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P. Liu
3.7 Unsteady Gradually Varied Flow in Open
Channel
3.7.1 Overview
Unsteady flow in open channel refers to the time-dependent flow of average
velocity V and water depth h in open channel or natural channel. In water
conservancy engineering, it is often seen in the evolution of flood in the
natural river, the change in channel water depth caused by the opening and
closing of the gate, and the tidal flow at the entrance to the sea. According to
the theory of one-dimensional flow, the hydraulic elements of unsteady flow
in open channel, such as the average velocity (or discharge) of cross section
and water depth, can be expressed as the function of flow path s and time t,
that is
V = V (s, t), h = h(s, t) or Q = Q(s, t), h = h(s, t).
Different from the unsteady flow of pressure pipeline, there is a free water
surface in the open channel flow, and the wave propagation is not a pressure
wave but a gravity wave. In the flow process, the main forces of water are
inertia force, gravity, and resistance. Although these waves belong to gravity
waves, they are essentially different from the wind-driven waves on the surface
of oceans and lakes. In the wind-driven wave motion, the water particles
basically move in a circular motion along a certain track, almost no flow
transfer, there is a certain phase difference between the particles, resulting in
the propulsion of water surface wave, which is called propulsion wave. But
for the unsteady flow in the open channel, not only the surface wave moves
forward, but also the water particle moves forward. This wave is caused by
the water particle moving, so it is called displacement wave or mass transfer
wave. In the fluctuation area, the water depth and velocity of each section
are not single value relations, but form the rope sleeve curve as shown in
Fig. 3.62. For example, in the process of water rising, the upstream water
level in the channel rises first, the water surface slope becomes steep, and
the flow is larger than the constant flow; in the process of precipitation, the
upstream water level falls first, the water surface slope becomes slower, and
the flow is smaller than the constant flow. The wave of unsteady flow in open
channel is generally a shallow water wave or long wave, and the ratio of water
depth h to wavelength is less than 1/20. The flow resistance should be taken
into account in the analysis. In addition, the unsteady flow in open channel
can be divided into continuous wave and discontinuous wave according to
the change in hydraulic elements with time. When the wave process evolves
P. Liu
3.7 Unsteady Gradually Varied Flow in Open
Channel
3.7.1 Overview
Unsteady flow in open channel refers to the time-dependent flow of average
velocity V and water depth h in open channel or natural channel. In water
conservancy engineering, it is often seen in the evolution of flood in the
natural river, the change in channel water depth caused by the opening and
closing of the gate, and the tidal flow at the entrance to the sea. According to
the theory of one-dimensional flow, the hydraulic elements of unsteady flow
in open channel, such as the average velocity (or discharge) of cross section
and water depth, can be expressed as the function of flow path s and time t,
that is
V = V (s, t), h = h(s, t) or Q = Q(s, t), h = h(s, t).
Different from the unsteady flow of pressure pipeline, there is a free water
surface in the open channel flow, and the wave propagation is not a pressure
wave but a gravity wave. In the flow process, the main forces of water are
inertia force, gravity, and resistance. Although these waves belong to gravity
waves, they are essentially different from the wind-driven waves on the surface
of oceans and lakes. In the wind-driven wave motion, the water particles
basically move in a circular motion along a certain track, almost no flow
transfer, there is a certain phase difference between the particles, resulting in
the propulsion of water surface wave, which is called propulsion wave. But
for the unsteady flow in the open channel, not only the surface wave moves
forward, but also the water particle moves forward. This wave is caused by
the water particle moving, so it is called displacement wave or mass transfer
wave. In the fluctuation area, the water depth and velocity of each section
are not single value relations, but form the rope sleeve curve as shown in
Fig. 3.62. For example, in the process of water rising, the upstream water
level in the channel rises first, the water surface slope becomes steep, and
the flow is larger than the constant flow; in the process of precipitation, the
upstream water level falls first, the water surface slope becomes slower, and
the flow is smaller than the constant flow. The wave of unsteady flow in open
channel is generally a shallow water wave or long wave, and the ratio of water
depth h to wavelength is less than 1/20. The flow resistance should be taken
into account in the analysis. In addition, the unsteady flow in open channel
can be divided into continuous wave and discontinuous wave according to
the change in hydraulic elements with time. When the wave process evolves