DIY · Card 87 · Engineering · Geometry
A plastic bottle wrapped in a spiral of tubing. Dip one end in a bowl, turn the bottle, and water climbs up the spiral and pours out at the top, though not a drop ever flows uphill.
01The brief
Lift water without pumping it uphill.
1 pocket
of water delivered to the top with every turn
~30°
a good tilt for a home-made screw
2,200+
years that screws like this have been lifting water
A bucket lifts water by carrying it. A pump pushes it. An Archimedes screw does something cleverer: it gives the water a series of little valleys to sit in, then moves the valleys upwards.
Wind a tube round a bottle and you can watch it happen, pocket by coloured pocket. It is a helix doing useful work, like the spiral of tape on the decorated cords, and a cousin of the water clock.
02Kit
A bottle, some tubing and a bowl of water.
Tick off what you have
0 of 5 ready
03Method
Wind, tape, tilt and turn.
Step 1 of 8 · Minute 0
You need a clear plastic bottle or a cardboard tube about 6 cm across and 30 to 40 cm long, about 1.5 m of clear plastic tubing (8 to 10 mm across), strong tape, a bowl of water with a drop of food colouring, and a cup.
No water comes out at the top.
Why
You are turning the wrong way, or the tilt is too steep.
Fix
Turn the other way so the open end scoops into the water, and lower the angle to about 30°.
Water runs back down.
Why
The turns are unevenly spaced or have slipped.
Fix
Rewind the tube with even spacing and tape it firmly every few centimetres.
Only a trickle comes out.
Why
The scoop end isn’t dipping deep enough.
Fix
Push the bottom of the screw further into the water so the open end goes under every turn.
04Pockets of water
Follow the tube round one turn and its height goes down, then up again. Water settles in that dip. Turn the screw and the dip slides along the tube, upwards, so the water rides with it.
Change the tilt and the spacing and watch the pockets:
Steepest that works
78°
Each turn is full
79 %
Lift per turn
2.0 cm
The line is the height of the tube as you follow it round, here wound round a 6 cm bottle. In every turn it dips and climbs, and water collects in each dip (blue). Turn the screw and the dips march upwards, carrying their water with them. A gentle tilt holds lots of water but lifts it slowly; a steep one lifts more per turn but holds less, until past 78° the dips disappear altogether.
Now crank it and see how much water comes out of the top:
Water per turn
7.7 ml
Flow
0.23 L/min
Lifted
20 cm
Power needed
8 mW
Each turn of the handle tips one pocket of water out of the top: about 7.7 ml here, so 30 turns a minute deliver 0.23 litres. Lifting it 20 cm takes only 8 milliwatts in theory; your arm supplies a lot more, mostly lost to friction and spills. The water itself never climbs: it keeps sliding to the bottom of its pocket while the pocket rises.
05The big idea
Move the valley,
not the water.
Gravity always pulls the water to the lowest point it can reach. The screw doesn’t fight that; it simply keeps moving where the lowest point is.
Many clever machines work like this, by reshaping the landscape a thing sits in rather than pushing the thing itself. A conveyor belt, a lock on a canal and the wave in a stadium crowd all move a ‘place’ rather than the stuff in it.
06The math
1 · Height round the tube
h = p φ ⁄ 2π · sin θ − R cos θ cos φ
R the radius, p the pitch, θ the tilt, φ the angle round.
2 · Pockets exist if
tan θ < 2π R ⁄ p
Too steep and each turn no longer dips.
3 · Lift per turn
p · sin θ
Each pocket rises one pitch along the screw.
Wound round a 6 cm bottle (R = 3 cm) with turns 4 cm apart, pockets form as long as tan θ < 2π × 3 ⁄ 4 ≈ 4.7, below about 78°. At 30°, each turn lifts the water 4 × sin 30° = 2 cm.
