HydrologyandHydraulicsSEV322

HydrologyandHydraulics(SEV322) T1 2025

ProblemSolvingTask1

Hydraulics

(Weight=30%)

Due:

Week7,8:00PM(AEST)

Thursday17April2025, Via CloudDeakin

Thisisanindividualassessmenttask.

Plagiarism and collusion is unacceptable practice at Deakin University. Whereapplicable,you must appropriately referenceyour work. Failureto do so will result in disciplinary action. For more information on plagiarism and collusion please see the CloudDeakin website.

Allsubmissionsmustbetyped,nothandwritten,andmustberecognisable to Turnitin. Submissions that cannot be assessed by Turnitin will not be awarded a mark.

LearningOutcomes

This assessment task has been devised to allow students to demonstrate progress towards achieving the following Unit Learning Outcomes and Deakin Graduate Learning Outcomes:

SEV322ProblemSolvingTask1-Hydraulics,T12025

Rubric(appliestoeachsub-question)

BackgroundoftheProblem

You are working in a water engineering consulting company as a graduate civil engineer. Your company has just won a contract from Crab River Irrigation Trust to design an open channeltodeliverwaterfromRedfinReservoirtoTortoiseDam,fromwherethewaterwill be distributed for irrigation purpose.

The conceptual design has been developed by senior engineers and illustrated in Table 1 and Figures 1 and 2. The first reach of the channel will be a rectangular concrete (gunite) channel with a total length of 280 m, a width of 1.8 m and a depth of 2.5 m. The first 95 m of the rectangular concrete channel will be horizontal, then the bed slope will change to 1- in-1000(0.1%).Attheupstreamendofthefirstrectangularreach,asluicegatewillbebuilt for flow control.

Thesecondreachwillbeacircularchannelmadefromreinforcedconcretepipes(RCP).The diameterwillbe2.0m,thelengthwillbe195mandtheslopewillbe1-in-500(0.2%).Itwill be buried underground since there is a small hill to get across.

The third reach will be a trapezoidal earth channel (straight and uniform in each section) withatotallengthof2005m,abottomwidthof1.2m,asideslopeof1.5-horizontalto1- vertical (1.5H:1V), and a depth of 1.8 m. The first 995 m of the second reach will have a slope of 1-in-500 (0.2%), then it will change to 1-in-200 (0.5%) for 240 m, and finally will change back to 1-in-500 (0.2%) for the rest 770 m.

Thefourthandfinalreachwillbearectangularearthchannel(straightanduniform)witha total length of 585 m, a width of 2.0 m, a depth of 2.5 m, and a bed slope of 1-in-250 (0.4%).

Youaretaskedtosolveanumberofspecificengineeringproblemsforthedesign.Critical steps of the calculations should be documented such that your results can be double checked by your colleagues.

Table1Proposeddesignoftheirrigationchannel

Figure1.Schematicoftheirrigationchannelsystem(topview).

SEV322ProblemSolvingTask1-Hydraulics,T12025

Redfin Reservoir

H₁

1^stReach: Rectangular concrete channel

2^ndReach: Circular RCP

channel

rd

• Reach:

Trapezoidalearth channel

th

• Reach:Rectangular

earthchannel

ChainageH2

• 0 95

280

475

1470 1710 2480 3065

Tortoise

Dam

Figure2.Schematicoftheirrigationchannelsystem(sideview).

Q1

Youaretaskedtoprovideinformationtotheclientonhowtheopeningofthesluicegate should be set to achieve the designed flow in the channel during normal conditions and prevent flooding during storm events.

The sluice gate used in the rectangular concrete channel has a width same to that of the channel, as shown in Figure Q1. The sluice gate is installed close to the reservoir outlet. The maximum depth of the channel bank upstream of the sluice gate is 3.5 m and that downstream of the gate is 2.5 m. Under the normal reservoir operation condition, water surface level in the Redfin reservoir is 2.0 m higher than the bottom of the channel (i.e.y₁= 2.0 m). During storm events, the reservoir levelcan be up to 3.0 m above the bottom of the channel(i.e.y₁=3.0).Itisknownthattheenergylosswhenwaterpassingthroughthesluice gate is 10% of the velocity head of the flow just underneath the gate (cross-section 3). A designed flow rate of 3.0 m³/s is to be achieved in the channel under normal reservoir operation conditions. Frictional loss due to wall sheer stress can be neglected due to the short distance considered in this scenario.

