Fluid Mechanics: Flow Types Classifications in open channel flow

Kariba Dam (Zimbabwe)

Quick Introduction to Fluid Mechanics

Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them.

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As civil engineers, we use fluid mechanics analysis in two types of flows:

1. Open channel flow

2. Pipe flows

The main difference open channel flow and pipe flows is the boundary conditions and the free surface of the liquid.

1. Open Channel flow:

• Open channel flows are characterised by a free surface (usually) open to the atmosphere.

• Open channel flows examples are streams, rivers, artificial canals, irrigation ditches, flumes, pipe-lines, culverts, tunnels, sewer lines, gutters, domestic draining boards.

2. Pipe or duct flow:

• All of the cross-section is taken up with the fluid. This is referred to as a "closed conduit".

• The energy in pipe flow is expressed as head and is defined by the Bernoulli equation.

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Classification of flow types

1. Steady and Unsteady flow

Flow is termed steady or unsteady according to whether the velocity and hence the depth at a particular point on the channel - varies with time (=temporal variations)

Steady flow: Flow is one in which the conditions of velocity, pressure and cross-section may differ from point to point but does not change with time.

Unsteady flow: If at any point the conditions change with time. (However most open channels are considered steady)

2. Uniform and Non-uniform flow

Uniform flow: Is the flow that occurs when the various quantities do not change from point to point over a specified region - at a particular instant in time.

• When the average velocities in successive cross-sections of a channel are the same.

• This only occurs when the liquid surface is parallel to the base of the channel.

constant cross-section = uniform = equilibrium form

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River - An open channel flow

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Non-uniform flow: or varied flow occurs when the various quantities change from point to point over a specified region - at a particular instant in time.

• When depth or velocity changes over a distance either in the direction of flow or perpendicular to it.

Definitions:

Gradually varied flow: Small change

Rapidly varied flow: Wave

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Combinations of flows

1. Uniform (constant depth) flow

2. Non-uniform (variable depth) flow

3. Non-uniform(variable depth) rapidly and gradually varied flow

4. Steady uniform flow (easiest to analyse - common flow in pipes)

5. Steady non-uniform flow

6. Unsteady, uniform flow (pumping)

7. Non-steady, non-uniform flow ( decelerating flow channels)

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Big wedeene River

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3. Laminar and Turbulent flow

a.Laminar flow

At lower velocities, fluid particles move in straight lines through the velocity of the particles along each line may not necessarily be the same - move in layers or laminae

tub water is an example of laminar flow

b. Turbulent flow

At higher velocities, the fluid particles no longer move in a straight path but are intertwining and crossing one another in a disordered, chaotic manner.

Turbulent flow is assumed in open channels analysis

Fact: Even if the surface of a flowing liquid appears smooth and glassy, is no indication that turbulent flow does not exist underneath.

Waterfalls are an example of turbulent flows in open channels

Representation a) laminar and b) turbulent flows diagrams

4. Tranquil and Rapid flow

Tranquil and Rapid flows are fully dependant on the Froude number of the flow classified.

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Froude number: a dimensionless value that describes different flow regimes of open channels

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Tranquil flow: ( Fr<1.0) When the flow velocity is small it is possible for a small disturbance to travel against the flow and thus affect the conditions upstream

Rapid flow: (Fr>1.0) When the flow velocity is high enough that a small disturbance cannot travel ( propagate) against the flow hence cannot affect the conditions upstream.

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