design of open channel.pdf

7/27/2019 DESIGN OF OPEN CHANNEL.pdf

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2.6 Design of Open Channels

Open channels have uses in

urban stormwater drainage urban sanitarysewer systems irrigation delivery systems

In the next few lectures, well discuss the design procedure for 3types of open channels:

lined (nonerodable channels) are primarily used to maximize flowrates and minimize construction costs

unlined (erodible channels) are the least expensive and what iscommonly found in nature, but often experience unacceptable levelsof sediment transport and erosion.

grasslined are commonly used to transmit intermittent irrigationand stormwater flows and to control erosion

Open Channel Flow 1/27 2.5 Design of Channels


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Open Channel Design Fundamentals

There are many design considerations which are common to all 3types of channels. This includes the determination of the besthydraulic section. The best hydraulic section will accommodate

the design flow at a reasonable cost and limit erosion/deposition ofsediment and other material.

Trapezoidal Channel

To determine the optimum channel size for a trapezoidal channel,we need to determine the optimum channel width and side slope (tominimize excavation costs) which will maximize the flowrate. Firstrecall Mannings Equation,

Q=1

nAR

23S

o

12

Rearranging

A=Qn

So

3

5

P

2

5

Restating the above statement another way, we need to minimize A& P with respect to Q or

Qn

So

3

5

Recall the area and wetted perimeter definitions for a trapezoidalcross section

combining these two equations



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substituting into Mannings equation

The optimum perimeter/area is determined by differentiating withrespect to y (while holding m constant).

Similarly, the optimum channel side slope is determined bydifferentiating with respect to m (while holding y constant).

Combing the optimum perimeter and optimum slope equations, wecan determine the best hydraulic section for a trapezoid is

This solution assumes the channel slope can be set to any value.Often this is not possible, in which case use a known (or specified)m value to determine the optimum perimeter. Please note, for linedchannels, the side slope is often specified as being less than 33.7o.The best hydraulic section for a variety of channels is given in thebelow table



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Other considerations

The previous derivations does not consider the following points:

freeboard (distance between water surface and top of channel) whether or not its possible to excavate the optimum channel cost of lining access to site

Minimal permissible velocity

0.60.9 m/s (23 ft/s) to prevent sedimentation 0.75 m/s (2.5 ft/s) to prevent vegetation growth

Channel Slopes

Longitudinalgoverned by topography (unless velocities are too low) Side Slopesa function of material



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Other considerations (continued)

Freeboard

The freeboard is the vertical distance between the water surface and

the top of the channel slope. Its basically a factor of safety to keepthe channel from overflowing. For unlined channels, the freeboard isestimated with:

F=0.55 Cywhere

F is the freeboard in metersy is the design flow depthC is a coefficient

Generally, ASCE recommends a minimum freeboard of 30 cm. Insinuous channels, additional freeboard is need at he channel bendsto account for the superelevation of the water surface. Thesuperelevation in the vicinity of the bend is approximated with

hs=

V2T

grc

whereV is the average velocityT is the top width of the channelrc is the bend radius

According to the USACE (1995) rc > 3T



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Design of Lined Channels

Lined (or rigidboundary channels) are used in the followingsituations:

transmit flow at high velocities decrease seepage losses decrease maintenance and operation costs ensure channel stability

The design procedure for lined channels is as follows:1. Estimate the roughness coefficient, n, and the freeboard

coefficient, C, for the desired channel lining and flowrate

2. Compute the normal depth of flow, yn, with Mannings equation

Q=1

nAR

2

3S

o

1

2

3. Verify that: minimum permissible velocities are being met

flow is subcritical, Fr < 0.8

maximum permissible velocities are being metV < 2.1 m/s unreinforced channelV < 5.5 m/s reinforced channels

If necessary, choose new channel dimensions and recalculate ynto ensure above criteria are satisfied.

