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Chapter 5
Free surface flows
5.1 QUASI-HORIZONTAL FREE SURFACE FLOWS
Free surface flows are gravity-driven flows that occur in open water systems
such as canals, rivers, lakes and oceans. For the majority of practical applications, the study of free surface flows can be simplified by assuming that
the curvature of streamlines is small, leading to negligible vertical velocities and accelerations, and consequently to hydrostatic pressure distribution (Figure 5.1). The assumption of this type of ‘quasi-horizontal’ flows
facilitates the mathematical solution since the pressure can be estimated
directly from the water depth.
Quasi-horizontal flows are common in rivers and artificial channels,
in lakes and reservoirs and in coastal basins. Although the assumption of
small-flow curvature may be deviated locally, such as in flow over a weir,
the quasi-horizontal conditions are re-established after a short distance and
do not affect the far-field conditions. The assumption of quasi-horizontal
flow can be extended to bed slopes up to 1/4 even 1/3 with sufficient accuracy (Chow 2009).
5.2 ONE-DIMENSIONAL OPEN CHANNEL FLOW
The main assumptions made for the mathematical treatment of onedimensional open channel flows are the following:
1. The longitudinal dimension of the flow domain is much larger than the
transverse dimensions (width and depth of the channel).
2. The unknown variables are the average cross-sectional velocity u(x,t)
and the water depth y(x,t) measured from the free surface to the lowest
point of the channel bed. This depth can be expressed either as the sum
of the initial depth, h o (x) and the surface elevation ζ(x,t) above the initial
depth, or the difference between the elevation of the free surface and the
elevation of the channel bed, measured from a certain reference datum.
Chapter 5
Free surface flows
5.1 QUASI-HORIZONTAL FREE SURFACE FLOWS
Free surface flows are gravity-driven flows that occur in open water systems
such as canals, rivers, lakes and oceans. For the majority of practical applications, the study of free surface flows can be simplified by assuming that
the curvature of streamlines is small, leading to negligible vertical velocities and accelerations, and consequently to hydrostatic pressure distribution (Figure 5.1). The assumption of this type of ‘quasi-horizontal’ flows
facilitates the mathematical solution since the pressure can be estimated
directly from the water depth.
Quasi-horizontal flows are common in rivers and artificial channels,
in lakes and reservoirs and in coastal basins. Although the assumption of
small-flow curvature may be deviated locally, such as in flow over a weir,
the quasi-horizontal conditions are re-established after a short distance and
do not affect the far-field conditions. The assumption of quasi-horizontal
flow can be extended to bed slopes up to 1/4 even 1/3 with sufficient accuracy (Chow 2009).
5.2 ONE-DIMENSIONAL OPEN CHANNEL FLOW
The main assumptions made for the mathematical treatment of onedimensional open channel flows are the following:
1. The longitudinal dimension of the flow domain is much larger than the
transverse dimensions (width and depth of the channel).
2. The unknown variables are the average cross-sectional velocity u(x,t)
and the water depth y(x,t) measured from the free surface to the lowest
point of the channel bed. This depth can be expressed either as the sum
of the initial depth, h o (x) and the surface elevation ζ(x,t) above the initial
depth, or the difference between the elevation of the free surface and the
elevation of the channel bed, measured from a certain reference datum.