# Currents in open channels

Natural or near-natural open channel
Artificial channel
(channeling the line in Göttingen)

Currents in open channels and standing waters are a type of physical flow that is important for many areas of hydrology . The subject is also known as channel hydraulics .

Flumes are natural or artificially created drainage possibilities with a free water level, the hydraulics of which differ from flows in pipelines . The natural channels include z. B. rivers and streams . Examples of artificial flume are inflow and outflow channels , irrigation ditches and channelization of naturally formed clotting.

## Open channel as a flow guide

Like rivers, channels have a water level, here called a gauge . Open channels are - at water level - always under atmospheric pressure (with closed channels there can be overpressure above the liquid level). Flow characteristics are, for example, flow profile and flow velocity .

The opposite are currents in pipelines (e.g. in water pipes and pressure tunnels ). The difference is that in the classic case the line cross-section is constant. A larger amount of water ( flow , hydrological discharge ) increases the pressure and the flow speed in the closed pipe. The level also rises in open water. In the natural bed of rivers, complex changes in the cross-sectional areas and the local flow directions of the water result.

A third type of flow is the seepage flow of the groundwater in a porous medium.

## application areas

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

## Types of flow processes

Currents in open channels and standing water are usually unsteady (at a certain point dependent on time) and must also be viewed in all three spatial directions. Such calculations are extremely complex. In many cases, however, simplifications are permitted. A model test is also often required.

For the calculation in channels, stationary, one-dimensional calculation methods are mostly used. A constant discharge over time along the channel axis is considered. Is provided in most cases - as in other fluid mechanical problems - friction freedom and laminar flow , so irrotationality.

Due to the increasing demands on the calculation accuracy and the continuously improved performance of the computing systems, however, transient, two- and three-dimensional calculations have also been carried out in the recent past. So that the timing z. B. floods can also be displayed in complex runoff situations (e.g. flat, wide valleys, dam breaks). This also applies to the calculation of currents in shallow lakes or areas of the seas close to the coast.

## One-dimensional drainage in open channels

### Stream and shoot

Nature observations show that there are (small) disturbances in surface waters (e.g. due to installations, stones on the ground, branches protruding into the water)

• at high flow velocity only have a downward or downward effect, i.e. in the direction of flow: rapid or supercritical discharge
• at low flow speeds, however, also have an upward or upward effect, i.e. also against the direction of flow: flowing or subcritical discharge .

Mathematically, this can be derived from Bernoulli's energy equation. As a quadratic equation , this has a minimum energy level at constant discharge, at which the critical velocity or critical discharge occurs. This condition lies exactly between the two above. States.

The mathematical criterion for the exact state of the flow is the Froude number of the channel, which describes the ratio of the flow velocity to the propagation velocity of a shallow water wave: ${\ displaystyle Fri}$ ${\ displaystyle v_ {fl}}$ ${\ displaystyle v_ {ausbr}}$

• ${\ displaystyle Fr> 1 \ Leftrightarrow v_ {fl}> v_ {ausbr}}$: supercritical condition / shooting
• ${\ displaystyle Fr = 1 \ Leftrightarrow v_ {fl} = v_ {ausbr}}$: critical condition
• ${\ displaystyle Fr <1 \ Leftrightarrow v_ {fl} : subcritical state / currents.

This is of great importance for the calculation of channels:

• If the discharge is running fast, the calculation of the energy line has to be done downstream
• in the case of flowing outflow, the energy line must be calculated upstream.
• At the intermediate point of the flow change (e.g. at weirs ), the initial conditions for a discharge calculation can be obtained.

The change from flowing to flowing discharge (e.g. when the gradient increases along the flow path or when there are large constrictions) takes place continuously, whereas the change from flowing to flowing discharge occurs abruptly ( alternating jump ), combined with high energy dissipation . The latter is used in the stilling basins of hydropower plants for targeted energy conversion.

### Uniform and uneven discharge

• In the case of uniform discharge , the flow velocity does not change along a streamline .
• In the case of stationary (constant over time) and uniform discharge , the water level is parallel to the channel bottom .
• Constrictions, expansions, thresholds and the like lead to discharge conditions in which the discharge is uneven and the water level is no longer parallel to the channel bottom.

### Flood and sink

If the discharge changes over time, one speaks of unsteady conditions . This occurs particularly clearly with sudden changes in discharge z. B. by opening and closing weirs or in the event of disasters such as dams breaking. A surge is understood to mean a sudden increase in the discharge and sink to mean a sudden decrease in the discharge.

### calculation

Under steady-state conditions , the calculation is carried out either according to simple formulas for given discharge cross-sections or in sections from profile to profile.

• In practice, the average flow velocity is usually calculated using empirical formulas (e.g. the flow formula according to Gauckler-Manning-Strickler or Darcy-Weisbach ) if the cross-section is known .
• An exact mathematical calculation of the water level is only possible for a rectangular channel after solving the one-dimensional equation of motion . The calculations using structured transverse profiles require a calibration of the numerical model on the basis of natural measurements or, alternatively, a higher dimensional calculation approach is chosen to calculate the water level.
• The course of the water level along the flow path with a known discharge is based on Bernoulli's energy equation and occurs with flowing discharge against the direction of flow and with swift discharge with the direction of flow, starting in an initial cross-section with a known level.

The calculation against the direction of flow with flowing discharge means that a possible misjudgment of the water level (both too high and too low) is compensated for in the following section. An overestimated water height results in a lower speed; which has a flatter energy line gradient in the next section and, as a result, a lower water height. The tolerance deviation from the first section is thus compensated for.

Surge and sink, as unsteady flow processes, can only be calculated with more complex formulas.

## sport and freetime

For river surfing and paddling acrobatics , natural or artificial waterfalls with recesses are used. Both in natural rivers and in artificial channels in the course of the use of water power, irrigation or drainage, as well as waterways built purely for sports, which sometimes pump the water in a circuit. Examples are Almkanal south of the city of Salzburg, Mur (until 2016) and Mühlgang in Graz, Paddelkanal on the Danube Island Vienna, Eiskanal in Augsburg and the Eisbach in Munich.

Counter-current systems and wave pools are used for swimming training in confined spaces and for experiencing water.

## Flood of wood, rafting

The Schwarzenbergsche Schwemmkanal , the Holztrift in the Reichraminger Hintergebirge are examples of the use of channels for timber transport without being occupied by people. The rafting down the river was done with rafts working on the rafts. In the past, bays on the west coast of North America were also used to collect and store delimbed logs, especially for processing into paper . Keeping it moist with water prevents insect infestation on logs.

## Flooding

Small channels for drainage with and without the floating of floating and / or sinking substances are used in many ways:

• Gutters diagonally across steep, especially unpaved roads to prevent their erosion by the flow of water
• Paved pointed ditch between the asphalt road and the sidewalk edge.
• on the streets of Freiburg im Breisgau , occasionally also in Villingen and historically in Bern (CH) for cleanliness, irrigation and irrigation
• Gutters under the eaves of a roof area
• Flumes in washrooms
• Flood protection structures on mountain slopes as barriers with small openings to catch debris that has swept away
• Deposition of gravel where a river becomes shallower and wider
• in cattle sheds for the drainage of excrement and urine including litter, sometimes with the support of pushing elements

## Ferries

Running waters can drive cable ferries .

## Flow tests

Technical-physical experiments, for example with boat models, can be carried out in flow or towing channels .