A workshop motor takes in 800 J of electrical energy. 600 J leaves as useful work, and 200 J leaves as heat.
How do we draw this budget as a Sankey diagram?
Check the budget first: 600 + 200 = 800. The outputs account for the whole input.
Pick a width scale and name it: here, 1 mm of width for every 20 J.
Draw the input arrow entering from the left, 40 mm wide: 800 ÷ 20 = 40.
Split it. The useful arrow carries straight on, 30 mm wide: 600 ÷ 20 = 30.
The wasted arrow bends away, 10 mm wide: 200 ÷ 20 = 10.
Label every arrow with its value in joules.
If a question gives only the input and the useful output, find the wasted value first: it carries the rest of the input.
Q: A hedge trimmer takes in 500 J, delivers 175 J of useful work, and wastes 325 J. Using 1 mm of width per 25 J, give each arrow's width.
Check the budget: 175 + 325 = 500.
Input arrow: 500 ÷ 25 = 20. 20 mm wide.
Useful arrow, carrying on: 175 ÷ 25 = 7. 7 mm wide.
Wasted arrow, bending away: 325 ÷ 25 = 13. 13 mm wide.
Check the widths: 7 + 13 = 20.
Input 20 mm; useful 7 mm; wasted 13 mm. The output widths add up to the input width.
Q: An electric pump takes in 900 J and delivers 630 J of useful work. Find the wasted arrow's value, then give each width at 1 mm per 18 J.
The wasted arrow carries the rest of the input: 900 - 630 = 270. 270 J.
Input arrow: 900 ÷ 18 = 50. 50 mm wide.
Useful arrow: 630 ÷ 18 = 35. 35 mm wide.
Wasted arrow: 270 ÷ 18 = 15. 15 mm wide.
Check the widths: 35 + 15 = 50.
Wasted value 270 J; widths 50 mm, 35 mm, and 15 mm.
A drone motor takes in 240 J: 168 J becomes useful work, and 72 J becomes heat. Its Sankey diagram uses 1 mm of width per 12 J. Enter the useful arrow's width, in mm.
A toy robot's motor takes in 360 J and delivers 216 J of useful work. Its Sankey diagram's wasted arrow must carry the rest. Enter the wasted arrow's value, in J.
A lamp takes in 400 J, sends on 300 J as light, and wastes 100 J as heat. Its Sankey diagram uses 1 mm of width per 20 J. Which set of widths is correct?
An aquarium air pump takes in 480 J, delivers 192 J of useful work, and wastes 288 J. Its Sankey diagram uses 1 mm of width per 30 J. Enter the input arrow's width, in mm.
A student draws a Sankey diagram: the input arrow is 30 mm wide, the useful arrow carries on at 24 mm, and the wasted arrow bends away at 9 mm. What is wrong with the diagram?
A karaoke speaker takes in 750 J; 225 J leaves as sound toward the room, and the rest leaves as heat. Its Sankey diagram uses 1 mm of width per 25 J. Enter the heat arrow's width, in mm.