Open Channel Module1

7/27/2019 Open Channel Module1

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Open channelAn open channel may be defined as a passage in which liquid flows with its upper surface exposed toatmospheric pressure.

Comparison between open channel and pipe flow

Classification of open channelsOpen channels are classified according to:1)Cross sectional form2)Geometrical shape3)Covering

Types of channels based on cross-sectional form:a)Natural channels:

Sl.No. Aspects Open channel flow Pipe flow

1 Cause of flow Gravity force, provided bysloping bottom

Flow generally takes place atthe expense of hydraulicpressure.

2 Geometry of c/s May have any shape-triangular, rectangular,trapezoidal etc.

Generally round in shape

3 Surfaceroughness

Varies with the depth offlow

Varies from low to highervalues and depends on thematerial of pipe

4 Piezometrichead

Equal to (Z+y); Z=datumhead, y=depth of flow

Equals to (Z+p/w);p/w=pressure head

5 Velocitydistribution

Maximum velocity occursat a little distance belowthe outer surface

Distribution is symmetricalabout the pipe flow.


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It is the one which has irregular section of varying shapes, which is developed in a natural way.Eg:rivers,streams etc.b)Artificial channel:These are which is built artificially for carrying water for various purposes. These have regulargeometric shape.Eg: Aqueduct, canal etc.

Based on shape:a)Rectangular channeltrapezoidal channelc)Circular4)ParabolicBased on covering:a)Closed channelb)Open channel

Prismatic channelThis is the channel with constant bed slope and same cross sectional area along its length.Two types are there:1)Exponential channel2)Non-exponential

Classification of flow in open channel:

1)Steady flow and Unsteady flow:If the flow characteristics such as depth of flow(y),velocity(v),rate of flow(Q) at any point in openchannel flow do not change w.r.t. time, the flow is said to be Steady flow.

If the flow characteristics such as depth of flow(y),velocity(v),rate of flow(Q) at any point in openchannel flow changes w.r.t. time, the flow is said to be Unsteady flow.

2)Uniform and Non-uniform flow:If the flow characteristics such as depth of flow(y),velocity(v),slope of the bed of the channel (S) andcross section ,remains constant for a length of channel ,the flow is said to be Uniform flow.

If the flow characteristics such as depth of flow(y),velocity(v),slope of the bed of the channel (S) andcross section ,do not remains constant for a length of channel ,the flow is said to be Non-uniform flow.Non-uniform flow in an open channel is also known as varied flow and classified as:1)Gradually varied flow (G.V.F):If the depth of flow(y) in open channel changes gradually over a long length of the channel,then theflow is said to be Gradually varied flow.

2)Rapidly varied flow:If the depth of flow (y)in open channel changes abruptly over a small length of the channel.When there is any obstruction in the path of flow of water ,the level of water rises above theobstruction and then the falls and again rises over a small length of channel.Thus the depth of flowchanges rapidly over a short length of channel.

3)Laminar and turbulent flow:If Reynolds number(Re) is between 500 to 600,the flow is called Laminar.It is a layer by layer flow.


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Turbulent flow:It is a zig zag floe and for this flow Re>2000.

Critical flow:If the Froudes number,Fr=1,the flow is criticalIf Fr1,flow is super criticalTerms related to channel flow:

1.Depth of flow(y):It is the vertical distance between the bed and free surface of flow.

2.Top width(T):It is the width of the channel section at the free liquid surface exposed to atmospheric pressure.

3Channel slope(S):It is the inclination of the channel bed with horizontal axis.

4.Wetted area(A):It is the are area of cross-section of the channel normal to the direction of flow

5.Wetted Perimeter(P):It is the length of channel boundary in contact with the flowing water at any section

6.Hydraulic Depth(D):It is the ratio of wetted area to top width.ie D=A/T

7.Hydraulic mean depth or Hydraulic radius ( R):It is the ratio of wetted area and wetted perimeter.ie R=A/P.