Tobeabletoachieveawelljustifiedrecommendation,youtakethefollowingsteps:

• Establishanenergyequationbetweenapointatthesurfaceofthereservoirand the point just below the sluice gate. Determine the opening height of the sluice gatey₃that would result in the designed flow rate under the normal reservoir operation condition. If multiple solutions are obtained, determine which one should be adopted. (5 marks)
• Based on the results from part (i) and taken into consideration of practical constrains, the tentative sluice gate openingy₃is determined as 0.25 m. Under the normal operation condition,y₁is 2 m and less than the channel bank depth downstream of the sluice gate, such that there is no flooding risk. Considering thatthereservoirlevelwouldbehigher(y₁=3m)duringstormevents,youwant to estimate the flow condition downstream of the sluice gate for the maximum depth scenario. Based on the information obtained so far, determine the flow rate, velocity, Froude number and flow regime for the flow through the sluice gate under the maximum reservoir depth scenario.(10 marks)
• Basedontheinformationobtained,forrelativereservoirlevely₁=0 mandthe sluice gate openingy₃= 0.25 m, determine whether a hydraulic jump is likely to occur downstream of the sluice gate. If so, estimate the depth of flow downstream of the jump and the associated energy loss. (10 marks)

Topofchannel bank

3.5m

Topofchannel bank

Reservoir

y₁

Possible hydraulicjump

y₂

y₄

2.5m

Rectangular channel

1 23y3 4

FigureQ1Sideviewofthesluicegateusedforflowcontrol.

Q2

Theclientwantstoknowthemaximumflowcapacityandthecorrespondingflowcondition of the channel system (in particular, normal depth and critical depth). This would be useful fordevelopingfloodmitigationplans.Theageingofthechannelshouldbeconsideredsince it delivers raw water and ageing can occur not long after the commission. For the circular channel, the design maximum flow is the full pipe flow without pressurisation. For other types of channels, a minimum freeboard of 0.3m is required (i.e. the distance between the surface of the water and the top of the channel bank needs to be 0.3 m or more). The velocity should not be greater than 3.0 m/s under the maximum design flow.

Todeterminethemaximumflowcapacityofthechannelsystemunderagedcondition,you take the following steps:

• FindthesuitabledesignvaluesoftheManningscoefficientnforeachsectionofthe channelfrom credible references. Clearly specify howyoufindthe informationsuch that your colleague or the client can check if needed. Justify the values selected. (5 marks)
• UsingtheManningsequation,determinethemaximumallowablenormalflowrate and corresponding depth and velocityfor each individual channel section(except for the first horizontal section). Demonstrate the calculation and tabulate the results for all the channel sections. Summarise results in Table Q2-1. Based on the maximum allowable normal flow for individual sections, determine themaximum allowableflowforthewholechannelsystem,andexplainittothe(10marks)
• Based on information obtained previously and other practical considerations, the clientwouldliketosetthemaximumallowableflowforthewholechannelsystemas0m³/s. Basedonthisvalue,determine thecorrespondingnormaldepthsand critical depths for all the relevant channel sections. Demonstrate the calculation and tabulate the results for all the channel sections using Tabel Q2-2. (5 marks)
• Make a schematic of the side view of the channel (use Figure 2). Based on the normal depth and critical depth results obtained in part (iii), draw the normal depth line (NDL) and the critical depth line (CDL),Label the values of NDL and CDL. (5 marks)

SEV322ProblemSolvingTask1-Hydraulics,T12025

TableQ2-1Maximumnormalflowandvelocityforeachindividualsectionalongthechannel

Table Q2-2 Maximum allowable flow and corresponding normal depth and critical depth for the channel system

Q3

The flow surface profile is important since rapidly varied and gradually varied flows are expected to co-exist with normal flow. You are asked to visualise the possible flow surface profileforthewholechannel.Itisknownthatundertypicaloperationcondition,thewater surface in Tortoise Dam is about 0.5 m above the invert level of the channel end (i.e.H₂= 0.5 m, Figure 2).

