What is Open Channel Flow? What are the different flow in Channels?

Open channel flow is defined as the flow of the liquid with free surface. The free surface is a surface ( here water surface) which is subjected to constant atmospheric pressure. Hence, an open channel flow is the flow of water through the channel under the action of atmospheric pressure alone. 

An example of open channel flow is the flow of water through pipe under atmospheric pressure or the flow through pipe below the pipe.

In case of open channel flow, two important criteria you must keep in mind is the action of atmospheric pressure and  water flow due to gravity. As no other forces exist to facilitate the flow through the pipes, the water moves through the channel under the action of gravity. To move along gravity, the channel is provided with a slope.

Types of Flow in Open Channels

The different flow in open channels are:

1. Steady Flow and Unsteady Flow
2. Uniform and Non-uniform flow
3. Laminar flow and Turbulent Flow
4. Sub-critical, critical and super critical flow

1. Steady and Unsteady Flow in Open Channels

Steady Flow in Open Channels

The flow characteristics like depth, velocity and rate of flow at any point in the open channel do not change with respect to time.

δV/δt =0;δQ/δt=0;δy/δt = 0;

y = depth of flow , v = Velocity of flow and Q = Rate of discharge

Fig.1. Steady Flow in Open Channels; 

As shown in figure-1 above, any point is considered say p1 and p2 whose respective depth are y1 and y2. This is checked at a time T1. The depth at these points are checked at a time T2. If we get the depth value as y1 and y2 at p1 and p2 respectively, then it means with time there is no variation in depth with time. Hence the flow is steady. This is checked for any one point.

The example is given for depth. It must be checked for discharge and velocity at a point also.

Unsteady Flow in Open Channels

If the rate of flow, depth of flow and velocity of flow at any point on the open channel changes with time, then it is unsteady flow.

δV/δt ≠0; δQ/δt≠0 ; δy/δt ≠ 0                         y = depth of flow , v = Velocity of flow and Q = Rate of discharge

Fig.2. Unsteady Flow in Open Channels; Change in Velocity at points p1 and p2 with respect to time T1 and T2

2. Uniform Flow and Non-Uniform Flow

Uniform flow in Open Channels

For a given channel length, if the parameters- velocity of flow, depth of flow, cross-section of flow and the slope of the channel remains constant, then the flow through that length is uniform.

Non-Uniform Flow in Open Channels

δy/δS=0; δV/δS=0;

Fig.3. Uniform Flow in Open Channels; Consider a length, the depth is y1 at p1 and p2 points.

Non-Uniform Flow in Open Channels

For a given channel length, if the parameters- velocity of flow, depth of flow, cross-section of flow and the slope of the channel do not remains constant, then the flow through that length is non-uniform.

δy/δS ≠0;δV/δS ≠0

Fig.4. Non-Uniform Flow in Open Channels: Depth varies throughout the length.

The non-uniform flow is divided into two:

• Rapidly varying flow
• Gradually Varying Flow

Rapidly Varying Flow (R.V.F)

Rapidly varying flow is a non-uniform flow that shows abrupt change in flow for a small distance as shown in figure-5. 

As shown in the figure, due to a small obstruction, the water suddenly rises and moves down and again rises over  a small distance. 

For this small length of channel, the depth of flow vary rapidly. This is called as rapidly varying flow.

Gradually Varied Flow (G.V.F)

If the change in depth of the channel flow is very gradually, then the flow is called as gradually varied flow as shown in the figure-5 above.

Laminar and Turbulent Flow in Open Channel Flow

The flow in open channel is categorized as laminar and turbulent based on the Reynolds number(Re).

Re = ρVR/μ;

ρ = density of water

μ = viscosity of water

V = mean velocity of flow of water;

R = Hydraulic radius or hydraulic mean depth

• The flow is laminar when Re is < 500 or 600
• The flow is turbulent when Re is > 2000
• The flow is in transition state, when Re is between 500 and 2000

 

Note:
Hydraulic mean depth or hydraulic radius is R which is equal to the ratio of cross sectional area of the flow normal to the direction of flow to the wetted perimeter.

Sub-Critical, Critical and Super Critical Open Channel Flow

The flow is stated critical, sub-critical and super critical based on Froude's number. Froude's number is given by, Fe

V=Mean Velocity of Flow

D= Hydraulic depth of channel 

g = acceleration due to gravity

• For sub-critical or tranquil or streaming flow, Fe is < 1;
• For critical Flow, Fe = 1;
• For  super-critical or rapid flow or torrential flow, Fe > 1;

Also Read: Classification of Fluids Based on Newton's Law