's Law and a fluid that follows the law is called a Newtonian Fluid.