4. Calculate the required freeboard (including the additionalfreeboard at channel bends)



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Example~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Design lined channel to carry 20 m3/s on a longitudinal slope of0.0015. The lining of the channel is to be reinforced float finishedconcrete. Consider a) the best hydraulic section and b) a section

with side slopes of 1.5:1 (H:V).Solution~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a) given:

1. Estimate the roughness coefficient, n, and the freeboardcoefficient, C, for the desired channel lining and flowrate

2. Compute the normal depth of flow, yn, with Mannings equationdetermine best hydraulic section:

Q=1

nAR

2

3S

o

1

2

b=2.4 myn=2.09 m



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3. Verify that: minimum permissible velocities are being met

V=2.6 m/s flow is subcritical, Fr


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b)

Step 1. Estimate the roughness coefficient, n, and the freeboardcoefficient, C, for the desired channel lining and flowrate

Step 2. Compute the normal depth of flow, yn, with Manningsequation

determine the geometry given H:V=1.5:1

Q=

1

nAR

2

3

So

1

2

b=1.16 myn=1.94 m



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Step 3. Verify that: minimum permissible velocities are being met

V=2.53 m/s flow is subcritical, Fr


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Design of Unlined Open Channels

In the design of unlined channels, it is necessary to assure thatsediment wont be eroded from or deposited on channel beds. Todesign new (or analyze existing), well need to approximate the

stress applied to the channel walls by the fluid and the stressrequired to move the sediment particles.

Stress applied by the flow

The stress applied by the flow is not applied evenly to the channelsidewalls and bottom walls. For the two conditions it is defined with

bottom

side

Stress required to move sediment

The stress required to move particles on the bottom is a function ofthe immersed particle weight, the particle geometry, and the appliedfriction between particles.

Where

the critical stress required for sediment to move becomes



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For particles on the side slope of the channel, the relationship withgravity is more complicated. The above expression is modified, sothe critical stress to move particles on the channel sides becomes

where

The ratio of the critical shear stress on the side to the critical shearstress on the bottom is defined as the tractive force, K, with



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Design of Unlined Channels (continued)

1. Estimate the roughness coefficient, n, based on the perimetercharacteristics (attached table) of the channel, and select thefreeboard coefficient, C, based on the design flowrate in the

channel.

2. Estimate the angle of repose (attached figure 4.31)

3. Estimate the channel sinuousness and the tractive forcecorrection factor (attached table 4.15)

4. Specify a side slope angle (attached table 4.13)

5. Estimate the tractive force

6. Estimate the permissible tractive force on the bottom and sides ofthe channel



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7. Assume permissible shear stress on the channel sides is thelimiting design factor, and determine the normal depth

8. Calculate the required bottom width, b, of the channel usingMannings equation

9. Compare the permissible tractive force on the bottom with theactual tractive force

10.Compare the permissible velocity and calculate the Froudenumber (verify that it is subcritical)

11. Estimate the required freeboard and super elevation if needed



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Example~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Design a trapezoidal channel to carry 20 m3/s through a slightlysinuous channel on a slope of 0.0015. The channel is to beexcavated in course alluvium with a 75percentile diameter of 2 cm

(.8 in) and with particles on the perimeter of the channel moderatelyrounded.

Solution~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Step 1. Estimate the roughness coefficient, n, and select thefreeboard coefficient, C, based on the design flowrate in the channel.

Step 2. Estimate the angle of repose (attached figure 4.31)

Step 3. Estimate the channel sinuousness and the tractive forcecorrection factor (attached table 4.15)

Step 4. Specify a side slope angle (attached table 4.13)

Step 5. Estimate the tractive force

Step 6. Estimate the permissible tractive force on the bottom andsides of the channel



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Step 7. Determine the normal depth

Step 8. Calculate the required bottom width, b, of the channel usingMannings equation

Step 9. Compare the permissible tractive force on the bottom withthe actual tractive force

Step 10. Verify permissible velocity and that flow is subcritical

Step 11. Estimate the required freeboard

The total depth of the channel to be excavated (including thefreeboard) is 1.27. The channel is to have a bottom width of 24.2and sides slopes of 2:1 (H:V).



