# solution

(30 marks) Burrendong dam is located on the Macquarie river near the town of Wellington in New South Wales. The water it holds is used for irrigation, water supply and hydroelectricity. The dam, when filled to capacity, holds water at a depth of 76m. To maintain the health of the river, the dam needs to release a certain amount of water into the river as a so-called “environmental flow”. However, this cannot simply be released by opening valves or a sluice gate from the bottom of the dam. Its large depth means that the water becomes temperature stratified, with a layer of warm water at the top, and very cold water at the bottom. If the cold water from the bottom is released, it causes a large temperature change in the river which kills the fish and causes other ecological damage. To mitigate this, engineers have designed a temperature control structure. This is effectively a curtain that encircles a control tower and release point. Water is only allowed to pour over the curtain, so only warm water from the top of the dam is allowed to enter the release point – see https://www.waternsw. com.au/projects/regional-nsw/burrendong. A schematic of the curtain in place is shown in figure 1. Your task is to provide input on the design of this curtain, and the subsequent system that will provide water to the river. Questions to address a. The dam can be taken to have a total design depth of 55m, and the curtain is set so only water from the top 5m can enter the space between the curtain and tower as shown in figure 2. The curtain has an average diameter of 12m, and will have an estimated wall thickness of 5cm. The water in this top layer (and therefore the water between the curtain and tower has a temperature of 20?C, the rest of the dam has a temperature of 4?C. i. Calculate the vertical force on the curtain. You can assume that the curtain extends almost all the way to the bottom of the dam, and the average temperature just under the curtain is the average of the temperature on each side of the curtain. What weight will the curtain need to be to ensure it does not need to be tethered to the bottom of the dam? ii. Calculate the radial stress on the curtain. The curtain will have a horizontal connection to the tower for stability. At what depth should this connection be installed to avoid any torques or moments on the curtain? b. Once water is behind the curtain, it needs to be piped out to a release point on a horizontal spillway 500m away, and at an elevation 30m below the bottom of the tower. A single horiontal pipe with a sharp inlet will take water from the tower, but this needs to feed 4 exit pipes, spaced 3m apart, arranged in parallel across the spillway that eject water in free jets as shown in figure 3. i. Design a suitable layout for the pipe network required. Specify the path taken by the pipes, the pipe diameters, and the pipe materials (steel or concrete are probably good options to investigate). Provide a clear diagram of your design, clearly designating pipes and compenents. ii. Once you have designed your network, calculate the flow rate you expect onto the spillway. Justify any assumptions you make. iii. Can you specify a technique for controlling this flow rate if it needs to be reduced? If so, include this in your design diagram. c. Once on the spillway, the flow of water into the river is controlled via a sluice gate. The water behind the sluice gate will bank up to a depth of 6m and can be treated as essentially stationary.

In operation, the sluice gate will open and allow a flow of depth 50cm to flow under as shown in figure 4. The gate will be 10m wide. i. What is the total force in the flow direction on the sluice gate? ii. What flow rate to you expect to be released under the sluice gate? d. The water from the sluice gate will then enter the river. A subcritical flow is preferred for this. i. Will the flow from the sluice gate be subcritical? ii. If the flow is not subcritical, design a system to force the flow to become subcritical. Provide a diagram of your design. iii. Calculate the depth of the subcritical flow that your design will produce.

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