Lecture on Sankey Diagrams

Introduction to Sankey Diagrams

• A visual tool for representing energy flow within a system.
• Shows:
  • Total energy input.
  • Useful energy output.
  • Energy lost.
• Example:
  • Car engine: 100 Joules of chemical energy → 40 Joules of kinetic energy + 60 Joules of thermal energy.

Steps to Drawing a Sankey Diagram

Step 1: Decide Energy Representation

• Determine how much energy each square on the grid represents.
• Example: If 100 Joules are put in, choose each box to be 20 Joules for simplicity.

Step 2: Draw Input Energy Rectangle

• Draw a rectangle with a height corresponding to total energy input.
• Label with the type of input energy (e.g., chemical energy).
• Example: 100 Joules input = 5 boxes high (each box = 20 Joules).

Step 3: Draw Useful Energy Output Arrow

• Draw a horizontal arrow to the right of the rectangle.
• Height corresponds to useful energy output.
• Label with the type of energy (e.g., kinetic energy).
• Example: 40 Joules output = 2 boxes high.

Step 4: Draw Lost Energy Arrow

• Draw a curving arrow downward for lost energy.
• Width corresponds to lost energy (e.g., thermal energy).
• Example: 60 Joules lost = 3 boxes high.

Examples

Example 1: Car

• 100 Joules chemical energy → 10 Joules kinetic + 90 Joules thermal.
• Diagram:
  • 5 boxes high input.
  • 0.5 boxes high kinetic output.
  • 4.5 boxes high thermal loss.

Example 2: Coal Power Plant

• 160 Joules chemical energy.
  • 60 Joules thermal energy loss.
  • 40 Joules kinetic energy loss.
  • 20 Joules thermal energy loss in transmission.
  • Remaining energy as electrical energy in homes.
• Diagram:
  • 8 boxes high input.
  • Arrows representing each loss.

Applications of Sankey Diagrams

• Show energy flow for complex systems.
• Example: U.S. energy consumption by sector.
• Highlight the proportion of energy lost vs. useful energy.

Calculating Efficiency with Sankey Diagrams

• Efficiency = Useful energy output / Total energy input.
• Example:
  • 2 boxes of kinetic energy (output) vs. 5 boxes of chemical energy (input).
  • Efficiency ratio = 2/5 = 0.4 or 40%.

Conclusion

• Sankey diagrams effectively visualize energy distribution.
• Useful for understanding energy efficiency and losses in systems.