SEV322-Hydrology and Hydraulics Analyses - Engineering Assignment Help

Assignment Task

Task

Background of the Problem
You are working in a water engineering consulting company as a graduate civil engineer. Your company has just won a contract from Torrents River Irrigation Trust to design an open channel to deliver water from Redfish Reservoir to Bigpond Dam, from where the water will 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 300 m, a width of 2.0 m and a depth of 2.5 m. The first 100 m of the rectangular concrete channel will be horizontal, then the bed slope will change to 1- in-500 (0.2%). At the upstream end of the first rectangular reach, a sluice gate will be built for flow control.
The second reach will be a circular channel made from reinforced concrete pipes (RCP). The diameter will be 2.0 m, the length will be 200 m and the slope will be 1-in-500 (0.2%). It will 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) with a total length of 2 km, a bottom width of 1.0 m, a side slope of 1.5-horizontal to 1- vertical (1.5H:1V), and a depth of 2.0 m. The first 1 km of the second reach will have a slope of 1-in-500 (0.2%), then it will change to 1-in-100 (1%) for 200 m, and finally will change back to 1-in-500 (0.2%) for the rest 800 m. The fourth and final reach will be a rectangular earth channel (straight and uniform) with a total length of 500 m, a width of 2.0 m, a depth of 2.5 m, and a bed slope of 1-in-200 (0.5%).
You are tasked to solve a number of specific engineering problems for the design. Critical steps of the calculations should be documented such that your results can be double checked by your colleagues. 

Q1
You are tasked to provide information to the client on how the opening of the sluice gate 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 Redfish reservoir is 2.0 m higher than the bottom of the channel (i.e. y1 = 2.0 m). During storm events, the reservoir level can be up to 3.0 m above the bottom of the channel (i.e. y1 = 3.0). It is known that the energy loss when water passing through the sluice 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.

To be able to achieve a well justified recommendation, you take the following steps:

(i) Establish an energy equation between a point at the surface of the reservoir and the point just below the sluice gate. Determine the opening height of the sluice gate y3 that would result in the designed flow rate under the normal reservoir operation condition. If multiple solutions are obtained, determine which one should be adopted. 

(ii) Based on the results from part (i) and taken into consideration of practical constrains, the tentative sluice gate opening y3 is determined as 0.25 m. Under the normal operation condition, y1 is 2 m and less than the channel bank depth downstream of the sluice gate, such that there is no flooding risk. Considering that the reservoir level would be higher (y1 = 3 m) during storm events, you want 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. 

(iii) Based on the information obtained, for relative reservoir level y1 = 3.0 m and the sluice gate opening y3 = 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. 

Q2
The client wants to know the maximum flow capacity and the corresponding flow condition of the channel system (in particular, normal depth and critical depth). This would be useful for developing flood mitigation plans. The ageing of the channel should be considered since it delivers raw water and ageing can occur not long after the commission. For the circular channel, as per the convention, the design maximum flow is the full pipe flow without pressurisation. For other types of channels, a minimum freeboard of 0.3 m 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.

To determine the maximum flow capacity of the channel system under aged condition, you take the following steps:

(i) Find the suitable design values of the Manning’s coefficient n for each section of the channel from credible references. Clearly specify how you find the information such that your colleague or the client can check if needed. Justify the values selected.

(ii) Using the Manning’s equation, determine the maximum allowable normal flow rate and corresponding velocity for each individual channel section (except for the first horizontal section). Demonstrate the calculation and tabulate the results for all the channel sections. If the velocity is higher than the allowable maximum of 3 m/s, make adjustment to the maximum normal flow accordingly. Summarise results in Table Q2-1. (8 marks)

(iii) Based on the maximum allowable normal flow for individual sections as determined in part (ii), determine the maximum allowable flow for the whole channel system, and explain it to the client.

(iv) Based on information obtained previously and other practical considerations, the client would like to set the maximum allowable flow for the whole channel system as 4.80 m3 /s. Based on this value, determine the corresponding normal depths and critical depths for all the relevant channel sections. Demonstrate the calculation and tabulate the results for all the channel sections using

Tabel Q2-2. 
(v) 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

(iv), draw the normal depth line (NDL) and the critical depth line (CDL), respectively. Label the values of NDL and CDL.

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 profile for the whole channel. It is known that under typical operation condition, the water surface in Bigpond Dam is about 0.5 m above the invert level of the channel end (i.e. H2 = 0.5 m, Figure 2).

(i) Based on the Normal Depth Line (NDL) and Critical Depth Line (CDL) for the channel at the maximum allowable flow condition as you determined in Q2 (iv), create a separate drawing for the whole channel and sketch the possible flow surface profile when considering the surface level in Bigpond Dam is H2 = 0.5 m. Show the control points. Label the type of gradually varied flow surface profiles involved (M1, M2, S1 etc.; no detailed calculation needed). 

The rectangular earth channel that links to the Bigpond 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 Bigpond Dam is H2 = 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. 

To obtain all the details for the scenario H2 = 2.0 m, you take the following steps

(ii) Determine, with appropriate calculations and justifications, the type of flow surface profile for the rectangular earth channel upstream of the Bigpond Dam (chainage 2500 to 3000 m). 

(iii) Determine the detailed flow surface profile from end of the channel (where water depth is 2.0 m) to the upstream cross-section where the depth of water is the normal depth, or to the interface between the trapezoidal and the rectangular channels (i.e. chainage 2500 m) if the normal depth cannot be achieved. Use the step method with a step interval ????? = 0.20 m. Demonstrate the key calculation steps, fill in Table Q3, and sketch the flow surface profile.

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 at the upstream.

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 doesn’t have to be 0.2 m.

4. Depending on the normal depth you calculated previously, after calculating the gradually varied flow surface profile, you will see whether the normal flow would present or not. One approach is that you decrease y step 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. 

Q4
Although the upstream sluice gate can control how much water flowing into the channel from the Redfish Reservoir, the flow can increase due to runoff from surrounding catchment, or decrease due to evaporation, seepage or even water theft. The client Torrents River Irrigation Trust asks to have a flow measurement structure designed in the last reach 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) HL,hump is R% of the velocity head on top of the hump, where R is calculated by the last two digits of your student ID and the following formula R = ($$+50)/10
where $$ represents the last two digits of your student ID. For example, if your student ID ends with 57, then R = (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. assume the channel is effectively horizontal for the short section around the hump). To obtain the details of the design, you take the following steps.

(i) 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) in the original rectangular channel for flow ranging from 1.0 m3 /s to 5.0 m3 /s with an interval of 0.5 m3 /s. Tabulate the results using Table Q4. 

(ii) 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). 

(iii) Based on the information obtained from previous steps, and considering practical constrains, the height of the critical-depth flow meter (hump) is decided to be 0.6 m. The channel may subject to flooding and therefore higher flow than the designed maximum measurable flow. Calculate the new upstream depth y1, new when the flow rate is 8.0 m3 /s, and check if it is still in the safe range (i.e. considering the requirement of at least 0.3 m freeboard).

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