• Basedonthe NormalDepthLine (NDL) andCriticalDepthLine (CDL) for the channel at the maximum allowable flow condition as you determined in Q2, create a separatedrawingforthewholechannelandsketchthepossibleflowsurfaceprofile when considering the surface level in Bigpond Dam isH₂= 0.5 m. Show the control points. Label the type ofgradually varied flow surface profiles involved (M1, M2, S1 etc.; no detailed calculation needed). Justify the results. (10 marks)

The rectangular earth channel that links to the Tortoise Dam requires some further analysis. Since the dam only has a relatively small capacity, the water level in the dam can increase significantly after a storm event. The maximum possible surface level of the Tortoise Dam isH₂ = 2.0 m, i.e. 2.0 m above the invert level of the channel end, as illustrated in Figure Q3. It is important to understand how this high water level at the Dam will impact the water level upstream.

H2

S₀=0.004

Chainage(m)2480

3065

Tortoise Dam

FigureQ3schematicofthechannelsectionconnectingtoTortoiseDam.

ToobtainallthedetailsforthescenarioH₂=2.0m,youtakethefollowingsteps

• Determine, with appropriate calculations and justifications, the type of flow surface profile for the rectangular earth channel upstream of the Tortoise Dam (chainage 2480 to 3065m). (5 marks)
• Determine the detailed flow surface profile from end of the channel (where water depthis0m)totheupstreamcross-sectionwherethedepthofwateristhenormal depth,ortotheinterfacebetweenthetrapezoidalandtherectangularchannels(i.e. chainage2480m)ifthenormaldepthcannotbeachieved.Usethestepmethodwith a step interval????? = 0.20m. Demonstrate the key calculation steps, fill in Table Q3, and sketch the flow surface profile with detailed information noted in the plot. (10 marks)

Hints:

1. Identify the control points (cross-sections) to help determine the surface profile. Subcritical flow has control at the downstream; supercritical flow has the control.
2. When calculating the detailed surface profile using the step method, keep at least four significant figures in your calculation to avoid significant rounding error.
3. In the step method calculation, the final step will finish at the normal depth or at the upstream end of the rectangular earth cannel, so the step size of the final step doesnt have to be 0.2 m.
4. Dependingonthenormaldepthyoucalculatedpreviously,aftercalculatingthegradually variedflowsurfaceprofile,youwillseewhetherthenormalflowwouldpresentorOne approach is that you decreaseystep by step until reaching the normal depth and calculate the distance ?x. If the distance is more than the overall length of the channel section, it means the calculated surface profile beyond the length of the section will not be able to realise.

TableQ3Resultsofstepmethodcalculationsfortheflowsurfaceprofile

Q4

Although the upstream sluice gate can control how much water flowing into the channel from the Redfin Reservoir, the flow can increase due to runoff from surrounding catchment, or decrease due to evaporation, seepage or even water theft. The client Crab RiverIrrigationTrustaskstohaveaflowmeasurementstructuredesignedinthelastreach of the channel (the rectangular earth channel). You propose that a smooth hump can be built and used as a low-cost critical-depth flow meter, as shown in Figure Q4. The client likes your idea and asks you for details of the design.

It is estimated that the energy loss at the transition (when flowing from the original channel to the top of the hump)H_L,humpisR% of the velocity head on top of the hump, whereRiscalculatedbythelasttwodigitsofyourstudentIDusingthefollowingformula

R= ($$+50)/10

where$$representsthelasttwodigitsofyourstudentID.Forexample,ifyourstudentID ends with 57, theR= (57+50)/10 = 10.7.

Due to the short length of the hump and the relatively mild channel slope, the elevation difference caused by the slope of the channel can be neglected when analysing the hump (i.e.assumethechanneliseffectivelyhorizontalfortheshortsectionaroundthehump).To obtain the details of the design, you take the following steps.

• Assuming that the designed critical-depth flow meter can measure flow up to 5.0 m³/s, determine the normal depth, critical depth and flow regime (subcritical or supercritical)intheoriginalrectangularchannelforflowrangingfrom0m³/sto

5.0m³/swithanintervalof0.50m³/s.Tabulatetheresults.(5marks)

• Determine the minimum height of the hump ???????? that would result in critical flow on top of the hump for the designed maximum measurable flow (i.e. 5.0 m³/s). (10 marks)
• Based on the information obtained from previous steps, and considering practical constrains,theheightofthecritical-depthflowmeter(hump)isdecidedtobe50 m to ensure choking can be achieved. Develop an instruction on how to use the designed critical-depth flow meter to determine the flow rate in practice. Use figures, charts or formulas where appropriate.(10 marks)

FigureQ4Schematic(sideview)oftheproposedcritical-depthflowmeter.

EndofAssignment1