Discahrge through open channel:

1.Chezys formula:

The velocity flow of liquid in open channel, V=CRS,

where R=hydraulic radius, C=Chezys constant, S=bed slope

Then Discharge ,Q=Area x velocity =AxV=A CRS

ie Q= A CRS

Conveyance of the channel(K):


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It is the measure of the the carrying capacity of channel.

We have ,Q= A CRS, it can be expressed as Q=KS.

ie K= A CR

Mannings formula:

Let C=1/N(R)1/6

where N=Manningscoefficient or roughness coefficient.

Then Verlocity V=1/N(R)1/6 S

Q=A(1/N)(R)1/6 S

Shear stress at the bed of channel()

Shear stress =frictional resistance/areaie =wRS

where w=specific weight of water

R=hydraulic radius

S=slope of bed of channel

Hydraulic radius of channel sections:1.Recatngular channel:

Width =b,depth of flow=yArae,A=b x y, wetted perimeter=b+2yR=A/P=(by)/(b+2y)

2.Trapezoidal channel:

Bottom width=bSide slope=1/nTop width,T=b+ny+ny=b+2nyArea,A=(b+T)/2 x yA=(b+ny)yWetted perimeter,P=[b+2yn2+1]

R=A/P=[(b+ny)y]/[b+2yn2+1]


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3.Circular sectionR=d/4, d=diameter of channel

4.Circular section not running running full:

R=[r/ 2 (-sin2 /2)]Where = angle made by the free liquid surface at the center of the channel

Most economical section of channel:A section of a channel is said to be the most economical when the cost of construction of the channel isminimum.For maximum discharge(Q) wetted perimeter should be minimum.This condition is utilized todetermine the best section of a channel1.Rectangular channel:For most economical rectangular section:3either b=2y or4R=y/2

2.Circular section:a. For maximum velocity condition,the hydraulic radius R=0.3 times the diameter of channel. IeR=0.3db.For maximum discharge condition,the depth of y=0.94 times the diameter of channelie y=0.94d

3.Trapezoidal channel:a.Top width=half of the sloping length.b.Hydraulic radius,R=y/2c. A semi circle drawn from O with radius equals to depth of flow(y) will touches the three sides of thetrapezium

Safety Considerations

An important aspect of highway drainage design is that of traffic safety.

The shape of a roadside channel section should minimize vehicular impact and provide a traversable section forerrant vehicles leaving the traveled way. The ideal channel section, from a safety standpoint, will have flattenedside slopes and a curved transition to the channel bottom.

Maintenance Consideration

Design of open channels and roadside ditches should recognize that periodic maintenance inspection and repairis required. Provisions should be incorporated into the design for access to a channel by maintenance personneland equipment. When assessing the need for permanent or temporary access easements, entrance ramps and


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gates through the right of way fences, consideration should be given to the size and type of maintenanceequipment required.

Damaged channels can be expensive to repair and interfere with the safe and orderly movement of traffic. Minorerosion damage within the right of way should be repaired immediately after it occurs and action taken toprevent the recurrence. Conditions, which require extensive repair or frequently recurring maintenance, mayrequire a complete redesign rather than repetitive or extensive reconstruction. The advice of the DistrictHydraulics Engineer should be sought when evaluating the need for major restoration.

The growth of weeds, brush, and trees in a drainage channel can effectively reduce its hydraulic efficiency. Theresult being that a portion of the design flow may overflow the channel banks causing flooding and possibleerosion.

Accumulation of sediment and debris may destroy vegetative linings leading to additional erosion damage.

Channel work on some projects may be completed several months before total project completion. During thisinterim period, the contractor must provide interim protection measures and possibly advance the plannederosion control program to assure that minor erosion will not develop into major damage.

Economics

Economical drainage design is achieved by selecting the design alternative which best satisfies the established

design criteria at the lowest cost.The economic evaluation of design alternatives should be commensurate with the complexity and importance ofthe facility. Analysis of the channel location, shape, size, and materials involved may reveal possibilities forreducing construction costs, flood damage potential, maintenance problems and environmental impacts.

