Open-channel flow

Flows in open channels and stagnant waters are a type of physical flows, which are in many areas of hydrology of importance. The subject area is also known as channel hydraulics. Flume are natural or man-made drainage ways with a free water surface. Among the natural channels include, for example, rivers and streams. Examples of artificial flume are inflow and outflow canals, irrigation ditches and channelization of naturally formed channels.

Open flume as a flow director

Flumes come as a river water level, called here level. Open channels are - in water level - always at atmospheric pressure ( for closed flumes can above the liquid level, an overpressure to be). Characteristics of the flow are about flow profile and flow rate.

The opposite are flows in pipes (eg water pipes and penstocks ). The difference is that in the conventional case, the cross-section is constant. A larger amount of water (flow, hydrologic runoff ) increases the pressure and the flow rate in the closed conductor. In addition, the open water level rises. In natural flowing waters of the bed results in complex variations in cross-sectional areas and the local flow direction of the water.

A third type of flow is the seepage of ground water in the porous medium.

Areas of application

In hydrology the elaborated for flows in open channels or stagnant water models and solutions help, for example, to clarify the following questions about the flow behavior of waters:

• Modelling the flow regime of river systems
• The calculation of the capacity of rivers to flood conveyance or the identification of flood runoff areas
• The calculation of headrace channels of hydropower plants
• The water supply to irrigation systems and water supply in general
• The currents in lakes
• The ability of the flow to transport sediment

Types of flow processes

Flows in open channels and stagnant waters are usually non-stationary ( in a certain place of the time -dependent) and also to be regarded in all three spatial directions. Such calculations are extremely complicated. In many cases, however, simplifications are allowed. Often a pilot is required.

In most cases use is made in the calculation in channels on stationary, one-dimensional calculation method. Here, a over the time constant outflow along the Gerinneachse is considered. Provided is usually also - as in other fluid- mechanical problems - freedom from friction and laminar flow, ie eddy freedom.

Due to the increasing demands on the accuracy of the calculation and the continually improving performance of computer systems, however, are in the recent past also transient, conducted two - and three-dimensional calculations. Thus, the timing, for example, of floods in complex discharge situations (eg flat, wide valleys, dams ) is representable. This also applies to the calculation of flows in shallow lakes or coastal areas of the seas.

One-dimensional discharge in open channels

Streams and shooting

Show observations of nature that at low flow rate in surface waters (small ) disturbances (eg by structures, stone at the base, branch into the water Extending) (ie against the direction of flow) affect upwards and at fast flow rates downwards only.

• Flowing or subcritical discharge a flow of movement exists when disturbances also up - against the flow direction - impact
• Shooting or supercritical outflow when disturbances only down - in the flow direction - impact.

Mathematically, this is derived from Bernoulli's energy equation. As a quadratic equation, this has a minimum amount of energy at constant drain. For this, the critical velocity occurs.

• Faster drainage than the critical speed is shoot-
• Slower currents.

Mathematical criterion for the exact state of flow is the Froude number of the channel.

For the calculation of the clotting is of major importance. In the pouring drain the calculation of the energy line has to be done upstream, downstream at schießendem drain. At the point of flow change ( eg at weirs ) the initial conditions for a discharge calculation can be obtained.

The change from flowing to the shooting runoff ( eg increase of the slope along the flow path or major constrictions ) are quasi continuously, whereas the change from shooting to the flowing drainage by leaps and bounds (see hydraulic jump ) are associated with high energy dissipation. The latter is exploited in the stilling basin of hydropower plants for targeted energy conversion.

Pulsation-free and non-uniform outflow

• When uniform outflow, the flow velocity along a power line does not change.
• For stationary (time constant ) and uniform outflow of the water table is parallel to the channel bottom.
• Narrowings, extensions, thresholds and the like lead to runoff conditions, for which there is non-uniform discharge and the water level no longer runs parallel to the channel bottom.

Hydropeaking

In temporal changes of runoff is called transient conditions. Particularly evident occurs when sudden changes in discharge on, for example, by opening and closing of weirs or disaster, such as the breaking of dams. Under surge is defined as a sudden increase in outflow and Sunk the sudden decrease of the drain.

Calculation of the one-dimensional discharge in open channels

Under stationary conditions, the calculation is carried out either by simple formulas for given discharge cross -sections or sections from profile to profile.

• The calculation of the mean flow velocity occurs at a known durchflossenem cross section in practice mostly by empirical formulas (eg, floating formula according Gauckler - Manning - Strickler or Darcy - Weisbach ).
• The course of the water levels along the flow path at a known discharge is based on the Bernoulli energy equation and occurs when flowing runoff against the flow direction and shooting runoff with the flow direction, starting at an initial cross-section with already known mirror height.

The calculation against the flow direction in the pouring outlet has the consequence that any misjudgment of the water level ( both too high and too low) in the subsequent section is balanced. A too highly rated water level has a smaller speed result; the shallower energy line slope in the next section and resulting from a lower water level. Thus, the tolerance is compensated for deviation from the first section.

Hydropeaking shall be calculated as unsteady flow phenomena with complex formulas.