Sankey diagrams are a specific type of flow diagram, in which the width of the arrows is shown proportionally to the flow quantity. They are typically used to visualize energy or material or cost transfers between processes.

They are also commonly used to visualize the energy accounts or material flow accounts on a regional or national level. Sankey diagrams put a visual emphasis on the major transfers or flows within a system. They are helpful in locating dominant contributions to an overall flow. Often, Sankey diagrams show conserved quantities within defined system boundaries, typically energy or mass, but they can also be used to show flows of non-conserved quantities.

Example 

  In the Sankey diagram of the steam engine the arrow Ein is the amount of energy (or work) put into the steam engine.  For simplicity we consider the "energy in" to be 100 (100 percent).  The Eout arrow is the amount of energy that comes out.  As you can see the Eout arrow is much thinner then the Ein arrow.  As a matter of fact all of the arrow in the sankey diagram are smaller then the Ein arrow, that's because the width of the arrow represents the amount of energy traveling down that path way.  The arrows that peel off the Ein to Eout arrow is the wasted energy of a steam engine.  From the diagram we can see that smoke, alternator, pump, friction and condenser are pathways in which energy leaves the steam engine.  The condenser is the appears to be the major pathway of energy loss where friction and the alternator are the smallest. The alternator and the pump are blue for a reason, the energy is lost in these pathways but lost in a way that it's turned into useful energy (the alternator turns Ein to electrical energy and the pump creates kinetic energy)