A Sankey diagram is a scaled arrow diagram that shows how energy is transferred in a system. The width of each arrow is proportional to the amount of energy it represents.
Reading a Sankey diagram
- The input arrow enters from the left.
- Useful output arrows continue to the right.
- Wasted output arrows branch downward (or to the side).
- The total width of all output arrows equals the width of the input arrow (conservation of energy).
Drawing a Sankey diagram
- Determine the total energy input.
- Identify the useful energy output and the wasted energy.
- Choose a scale (for example, 1 cm = 10 J).
- Draw the input arrow with the correct width.
- Split the arrow: the useful output continues forward, the wasted output branches downward.
- Label each arrow with the energy value and the store.
Worked example
A motor receives 200 J of electrical energy. It transfers 150 J as kinetic energy (useful) and 50 J as thermal energy (wasted).
- Input arrow width: 200 J (e.g. 4.0 cm at a scale of 1 cm = 50 J).
- Useful output: 150 J (3.0 cm, continues right).
- Wasted output: 50 J (1.0 cm, branches downward).
Efficiency from the diagram: useful output / total input = 150 / 200 = 0.75 = 75%.
Common errors and how to correct them
Drawing output arrows that do not add up to the input. Check: useful + wasted = input. If the widths do not match, the diagram is not to scale.
Forgetting to label the arrows. Each arrow must state the amount of energy and the store (e.g. “150 J kinetic energy”).
How to apply this in an exam
Measure or calculate arrow widths carefully. If asked to find efficiency from a Sankey diagram, measure the useful output width and the input width, then divide. Always use the same scale for all arrows.
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