Theme A — Space, Time and Motion
A.3.2 Sankey Diagrams — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 33 of 63 1 quiz
Lesson summary
A.3.2 Sankey Diagrams — IB PHYSICS SL notes: Draw and interpret Sankey diagrams to show energy flows and calculate useful output, wasted energy and efficiency.Sankey diagram = a flow diagram in which arrows represent energy transfers.Width — the width of each arrow is proportiona…
- Conservation
- Power diagrams
- Percentages
- Design use
- Power station
- Overall efficiency
Part 1 of 7What a Sankey diagram shows
Sankey diagram
Sankey diagram a flow diagram in which arrows represent energy transfers.
Width
- Width the width of each arrow is proportional to the amount of energy (or power) it carries.
Input
- Input a wide arrow at the left shows the total energy in.
Useful output
- Useful output the arrow continuing to the right shows energy in the desired store.
Waste
- Waste arrows branching away, usually downwards, show wasted energy.
Conservation
- Conservation total energy in = useful energy out + wasted energy.
- The widths of the outputs add up to the input arrow.
Part 2 of 7Reading a diagram
Scale
- Scale read the scale first, then measure the arrow widths.
Wasted energy
- Wasted energy wasted energy = total energy in − useful energy out.
Power diagrams
- Power diagrams the same rule applies, with watts on every arrow.
- Total power in = useful power out + the sum of all losses.
Efficiency
- Efficiency useful output arrow divided by input arrow.
- An input of 400 J with a useful arrow of 100 J is 25% efficient.
Units
- Units they must be the same on every arrow.
Part 3 of 7How to draw one
1
Choose a scale, for example 1 cm of width = 100 J.
2
Draw the input arrow with the width of the total input.
3
Work out each output: useful energy and each form of waste.
4
Draw the left side and the top line, then add the useful output arrow at the correct width.
5
Mark the start and end of the wasted arrow at the correct distance apart and join them.
6
Label each arrow with its form of energy and its value and unit.
7
Check that the output widths add up to the input.
- Percentages
- treat the input as 100 units and divide the arrows in proportion.
Part 4 of 7Comparing devices
| Device | Waste arrow | Useful arrow |
|---|---|---|
| Filament lamp | Very wide thermal arrow | Narrow light arrow (a few per cent) |
| LED lamp | Much narrower | Wider light arrow (higher efficiency) |
| Electric motor | Small branch for heating and friction | Most of the input as kinetic energy |
| Car engine | Largest branch is thermal energy via exhaust and cooling | Modest fraction as kinetic energy |
- Design use
- the diagram shows where changes would reduce the losses.
Part 5 of 7Multi-stage devices
1Power station
- Power station chemical energy becomes thermal energy in steam, then kinetic energy in turbines, then electrical energy.
2Overall efficiency
- Overall efficiency it is the product of the stage efficiencies, ηtotal = η1 × η2 × η3.
- Three 80% stages give only about 51%.
3Long chains
- Long chains they waste more, so combined heat-and-power systems that use waste heat improve usefulness.
Part 6 of 7Links
Efficiency and power
- Sankey diagrams connect to efficiency and to power.
Heat engines
- Heat engines the diagram shows heat in, work out and heat rejected to the cold reservoir.
Preparing data
- Preparing data convert all quantities to the same unit and time basis, such as watts, before drawing.
Marks
- Marks correct labels as well as correct proportions are usually credited.
Part 7 of 7More from the specification
1
Energy flow visualization via Sankey diagrams
- Energy flow visualization via Sankey diagrams drawing proportional energy arrow widths provides an intuitive graphic means to represent input and wasted energy.
2
Elastic potential energy in springs
- Elastic potential energy in springs compressing a mechanical spring with spring constant k stores elastic strain energy calculated from E = ½kx².
3
Gravitational potential energy conversion
- Gravitational potential energy conversion as a falling object loses gravitational potential energy, it gains equivalent kinetic energy, accelerating to higher downward speed.
4
Work done by horizontal forces
- Work done by horizontal forces applied horizontal force multiplied by parallel displacement equals mechanical work done transferring energy to moving bodies.
5
Sankey Diagrams of Energy Transfers
- A Sankey diagram visually represents energy conservation in a system,
- where the width of each arrow is directly proportional to the amount of energy transferred along that pathway.
6
Gravitational Potential Energy (GPE)
- The change in gravitational potential energy when an object of mass m moves vertically through height h is calculated using the equation ΔEp = mgΔh, measured in joules (J).
7
Elastic Potential Energy in Springs
- Work done in extending or compressing a spring with force constant k is stored as elastic strain energy, given by the equation Ee = ½kx² = ½Fx.
8
Energy Efficiency of Mechanical Systems
- Energy efficiency is defined as useful energy output divided by total energy input; wasted thermal energy is dissipated to the surroundings.
- (η = Euseful / Etotal)
9
Resultant force
- Another name for net force.
10
Final speed
- Speed at the end, v
11
Elastic
- Returns to original shape when force is removed.
12
Constant
- Not changing.
13
Density
- Mass per unit volume.
14
Component
- Part of a vector along one axis.
15
Position
- Location relative to a reference point.
16
Potential energy
- Energy stored by the configuration of a system.
17
Gravitational potential
- Work done per unit mass in bringing a test mass from infinity to the point.
18
Mechanical energy
- Sum of kinetic and potential energy.
19
W = Fs
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
20
W
Fs = 25.6 × 20 = 512 J
What the symbols mean: W = work done = energy transferred (J) · F = force (N) · d, s or x = distance moved in the direction of the force (m)
Key terms
| Term | Meaning |
|---|---|
| Sankey diagram | Diagram whose arrow widths are proportional to the energy or power transferred |
| Useful energy output | Energy transferred to the desired store |
| Wasted energy | Energy transferred to stores that are not wanted |
| Efficiency | Useful output divided by total input |
| Multi-stage efficiency | Product of the efficiencies of each stage in sequence |
| Combined heat and power | System that finds a use for waste heat |
Avoid these mistakes
1
Making arrow widths unrelated to the values — the widths must be proportional.
2
Letting the outputs add up to more or less than the input — they must equal the input.
3
Mixing joules and watts on one diagram — use one unit throughout.
4
Forgetting to label the forms of energy — label each arrow.
5
Adding stage efficiencies — multiply them.
Marked practiceQuizzes for this lesson
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