# Basic principles of open-channel flow

Open-channel flows are widely spread. Typical examples include rivers and canals, drainage channels, gutters, water rides at amusement parks or sewerage. The driving force of this normally turbulent flow is gravity. Open-channel flows are characterised by their free surface. Compared to pipe flows, open-channel flows have one more degree of freedom as a result of the free surface.

There are essentially two types of open-channel flow:

• uniform flow (the discharge depth (water depth) remains equal; acceleration = deceleration)

• non-uniform flow (the discharge depth is changed by acceleration or deceleration)

The discharge can be either subcritical, critical or supercritical. 1 rapidly varied discharge under a gate, 2 gradually varied discharge, 3 hydraulic jump (rapidly varied), 4 weir overfall (rapidly varied), 5 gradually varied discharge, 6 non-uniform flow at a change of slope

### Typical flume profiles

In most cases an approximation of the respective cross-section of an open-channel flow can be illustrated with only a few geometric profiles. Circular, semi-circular, square, trapezoidal and combinations of these profi les are perfectly suited to making the flume easier to model and calculate mathematically. It is often important to determine the discharge Q and the discharge depth h at defi ned locations. Typical variables for calculations are the fl ow area A (or the area of flow), the wetted perimeter P and the hydraulic radius R.

In the case of a rectangular cross-section, these variables are defined as follows:

• flow area A = bh

• wetted perimeter P = b+2h

• hydraulic radius R = A/P = bh/(b+2h)

In wide, shallow flumes the hydraulic radius R therefore corresponds to the discharge depth h.

In the case of artificial flumes, such as ducts, the hydraulically efficient profile is an important variable – an optimum profile design saves materials and costs:

• given discharge Q + energy grade line J: determine minimum flow area A

• given discharge Q + flow area A: determine minimum energy grade line J

### Optimal hydraulic flume cross-section

In the case of the smallest wetted perimeter, based on the given area, we refer to the optimal hydraulic cross-section. Rectangle, trapezoid with 60° angles, triangle; h discharge depth, b flume width

The HM 250.11 Open channel has a rectangular cross-section.