4.2 Methods for Solving Flow Problems

Inspection

  • In small flow networks, it may be possible to determine the maximum flow.
  • Remember that flow networks show the capacity of each edge. The maximum flow for an edge is often limited by the capacity of other edges. For example, if a pipe capable of carrying 100L/h is attached to one only capable of 50L/h, the maximum flow through the 100L/h pipe will be limited to 50L/h.

Example

Picture 1
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4.1 Introduction to Flow Problems

Flow Problems and Capacity

  • Many networks rely on the transport of fluids, people, objects or other quantities between different locations. Generally, the medium that is taken from one location to another (the pipe, road, etc.) is capable of transporting a certain number or amount per unit of time. This is known as the capacity.
  • Flow problems involves analysing movement through networks made up of a number of vertices connected via edges each with their own capacity.
  • In Further Maths, we will generally analyse flow problems involving digraphs.
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