Coordination with Other AgenciesThere are many Federal, State and local agencies and private entities engaged in water related planning,construction and regulation activities whose interests can affect the design of highway drainage channels. Suchagencies may request the channel design satisfy additional and perhaps governing design criteria. Earlycoordination with these agencies may help avoid delays in the project development process.

Environment

Many of the same principles involved in sound highway construction and maintenance of open channels parallelenvironmental considerations. Erosion, sedimentation, water quality, and aesthetics should be of prime concernto the highway design engineer. Refer to Index 110.2 for discussion on control of water pollution.

Channel Location

General

Assuming adequate functional design, the next most important design consideration is channel location.Locations that avoid poorly drained areas, unstable soil conditions, and frequently flooded areas can greatlyreduce drainage related problems. Refer to Index 110.4 for discussion on wetlands protection.


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Often drainage and open channel considerations are not considered the primary decision factors in the roadwaylocation; however they are factors which will often directly or indirectly affect many other considerations. Oftenminor alignment adjustments can avoid serious drainage problems.

If a channel can be located far enough away from the highway, the concerns of traffic safety and aesthetics canbe somewhat mitigated. The cost of additional right of way may be offset somewhat by the reduced cost oferosion control, traffic protection, and landscaping.

Alignment and GradeOrdinarily, the highway drainage channel must be located where it will best serve its intended purpose, using thegrade and alignment obtainable at the site. Insofar as practicable, abrupt changes in alignment and grade shouldbe avoided. A sharp change in alignment presents a point of attack for flowing water, and abrupt changes ingrade can result in possible scour when the grade is steepened or deposition of transported material when thegrade is flattened.

Ideally, a drainage channel should have flow velocities that neither erode nor cause deposition in the channel.This optimum velocity is dependent on the size and slope of channel, the quantity of flowing water, the materialused to line the channel, the nature of the bedding soil and the sediment being transported by the flow. Refer toTable 862.2 for recommended permissible flow velocities in unlined channels.

The point of discharge into a natural watercourse requires special attention. Water entering a natural watercoursefrom a highway drainage channel should not cause eddies with attendant scour of the natural watercourse. Inerodible embankment soils, if the flow line of the drainage channel is appreciably higher than that of thewatercourse at the point of discharge, then the use of a spillway may be advisable to prevent erosion of thechannel.

Recommended Permissible Velocities for Unlined Channels

Type of Material in ExcavationSection

Permissible Velocity (m/s)

Intermittent Flow Sustained Flow

Fine Sand (Noncolloidal) 0.8 0.8

Sandy Loam (Noncolloidal) 0.8 0.8

Silt Loam (Noncolloidal) 0.9 0.9

Fine Loam 1.1 1.1

Volcanic Ash 1.2 1.1

Fine Gravel 1.2 1.1


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Stiff Clay (Colloidal) 1.5 1.2

Graded Material (Noncolloidal)

Loam to Gravel 2.0 1.5

Silt to Gravel 2.1 1.7

Gravel 2.3 1.8

Coarse Gravel 2.4 2.0

Gravel to Cobbles (Under150 mm)

2.7 2.1

Gravel and Cobbles (Over200 mm)

3.0 2.4

Channel Section

Natural Channels

Natural channels are water conveying sections such as streams, rivers, creeks and swales which have beenformed by natural forces. Good drainage design involving natural channels will maintain the existing flowcharacteristics such as size and shape of channel, flow velocities, and flow distributions.

It should be recognized by the design engineer that streams have inherent dynamic qualities by which changescontinually occur in stream position and shape. These changes may be slow or rapid, but all streams are

subjected to the forces that cause these changes to occur. For example, in alluvial streams, i.e., streams whosebeds and banks are composed of materials deposited in water, it is the rule rather than the exception that bankserode, sediments are deposited, and islands and side channels form and disappear with time. A generalunderstanding of fluvial geomorphology and river mechanics can help evaluate and resolve problems associatedwith alluvial streams. Reference is made to the FHWA publication entitled Highways in the River Environment -Hydraulic and Environmental Design Considerations.

Triangular V-Ditch

The shape of a channel section is generally determined by considering the intended purpose, terrain, flowvelocity and quantity of flow to be conveyed.

