Hydraulic 2

4.0 FLOWS IN OPEN CHANNEL

Definitions

Open Channel flow: The flow of water in a conduit with a free surface at atmospheric pressure. The flow in open channel mainly governed by gravity (i.e. channel bed slope)

Critical flow: The variation of specific energy with depth at a constant discharge shows a minimum in the specific energy at a depth called critical depth at which the Froude number has a value of one. Critical depth is also the depth of maximum discharge, when the specific energy is held constant.

Froude number: The Froude number is an important dimensionless parameter in open-channel flow. It represents the ratio of inertia forces to gravity forces. This expression for Froude number applies to any single-section channel of nonrectangular shape.

Hydraulic jump: Hydraulic jumps occur at abrupt transitions from supercritical to subcritical flow in the flow direction. There are significant changes in the depth and velocity in the jump, and energy is dissipated. For this reason, the hydraulic jump is often employed to dissipate energy and control erosion at stormwater management structures.

Kinetic energy coefficient: As the velocity distribution in a river varies from a maximum at the design portion of the channel to essentially zero along the banks, the average velocity head.

Normal depth: For a given channel geometry, slope, and roughness, and a specified value of

discharge Q, a unique value of depth occurs in a steady uniform flow. It is called the normal depth. The normal depth is used to design artificial channels in a steady, uniform flow and is computed from Manning’s equation.

Specific energy: Specific energy (E) is the energy head relative to the channel bottom. If the

channel is not too steep (slope less than 10%), and the streamlines are nearly straight and parallel (so that the hydrostatic assumption holds), the specific energy E becomes the sum of the depth and velocity head. The kinetic energy correction coefficient is taken to have a value of one for turbulent flow in prismatic channels but may be significantly different from one in natural channels.

Steady and unsteady flow: A steady flow is when the discharge passing a given cross section is constant with respect to time. When the discharge varies with time, the flow is unsteady. The

maintenance of steady flow requires that the rates of inflow and outflow be constant and equal.

Subcritical flow: Depths of flow greater than critical depths, resulting from relatively flat slopes. Froude number is less than one. Flow of this type is most common in flat streams.

Supercritical flow: Depths of flow less than critical depths resulting from relatively steep slopes.

Froude number is greater than one. Flow of this type is most common is steep streams.

Total energy head: The total energy head is the specific energy head plus the elevation of the

channel bottom with respect to some datum. The curve of the energy head from one cross section to the next defines the energy grade line.

Uniform flow and non-uniform flow: A non-uniform flow is one in which the velocity and depth vary over distance, while they remain constant in uniform flow. Uniform flow can occur only in a channel of constant cross section, roughness, and slope in the flow direction; however, non-uniform flow can occur in such a channel or in a natural channel with variable properties.

Properties of open channel

Artificial channels

These are channels made by man. In the field they are commonly constructed of concrete, steel or earth and have the surface roughness reasonably well defined. They include irrigation canals, navigation canals, spillways, sewers, culvert and drainage ditches.

Natural channels

Natural channels can be very different. They are not regular or prismatic and their materials of construction can very widely. They are including river, lake and sea water.

Types of open channel flows –

Steady flow – when discharge (Q) does not change with time.

Uniform flow – when depth of fluid does not change for a selected length or section of the channel

Uniform steady flow – when discharge does not change with time and depth remains constant for a selected section - cross section should remain unchanged – referred to as a prismatic channel

Varied steady flow – when depth changes but discharge remains the same (how can this happen?)

Varied unsteady flow – when both depth and discharge change along a channel length of interest.

Rapidly varying flow – depth change is rapid

Gradually varying flow – depth change is gradual

Geometric properties necessary for analysis

The commonly needed geometric properties are shown in the figure below and defined as:

Depth (y) –  the vertical distance from the lowest point of the channel section to the free surface.

Stage (z) – the vertical distance from the free surface to an arbitrary datum.

Area ( A) – the cross-sectional area of flow, normal to the direction of flow.

Wetted perimeter (P) – the length of the wetted surface measured normal to the direction of flow

Surface width (B) – width of the channel section at the free surface

Hydraulic radius ( R ) – the ratio of area to wetted perimeter .