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Design of GrassLined Open Channels

Grasslined are often used to transmit intermittent irrigation andstorm water flows. They are often preferable to lined channelsbecause they provide increased storage, low velocities, and

aesthetic benefits. The additional design considerations for grasslined channels include:

Channel Roughness The Mannings n value is a function of thevelocity and channel geometry, in addition to the roughnessprovided by the grass.



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The mannings n for the various retardances is given in the belowfigure.

Permissible Velocities There exists a variety of considerations fordetermining the maximum permissible velocities in a grasslinedchannel. Those include the table on the next page (table 4.18) andthe below considerations from the soil conservation service

Vmax(m/s) Conditions

0.9 Sparse vegetive cover possible

0.91.2 Vegetation to be established by seeding

1.21.5 Dense sod (or temporarily diverted flow)

1.51.8 Wellestablished sod

1.82.1 Very special conditions ???



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Channel Cross Sections In addition to the best hydraulic sectionand slope stability, grass lined channels may have to be designed toallow farm equipment to cross.

Freeboard The freeboard on a grass lined channel is defined with



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Design Procedure for grasslined channels

This procedure must completed for BOTH upper and lower bound ofretardance (ie. Mowed and unmowed conditions).

Stage I Lower Bound Retardance1. Assume the value of the roughness coefficient and determine the

value of VR

2. Select the maximum permissible velocity (attached table)

3. Using Mannings equation, compute new VR

4. Repeat until VR is converged

5. Determine A from design flow and maximum permissible velocity

6. Determine the channel proportions for the calculated values of Rand A



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Stage II Upper Bound retardance

1. Assume a depth of flow for the channel assumed in Stage I andcompute A and R.

2. Compute the averaged velocity

3. Compute VR using the results of 1 & 2

4. determine n from the attached figure using the upper boundretardance

5. Use the n from step 4, R from step 1, compute V from themannings equation

6. Repeat 1 5 until V has converged

7. Add the appropriate freeboard and check the Froude number



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Example~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Design a triangular grasslined channel to handle intermittent flow of0.7 m3/s. The channel is to be excavated in an easily erodible soil,on a longitudinal slope of 2%, and lined with Bermuda grass. During

the early stages of channel development, the height of the grass willbe maintained at about 4 cm (a retardance of E); during the latterstages of development, the Bermuda grass is expected to be at aheight of about 30 cm (a retardance of B).

Solution~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

given:Q=0.7m3/sSo=0.02

Bermuda grasseasily eroded soilStage I: E retardanceStage II: B retardance

Stage I1. 4. guess at n, determine VR

determine Vmax from table

compute R=VR/Vmaxfind new VR from Mannings eqrepeat with adjusted n

n VR(ft2/s)fig4.33

VR(m2/s)fig4.33/10.76

R(m)VR/Vmax

VR(m2/s)=R5/3So1/2/n

n



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n VR(ft2/s)fig4.33

VR(m2/s)fig4.33/10.76

R(m)VR/Vmax

VR(m2/s)=R5/3So1/2/n

n

Find the Area (triangle)

Determine channel geometry from A and R

m=1.71y=0.48 m

note: youll get two solutions for m and have to choose the best

Stage II:

1. 4. guess at y, from stage I from stage I geometrycompute A & R from known geometrycompute the average velocity (=Q/A)compute VRdetermine n (fig 4.33)compute V from mannings equation



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Y(m)

A(m2)

R(m)VR/Vmax

V(m/s)=Q/

A

VR(m2/s)

VR(ft2/s)VR*10.76

n

fig4.33

V(m/s)=R2/3So1/2/n

V

Find the freeboard

F=0.3

Check for subcritical flow

Fr=0.38, subcritical, ok design

The total depth of flow is 1.05 m. The triangular channel is to haveside slopes of 1.7:1 (H:V).


design of open channel.pdf

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