The triangular channel or V-ditch is intended primarily for low flow conditions such as in median and roadside

ditches. V-shaped ditches are susceptible to erosion and will require lining when flow velocities exceed thepermissible flow velocities in Table 862.2.

Trapezoidal

The most common channel shape for large flows is the trapezoidal section.

Trapezoidal channels are easily constructed by machinery and are often the most economical.


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When a wide trapezoidal section is proposed, both traffic safety and aesthetics can be improved by rounding allangles of the channel cross section with vertical curves. The approximate length of these vertical curves can bedetermined by the formula:

L = 12/X

where L = length of vertical curve in meters X = horizontal component of side slopes expressed as x,ycoordinates with y = 1

For narrow channels, L, is limited to the bottom width.

For large flows, consideration should be given to using a minimum bottom width of 4 m for construction andmaintenance purposes, but depths of flow less than 0.3 m are not recommended.

Rectangular

Rectangular channels are often used to convey large flows in areas with limited right of way. At some locations,guardrail or other types of positive traffic barrier may be necessary between the traveled way and the channel.

Though rectangular channels are relatively expensive to construct, since the walls must be designed as earthretaining structures, the construction costs can be somewhat offset by the reduced costs associated with right ofway, materials, and channel excavation.

Open channel hydraulic design is of particular importance to highway design because of the interrelationship ofchannels to most highway drainage facilities.

The hydraulic principles of open channel flow are based on steady state uniform flow conditions, as defined inIndex 864.2. Though these conditions are rarely achieved in the field, generally the variation in channelproperties is sufficiently small that the use of uniform flow theory will yield sufficiently accurate results.

Flow Classifications

(1) Steady vs. Unsteady Flow. The flow in an open channel can be classified as steady or unsteady. The flow issaid to be steady if the depth of flow at a section, for a given discharge, is constant with respect to time. Theflow is considered unsteady if the depth of flow varies with respect to time.

(2) Uniform Flow. Steady flow can further be classified as uniform or nonuniform. The flow is said to beuniform if the depth of flow and quantity of water are constant at every section of the channel underconsideration. Uniform flow can be maintained only when the shape, size, roughness and slope of thechannel are constant. Under uniform flow conditions, the depth and mean velocity of flow is said to benormal. Under these conditions the water surface and flowlines will be parallel to the stream bed and ahydrostatic pressure condition will exist, the pressure at a given section will vary linearly with depth.

As previously mentioned, uniform flow conditions are rarely attained in the field, but the error in assuminguniform flow in a channel of fairly constant slope, roughness and cross section is relatively small whencompared to the uncertainties of estimating the design discharge.

(3) Non-uniform Flow. There are two types of steady state non-uniform flow:

1 Gradually varied flow.

Gradually varied flow is described as a steady state flow condition where the depth of water varies graduallyover the length of the channel. Under this condition, the streamlines of flow are practically parallel andtherefore, the assumption of hydrostatic pressure distribution is valid and uniform flow principles can beused to analyze the flow conditions.


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1 Rapidly varied flow.

With the rapidly varied flow condition, there is a pronounced curvature of the flow streamlines and theassumption of hydrostatic pressure distribution is no longer valid, even for the continuous flow profile. Anumber of empirical procedures have been developed to address the various phenomena of rapidlyvaried flow. For additional discussion on the topic of rapidly varied flow, refer to "Open-ChannelHydraulics" by Chow.

Open Channel Flow Equations

The equations of open channel flow are based on uniform flow conditions. Some of these equations have beenderived using basic conservation laws (e.g. conservation of energy) whereas others have been derived using anempirical approach.

(1) Continuity Equation. One of the fundamental concepts which must be satisfied in all flow problems is thecontinuity of flow. The continuity equation states that the mass of fluid per unit time passing every section ina stream of fluid is constant. The continuity equation may be expressed as follows:

Q = A1V1 = A2V2 = ... = AnVnWhere Q is the discharge, A is the cross-sectional flow area, and V is the mean flow velocity. This equation is

not valid for spatially varied flow, i.e., where flow is entering or leaving along the length of channel underconsideration.

