QUESTION 1
2+2+2+2+2 = 10 marks
a. Across a hydraulic jump
i. there is a significant loss of energy
ii. there is an increase in the flow depth
iii. the flow transits from supercritical to subcritical
iv. all of the above
b. Bernoulli’s equation is applicable only when
i. a flow is unsteady
ii. a flow is steady, incompressible and can be treated as inviscid
iii. a flow is only incompressible and inviscid iv. None of the above
c. Separation is likely to occur
i. only in regions of a flow where there are no solid objects
ii. only in flows that are turbulent
iii. when viscous stresses can be neglected
iv. when the flow is forced to change direction suddenly such as around sharp corners
d. Gauge pressure is
i. always positive
ii. always negative
iii. equal to the atmospheric pressure everywhere in a flow
iv. the difference between the true pressure and a reference pressure, and the reference pressure is usually the atmospheric pressure e. In a static fluid of constant density
i. it is impossible to tell how the pressure varies without knowing if the fluid is a liquid or a gas
ii. pressure varies quadratically with the depth
iii. pressure varies linearly with the depth iv. pressure is constant
QUESTION 2
10 marks
A homogeneous plate which is 2m wide (into the page) and weighing 350kg is held in place by a horizontal, flexible cable as shown in the figure below. Water at 15◦C is being held back by the gate which is hinged at point A. Find
• The total force on the gate due to pressure
• The location where this force acts (the centre of pressure)
• The tension force in the cable.
QUESTION 3
10 marks
Water at 15◦C is flowing steadily from a reservoir through a pipe system including a narrow section of thin-walled tubing as shown in the figure below. The flow can be treated as incompressible and inviscid. The thin-walled tubing section will collapse if the absolute pressure within it becomes less than 70kPa below atmospheric pressure. Find
• A relationship between the height marked h and the flow rate
• A relationship between the flow rate and the pressure in the thin-walled tubing
• The maximum value that h can take without the tube collapsing
QUESTION 4
(10 marks)
A constant-velocity flow enters a wide channel as shown in the figure below. At some distance downstream, the velocity profile is parabolic. The flow does not vary across the channel and can be considered steady.
i. Is the flow in this section of the channel uniform?
ii. Is the flow in this section of the channel one-, two-, or three-dimensional?
iii. Is there any local acceleration in this section of the channel?
iv. Is there any convective acceleration in this section of the channel?
v. Sketch a suitable control volume that you could use if you wanted to find the force exerted on the channel bottom by the flow.
QUESTION 5
(15 marks)
Air, of density 1.23kg · s −1, flows over a flat plate that is pointing directly into the flow as shown in the figure. The air approaching the plate edge has a uniform velocity of 16ms−1. As some distance downstream, the velocity profile in the boundary layer (viscour region) is described by the function u = 16(20y−100y 2) until it reaches the edge of the boundary layer, which is the point at which the velocity returns to its freestream value of 16ms−1. Here y is the distance perpendicular to the plate in metres. The pressure can be assumed to be constant everywhere, and the plate taken as 1m wide into the page.
• Find the discharge in the boundary layer at the downstream point.
• Define and sketch a suitable control volume for a momentum conservation analysis (hint: find a height at the inlet that gives the same discharge as the point downstream, and use a streamline as the upper boundary).
• Find the horizontal force exerted on the plate by the air flow
QUESTION 6
(10 marks)
Water is being pumped from a low reservoir to a high reservoir as shown in the figure. The water temperature is 15◦C. The pipe network consists of a sharp entry, two threaded 90◦ elbows, and a total of 50m of straight 16cm wrought iron pipe and a pump (marked with P in the figure).
• Sketch the energy grade line and hydraulic grade line for this system
• Find an expression for the required pump power in terms of the flowrate, Q.
• If the average velocity in the straight pipe sections is 1.6ms−1, find the pump power.
QUESTION 7
(10 marks)
The flow rate in a clay-lined channel with Manning coefficient n = 0.025 is to be 1.7m3 s −1. The geometry of the channel cross section is shown in the figure below. The depth of the flow in the channel should be maintained at 0.6m, and to prevent erosion of the sides, the maximum flow speed should be limited to 1.6ms−1. For this maximum velocity, determine the width of the bottom, b, and the slope of the channel So.
QUESTION 8
(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 horizontal 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 components.
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 sub-critical flow that your design will produce.