One turn of tube is √((2π × 3)² + 4²) ≈ 19.3 cm long. An 8 mm tube holds 0.5 ml per centimetre, so a pocket filling about 80 % of a turn carries roughly 7.8 ml. Thirty turns a minute: about a quarter of a litre.
07Real life
From sewage works and rivers to farms and chocolate fountains.
Sewage works
Giant screws, some several metres across, lift waste water at treatment plants. They turn slowly, don’t clog with rags and grit, and keep working for decades.
Fish-friendly power
Run an Archimedes screw backwards, with water flowing down through it, and it turns a generator. The slow-turning pockets let fish pass through unharmed, so these hydro screws suit rivers.
Grain augers
On farms, augers, screws turning inside tubes, carry grain up into silos and trucks. A combine harvester uses them to move grain from the field to its tank.
Chocolate fountains
Inside the central column of a chocolate fountain, a screw lifts melted chocolate to the top, where it pours down over the tiers: an Archimedes screw for dessert.
Mincers and extruders
A meat mincer and the machines that squeeze out plastic pipes and pasta use the same screw, pushing soft material steadily along a barrel.
Draining the land
In low-lying countries, screws and pumps keep farmland and towns dry, lifting water from drainage ditches into rivers that sit higher than the fields around them.
250 BC
Archimedes of Syracuse, the mathematician who shouted ‘Eureka!’ in his bath, is said to have devised the water screw, perhaps while visiting Egypt, where farmers needed to lift water from the Nile onto their fields.
Whether he truly invented it is uncertain: the historian Stephanie Dalley has argued that the Assyrian king Sennacherib cast water screws in bronze for his gardens at Nineveh four centuries earlier, a claim other scholars dispute. Either way, the design has hardly changed in more than two thousand years.
08Is and isn’t
The water climbs up the screw.
It never flows uphill. It sits in the low point of each turn, and turning the screw moves that low point upwards.
Steeper is always better.
Only up to a limit. Too steep and the spiral no longer dips within each turn, so there are no pockets and nothing is lifted.
Archimedes definitely invented it.
It carries his name, but some historians think similar screws were used in Assyria centuries earlier. The evidence is debated.
Faster turning always lifts more.
Up to a point. Spin it too fast and the water splashes and spills between turns instead of riding up in its pockets.
09Go further
A
Measure each pocket
Count 20 turns and measure the water in the cup. How many millilitres does each pocket carry?
B
Find the limit
Slowly steepen the screw while turning. At what angle does the water stop coming out?
C
Tight versus loose
Make a second screw with turns 8 cm apart. Does it lift more or less per turn?
D
Run it backwards
Pour water into the top of the screw and see if it turns by itself, like a hydro generator.
E
A rice auger
Try lifting dry rice or lentils instead of water. Does a screw work for solids too?
10Questions
Wind a length of clear plastic tubing in an even spiral round a bottle or cardboard tube and tape it in place. Hold it at about 30° with the bottom end in a bowl of water, and turn it so the open end scoops up water. Pockets of water climb the spiral and pour out at the top.
Each turn of the spiral has a low point where water collects. Turning the screw moves those low points up the screw. The water always stays at the bottom of its pocket, but the pocket itself rises, carrying the water up with it.
Large screws usually work at around 22° to 40°. Gentler angles hold more water per turn but lift it more slowly; steeper ones lift faster until the pockets disappear and the water runs back down.
It is named after Archimedes of Syracuse, in the 3rd century BC, but nobody is sure he invented it. Some historians argue that the Assyrian king Sennacherib used water screws in his gardens at Nineveh four centuries earlier, though that reading is disputed.
Yes. Large screws pump water in sewage works and drainage stations, and run in reverse as small hydroelectric generators that fish can pass through safely. Smaller screws, called augers, move grain, plastics and even chocolate.
Safety · Work over a tray or outdoors, and mop up spills so no one slips. Food colouring can stain clothes and surfaces. Never put the tubing in your mouth.
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