(2) Bernoulli Equation. Water flowing in an open channel possesses two kinds of energy: (1) potential energyand (2) kinetic energy. Potential energy is due to the position of the water surface above some datum. Kineticenergy is due to the energy of the moving water. The total energy at a given section as expressed by theBernoulli equation is equal to:

H = z + d +2gV2

Where:

H = Total head, in meters of water

z = Distance above some datum, in meters

d = Depth of flow, in meters

g = Acceleration of gravity= 9.81 m/s2

3) Energy Equation. The basic principle used most often in hydraulic analysis is conservation of energy or theenergy equation. For uniform flow conditions, the energy equation states that the energy at one section of achannel is equal to the energy at any downstream section plus the intervening energy losses. The energy

equation, expressed in terms of the Bernoulli equation, is:

(4) Manning's Equation. Several equations have been empirically derived for computing the average flowvelocity within an open channel. One such equation is the Manning Equation. Assuming uniform andturbulent flow conditions, the mean flow velocity in an open channel can be computed as:

V =(1/nR S2/3)1/2

Where V = Mean velocity, in meters per second

n = Manning coefficient of roughness


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S = Channel slope, in meters per meter

R = Hydraulic Radius, in meters = A/WP

Where A = Cross sectional flow area, in square meters

WP = Wetted perimeter, in meters

Commonly accepted values for Manning's roughness coefficient, n, based on materials and workmanshiprequired in the Standard Specifications, are provided in Table 864.3A. The tabulated values take into account

deterioration of the channel lining surface, distortion of the grade line due to unequal settlement,construction joints and normal surface irregularities. These average values should be modified to satisfy anyforeseeable abnormal conditions.

Direct solutions for Manning's equation for many channels of trapezoidal, rectangular, and circular cross sectionscan be found in FHWA's Hydraulic Design Series No. 3, "Design Charts for Open Channel Flow".

(5) Conveyance Equation. Often it is convenient to group the properties peculiar to the cross section into oneterm called the conveyance factor, K. The conveyance factor, as expressed by the Manning's equation, isequal to:

K=AR2/3nFor the non-pressure, full flow condition, the geometric properties and conveyance of a channel section can be

computed. Then for a given channel slope the discharge capacity can be easily determined.

Average Values for Manning's Roughness Coefficient (n)

Type of Channel n value

Unlined Channels:

Clay Loam 0.023

Sand 0.020

Gravel 0.030

Rock 0.040

Lined Channels:

Portland Cement Concrete 0.014

Air Blown Mortar (troweled) 0.012

Air Blown Mortar(untroweled)

0.016

Air Blown Mortar

(roughened)

0.025

Asphalt Concrete 0.018

Sacked Concrete 0.025

Pavement and Gutters:

Portland Cement Concrete 0.015

Asphalt Concrete 0.016


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Depressed Medians:

Earth (without growth) 0.040

Earth (with growth) 0.050

Gravel 0.055

(6) Critical Flow. A useful concept in hydraulic analysis is that of "specific energy". The specific energy at agiven section is defined as the total energy, or total head, of the flowing water with respect to the channelbottom.

When the depth of flow is plotted against the specific energy, for a given discharge and channel section, theresulting plot is called a specific energy diagram (see Figure 864.3C). The curve shows that for a givenspecific energy there are two possible depths, a high stage and a low stage. These flow depths are calledalternate depths. Starting at the upper right of the curve with a large depth and small velocity, the specificenergy decreases with a decrease in depth, reaching a minimum energy content at a depth of flow known ascritical depth. A further decrease in flow depth results in a rapid increase in specific energy.

Flow at critical depth is called critical flow. The flow velocity at critical depth is called critical velocity. Thechannel slope which produces critical depth and critical velocity for a given discharge is the critical slope.

Uniform flow within approximately 10 percent of critical depth is unstable and should be avoided in design, ifpossible. The reason for this can be seen by referring to the specific energy diagram. As the flow approachescritical depth from either limb of the curve, a very small change in energy is required for the depth toabruptly change to the alternate depth on the opposite limb of the specific energy curve. If the unstable flowregion cannot be avoided in design, the least favorable type of flow should be assumed for the design.

