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Networks, STD2 N3 2025 HSC 22

A network of pipes with one cut is shown. The number on each edge gives the capacity of that pipe in L/min.
 

  1. What is the capacity of the cut shown?   (1 mark)

  2. The diagram shows a possible flow for this network of pipes.
     

    1. What is the value of \(x\)? Give a reason for your answer.   (2 marks)

    2. Which of the pipes in the flow are at full capacity?   (1 mark)

    3. The maximum flow for this network is 50 L/min.
    4. Which path of pipes could have an increase in flow of 2 L/min to achieve the maximum flow?   (1 mark)

Show Answers Only

a.    \(\text{Capacity} =62\)

b.i.   \(x=30\) 

b.ii.  \(DE, DG, CF \ \text{and} \ FG\)

b.iii. \(ACEG\)

Show Worked Solution

a.    \(\text{Capacity} =26+24+12=62\)

♦ Mean mark (a) 51%.
b.i.    \(\text{Inflow into} \ C\) \(=\text{Outflow from} \ C\)
  \(x\) \(=5+13+12\)
    \(=30\)

 

b.ii.  \(DE, DG, CF \ \text{and} \ FG\)

\(\text{Full capacity occurs when a pipe’s capacity (top diagram) equals}\)

\(\text{its flow in the second diagram.}\)
 

b.iii.  \(ACEG\)

\(\text{These pipes are not at full capacity and can increase their flow.}\)

♦ Mean mark (b.i.) 38%.
♦♦♦ Mean mark (b.ii.) 15%.
♦♦♦ Mean mark (b.iii.) 6%.

Networks, STD2 N3 EQ-Bank 31

An oil pipeline network is drawn below that shows the flow capacity of oil pipelines in kilolitres per hour.
 


 

A cut is shown.

  1. What is the capacity of the cut.   (1 mark)

  2. Calculate the minimum cut of this network?   (2 marks)

  3. Copy the network diagram, showing the maximum flow capacity of the network by labelling the flow of each edge.   (2 marks)

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a.    `35`

b.    `text(See Worked Solutions)`

c.    

Show Worked Solution

a.    `text(Capacity of cut)= 7 + 15 + 13= 35\ text(kL/h)`
  

b. 

♦♦ COMMENT: Be very careful! RS is not included as it goes from sink to source.
 

`text(Minimum cut)= 7 + 14 + 9= 30\ text(kL/h)`

 

c.    

Networks, STD2 N3 EQ-Bank 5 MC

The network diagram below flows from the source \((S)\) to sink \((T)\).

Which of the edges is not at maximum capacity?
 

   

  1. \(AC\)
  2. \(BC\)
  3. \(CT\)
  4. \(DT\)
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\(C\)

Show Worked Solution

\(\text{Consider the minimum cut line: all edges are saturated.}\)
 


 

\(\text{Edge \(CT\) is not at maximum capacity.}\)

\(\Rightarrow C\)

Networks, STD2 N3 EQ-Bank 26

A network diagram is drawn below.

  1. Calculate the maximum flow through this network.   (2 marks)

  2. Copy the network above and illustrate the maximum flow capacity.   (2 marks)

Show Answers Only

a.    `28`

b.

Show Worked Solution
a.    

 

`text(Maximum flow)` `=\ text(minimum cut)`
  `= 8 + 8 + 7 + 5= 28`

 

b.