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ENGR30002 Fluid Mechanics

Assignment 1

Figure 1: Aerial photo of the Wonthaggi Desalination Plant (birds-eye tour)

The Victoria Desalination Plant, Wonthaggi (Figure 1) was built to meet ongoing water needs associated with population growth and climate change. This plant, located in southwest Victoria, can deliver up to 150 billion litres of high-quality drinking water a year (around 60,000 Olympic swimming pools). The plant uses Reverse Osmosis (RO) technology: this uses high powered pumps to generate huge pressures that push water through membranes for desalination (Figure 2). This assignment aims to identify the ﬂow speciﬁcations inside the branched pipes connecting the main saltwater storage open pool to two large pressurised RO unit feed water tanks. Note that each of these units has other sets of pumps to increase the pressure gradually before water runs into the membrane pressure vessels, but these are not the focus of this assignment.

A schematic of the branched pipes is shown in Figure 3. Unit 1 requires a pump placed in line to maintain the pressure of the feed water tank at 150 kPa. Unit 2 does not require a pump since it is located at a lower level than the main storage pool, and the tank in this unit incorporates a ﬂoating lid on top to maintain the pressure at 120 kPa. The volumetric ﬂow rate of water discharging from the main storage pool is Q = 0.1 m3 /s.

Patm = 101.3 kPa ρ = 1024 kg/m3 µ = 0.0025 Pa.s

Gate valves (fully open) K = 0.15 Elbows D(Leg) = 40

Unit 1:	Unit 2:
L1 = 50 m	L2 = 65 m
z1 = 16 m	z2 = 1 m
Q1 =?	Q2 =?
f1 = ?	f2 =?
D1 = 0.23 m	D2 = 0.18 m

Main line:

L0 = 400 m

z0 = 12 m

Q0 = 0.1 m3/s

f0 =?

D0 = 0.25 m

Pipe material: commercial steel

The pipelines are denoted 0, 1, or 2, indicating the main line (pool to Point J), the length of pipe associated with Unit 1 (joint J to tank 1), and the length of pipe associated with Unit 2 (joint J to tank 2), respectively.

Figure 2: Photo of the desalination facility using Reverse Osmosis technology.

Figure 3: Schematic diagram of the system.

Question 1 [7 marks]

Using the information provided, determine the volumetric ﬂow rate of water, Q [m3 /s] in the pipelines, the required pump head, hP [m], and the power required to drive the motor of the pump assuming a mechanical eﬃciency of 61%. Consider the following requirements in the solution:

● Demonstrate an iterative method to solve this question via MATLAB code.

● For the friction factors required in the solution process, use the Colebrook-White equation reported below (e is the absolute roughness of the pipe, D is the inner diameter, Re is Reynolds Number, andf is Darcy friction factor):

1,f = -2 log ╱ + R(2)e(.)51,f 、

● Consider the major and minor frictional losses associated with the pipe, elbows, and valves as shown in the schematic diagram. The number of elbows in unit 1 is 3. Do not consider the friction loss of contraction and entry. State all other assumptions made in the solution process.

Question 2 [7 marks]

Using the information provided:

(a) Plot the system characteristic curve (system head vs. ﬂow rate, Q) over a range of ﬂow rates from 0.00 to 0.05 m3 /s. The system head is the head required for pumping. To simplify the solution process, assume that the pressure at Joint J remains constant (as calculated in Question 1).

(b) Calculate the actual pump head assuming a hydraulic eﬃciency of 68%, and plot this vs. Q on the same graph and for the same range of ﬂow rates as Part (i). The pump has an impeller of radius 0.096m, and carries blades 0.0125 m wide which slope backwards to make angles of 35 О between tangents to their outer tips and the outer circumference of the impeller. The impeller rotates at 1750 revs/min.

(c) Determine the operating point of the system (ﬂow rate and system head) based on the selected pump. What is the percentage diﬀerence between this ﬂow rate and the volumetric ﬂow rate calculated in Question 1?

Question 3 [4 marks]

Calculate the maximum value of ∆h if the pump is moved to a more elevated point, where ∆h is the vertical distance between the pump mid-line and the joint J. Assume that the horizontal part of the pipeline (where it connects to the pump) is negligible compared to the vertical length of the pipeline. Based on your answer, would you recommend placing the pump at the same level as the water in Tank 1?

Hint:thevapourpressureofwater at 20 ОC is 2.34 kPa.

Question 4 [2 marks]

Explain the long-term impact of saltwater on the pipeline. How might this inﬂuence material selection and ﬂow regime considerations when designing the pipeline to maximise its lifespan? What would be your recommendation on the operating flow rate and the diameter of the pipelines in order to increase the lifespan and reduce the pumping power if the pipelines is upgraded in the future? Justify your answer.