When the depth of flow is greater than critical depth, the velocity of flow is less than critical velocity for a givendischarge and hence, the flow is subcritical. Conversely, when the depth of flow is less than critical depth,

the flow is supercritical.When velocities are supercritical, air entrainment may occur. This produces a bulking effect which increases the

depth of flow. For concrete lined channels, the normal depth of flow with bulking can be computed by usinga Manning's "n" value of 0.018 instead of the 0.014 value given in Table 864.3A. Air entrainment also causesa reduction in channel


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Specific Energy Diagram

Critical depth is an important hydraulic parameter because it is always a hydraulic control. Hydraulic controlsare points along the channel where the water level or depth of flow is limited to a predetermined level or canbe computed directly from the quantity of flow. Flow must pass through critical depth in going from

subcritical flow to supercritical flow. Typical locations of critical depth are at:(a) Abrupt changes in channel slope when a flat (subcritical) slope is sharply increased to a steep

(supercritical) slope,

(b) A channel constriction such as a culvert entrance under some conditions,

(c) The unsubmerged outlet of a culvert on subcritical slope, discharging into a wide channel or with a freefall at the outlet, and

(d) The crest of an overflow dam or weir.

(di)

Critical depth for a given channel is dependent on the channel geometry and discharge only, and is independentof channel slope and roughness.

When flow occurs at critical depth the following relationship must be satisfied

A3/T = Q2/g

Where A = Cross sectional area, in square meters T = Top width of water surface, in meters Q = Discharge,in m3/s g = Acceleration of gravity, 9.81 m/s2

Critical depth formulas, based on the above equation, for various channel cross-sections include:

1 Rectangular sections,

dc = (q2/g)1/3Where q = Flow per unit width, in m3/s

1 Trapezoidal sections. The tables in King's "Handbook of Hydraulics" provide easy solutions for criticaldepth for channels of varying side slopes and bottom widths.

2 Circular sections. The tables in King's "Handbook of Hydraulics" can be used for obtaining easy solutionsfor critical depth.

(7) Froude Number. The Froude number is a useful parameter which uniquely describes open flow. The Froudenumber is a dimensionless value:

Fr = V/(gD)1/2

Where D = A/T = Hydraulic depth, in meters

Fr < 1.0 ==> Subcritical flow

Fr = 1.0 ==> Critical flow

Fr > 1.0 ==> Supercritical flow


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NUMERICALS:

1. What are the types of open channel flow?

Solution

Types of Open-Channel Flow

A. Steady flow1. Uniform flow2. Varied flow

i. Gradually variedii. Rapidly varied

B. Unsteady flow1. Unsteady uniform flow2. Unsteady varied flow

i. Gradually variedii. Rapidly varied


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Steady flow

The flow of the open-channel is steady, if the depth does not change with time interval underconsiderations.

Unsteady flow

The flow of the open-channel is unsteady, if the depth changes with time interval underconsiderations.

Uniform flow

The depth of the open-channel at every section is same, the flow of the open-channel is said to beuniform.

Steady uniform flow

The depth of the open-channel at every section is same, and it also does not change with timeinterval under considerations.

Unsteady uniform flow

The depth of the open-channel at every section is same, and it changes from time to time, watersurface flocculates from time to time under considerations.

Varied flow

The flow is said to be varied, if the depth changes in the direction of the channel.

Steady gradually varied flow


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The depth of the flow changes gradually along the length of the channel and it does not changerswith time interval under consideration.

Steady rapidly varied flow

The depth of the flow varies rapidly with corporately short distance and it does not change duringtime interval under consideration.

Unsteady gradually varied flow

The depth of the flow varies gradually along its length of the channel and also it changes with itstime.

Unsteady rapidly varied flow

The depth of the flow varies rapidly over along short distance and also it changes with itstime.

