EduNinja

Read the width as energy

A Sankey diagram shows an input energy flowing into useful output and other transfers. Arrow width is proportional to energy, so the branches must account for the whole input.

Identify useful output

Label the useful branch before calculating efficiency. Other branches may represent heating, sound or unwanted mechanical transfers.

Connect to efficiency

The useful fraction of the input is

$\eta=\frac{E_{useful}}{E_{input}}=\frac{P_{useful}}{P_{input}}$

Common trap

Do not compare branch widths without checking whether the diagram uses the same scale and whether the requested quantity is energy or power.

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The Sankey diagram shows the energy input from fuel that is eventually converted to useful domestic energy in the form of light in a filament lamp.

What is true for this Sankey diagram?

Account for energy

Define the system, identify energy stores and describe transfers. Work done by a force transfers energy; total energy is conserved even when mechanical energy is not.

Use the mechanical model

$E_k= rac12mv^2,\quad \Delta E_{p,g}=mg\Delta h,\quad E_{p,elastic}= rac12k(\Delta x)^2$

Conserve their sum only when resistive transfers are absent or included explicitly.

Use rates and ratios

$P= rac{\Delta E}{\Delta t}=Fv,\qquad \eta= rac{E_{useful}}{E_{input}}= rac{P_{useful}}{P_{input}}$

Fuel energy density connects available input energy to a chosen volume.

Final checks

Check the system boundary, signs of work and potential-energy changes, the reference height, extension from natural length, and whether the quantity is energy, power, efficiency or energy density.

A.3.3—Sankey diagrams

Read a Sankey Diagram

Retrieve the A.3 Work, Energy and Power Model

A.3.3 Exam Analysis