After you have completed your design, or at least completed it conceptually, you now have
enough information to begin the basic analysis of an open channel.
The term “basic” used here is my reference to what is typically called
Steady state and Uniform conditions analysis.
Using this simplified profile view of an open channel, the phrase steady state, refers to
the fact that the flow rate does not change along our channel
boundary – no water entering or leaving the channel.
Uniform conditions refers to the fact that over the length of the channel the shape,
slope, and roughness remain constant.
So ‘steady’ refers to the water in the channel, while ‘uniform’ refers to the
channel itself.
The most common approach to steady/uniform analysis of an open channel is done with Manning’s
equation – or at least the formula we typically refer to as Manning’s equation.
Manning estimated the average velocity of flow in a channel as shown here – a function
of roughness, shape and slope.
The value 1.486 converts the inputs from metric into American units, so we can use units of
ft and ft/s.
The Sf term represents the Friction Slope, but under steady/uniform conditions, the friction
slope is equal to the bed slope.
Using continuity, We can substitute the flowrate Q into Manning’s
equation.
This is helpful to us because when we are presented with the challenge of creating a
new sewer collection or diversion channel, we typically only begin with the design flowrate,
Q. As you may recall, the hydraulic radius is
calculated as the Flow Area divided by the wetted perimeter.
Using the trapezoidal channel as the general case,
the flow area and wetted perimeter can be defined as a function of the flow depth, y,
the base width, b, and side-slopes, represented by the letter z.
When working with rectangular channels the z term is 0, while for triangular channels
the b term is 0.
When you are starting a new analysis project you are typically given, or you have calculated
previously, the flow rate, Q. For a given Q you must conceptually design
the channel which means you must pick the shape, slope and material of the channel,
as covered in the previous video.
Given these inputs the channel is analyzed to determine the normal depth, yn, and the
velocity V. Remember the normal depth is the depth of flow that a channel will have if
the flow is steady and the channel is uniform.
To analyze the channel you must first guess a value for the normal depth.
Next calculate the flow area, wetted perimeter, hydraulic radius, so that you can calculate
the flow rate, Q.
We will call this our Qguess.
We repeat these two steps until the Qguess is equal to the Q given in the problem statement.
This may seem tedious, but there is no way to solve manning’s equation directly for
the normal depth.
Therefore we must approach this situation iteratively.
Other alternatives include using proprietary software, or programming your own solution
into Excel or some other language.
Once the normal depth is determined you can now calculate the velocity in the
channel to make sure that it does not exceed the maximum permissible velocity for your
chosen material.
Finally the freeboard can be determined.
The freeboard is an air gap above the water surface of the channel that acts as a safety
“buffer” in the analysis against any errors made in the computations and the realities
in the field.
What this means is that the depth of the open channel can not simply be the normal depth.
The depth of the channel must be, at a minimum, the normal depth plus the freeboard.
There is no standard criterion for Freeboard.
Many agencies provide a formula which relates the freeboard to the energy in the channel.
Other agencies simply state the freeboard is 1-foot, or 18-inches.
Therefore when applying the freeboard to a channel analysis, you need to determine the
agency specific criteria for freeboard.