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2. Water is flowing at a velocity of 12 ft/s and depth of 10 ft in a channel ofrectangularsection.Find the change in depth and absolute water level produced by (a) the smooth upward step of0.5 ft, (b) the smooth downward step of 1 ft in the channel bed. Also (c) find the maximumallowable size of upward step for the upstream to be possible as specified.

Solution

V1 = 12 ft/s

y 1 = 10 ft

a. z (upward) = 0.5 ftY y2 y 1 = ? , y = ?b. z (downward) = 1ft Y y2 y 1 = ? , y = ?c. z (upward) = ? E2 = Ec


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(a) 0

E1 = E2 + z + losses

= 12.236 ft

E2= E1- z

= 12.236 0.5 = 11.736

Q = b1y1V1 = b2 y2 V2

V2 = y1 V1/ y2 = 12 x10/ y2 = 120/ y2

By trial error,

y 2 = 8.935 ft or y 2 = 6.59 ft

possible depth is 8.935 ft

change in depth = y1 y 2


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= 10- 8.935 = 1.065 ft

Change in absolute water level y = 10 ( 8.935 + 0.5 )

= 0.565 ft

E1 = E2 - z + losses

= 12.236 ft

E2 = E1+ z

= 12.236 + 1 = 13.236 ft

By trial error,

y 2 = 11.564 ft or y 2 = 5.31 ft

possible depth is 11.564 ft

Change in depth = y2 y 1 = 11.564 10 = 1.564 ft

Absolute water level y = 1.564 1 = 0.564 ft

(c) for the u/s flow to be possible as specified


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E2 = E c ( or ) E min

For the critical flow, q = Vy = 12 x 10 = 120 ft2 / s

= 7.647 ft

Ec = 3/2 yc = 11.471 ft

E1 = Ec + z

z = Ec - E1 = 12.236-11.471 ft

z (upward) = 0.765 ft

3. A trapezoidal channel having bottom width 5 m and side slopes 1:1 carries a discharge of 12m3/ s. Compute the critical depth and critical velocity. If the Mannings n = 0.02 determine thebottom slope required to maintain the critical depth.

Solution

T = b + 2zyc = 5 +2x1 yc = 5 +2yc

A = (b + zyc) yc = (b + yc) yc

For critical flow,

By trial error,


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yc = 0.792 m

A= ( 5 + 0.792 ) x 0.792 = 4.587 m2

= 2.616 m /s

n = 0.02 Y s = ?

Using Mannings formula,

S = 0.00503 , yc = 0.792 m , Vc = 2.616 m/s

4. Design an economical earthen trapezoidal channel with velocity of 1 m/s and to discharge 3m3/s having side slope 1 in 2. Take C = 55.

Solution

V = 1 m/s

Q = 3 m3/s

Z = ?

C = 55


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Foreconomicalsection,

b + 4y = 4.472 y

b = 4.472 y 4y = 0.472 y

A = ( b + zy ) y

= (0.472 y + 2 y ) y = 2.472 y2

P = b + 2y = 0.472 + 4.472 y = 4.944 y

A = 2.472 y2 = 3

y = 1.102 m , b = 0.52 m

P = 4.944 x 1.102 = 5.448 m

3 = 55 x 3 x

S = 0.0006

y = 1.102 m , b = 0.52 m , S = 0.006

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5. A trapezoidal channel carrying 400 cfs is built with non-erodible bed having a slope of 0.0016and n= 0.015. Proportion the section dimension.


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Solution

n = 0.015 , S = 0.016 , Q = 400 ft 3 / s

Assume b = 20 ft , z = 2

A = ( b + zy ) y

= ( 20 + 2 y) y

P = b + 2y = 20 + 4.472 y

By Mannings formula,

y = 2.519 ft

A = ( 20 + 2 x 2.519) x 2.519

= 63.071 ft

Check permissible velocity,

m/s > V min = 2.3 m/s O.K

The velocity should prevent sedimentation and vegetation growth.

T = b + 2 z y = 20 + 4 x 2.519 = 30.076 ft


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= 0.772 < 1

Sub critical flow.

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Documents

Open Channel Module1