DIY · Card 07 · Physics · Fluids
Swirl an upside-down bottle of water a few times and stop. A funnel of air drills down through the middle, and the glitter whirls round it fastest at the centre.
01The brief
Make a whirlpool inside a sealed bottle, a funnel you can watch from the side, using nothing but your wrist.
5×
faster: water swirling at 5 cm from the centre, pulled in to 1 cm
25×
more laps a second near the core than at the wall, in a typical bottle
1/10⁶
roughly how strong the Earth’s spin is, next to gravity, in a draining sink
Hold a bottle of water upside down by the neck, move it in a few small, fast circles and stop. For a moment nothing seems to happen. Then a slim funnel of air opens at the surface and drills down through the middle of the water, glitter streaming round it, until it nearly touches the cap.
It looks like weather in a bottle, and in a way it is. The same rule that shapes this funnel spins skaters, sharpens hurricanes and bends rivers. And it settles, once and for all, the old argument about which way the bath drains in Australia.
02Kit
A bottle and some water are the experiment. Soap and glitter only help you see it.
Tick off what you have
0 of 4 ready
03Method
Two minutes of setting up, a few seconds of swirling, and as long as you like watching.
Step 1 of 8 · Minute 0
Take a clean, clear plastic bottle, a smooth round one if you have it, and fill it with water to about three-quarters of the way up.
The water just sloshes about.
Why
The circles were too big and too slow, so the water rocked instead of turning.
Fix
Make small, fast circles with the bottle’s neck as the pivot, five or six of them, then stop.
A swirl forms but no funnel.
Why
Not enough spin, or a bottle with ridged sides that break up the flow.
Fix
Swirl a little harder and use a smooth, round bottle. Check there is an air gap at the top.
You can’t see anything.
Why
Too much soap, so the bottle is full of foam.
Fix
Empty it and start again with one drop of washing-up liquid at most.
04Physics
When you stop swirling, the bottle stops but the water keeps going: it has angular momentum, the spinning cousin of ordinary momentum, and nothing has taken it away yet. As the water circles, some of it drifts in toward the middle. Angular momentum is mass times speed times distance from the axis, and it stays the same unless something twists the water. So as the distance shrinks, the speed must grow. Water that moves in from 5 cm to 1 cm goes five times faster.
Fast water moving in a tight circle needs a big push toward the centre to keep curving, the same rule that kept the ball in the hair dryer’s jet. In a fluid that push comes from a difference in pressure: higher at the outside, lower at the middle. The faster the spin, the lower the pressure on the axis, until the water surface sinks into a funnel and air fills the hole. Slide the two numbers and watch the funnel’s shape change:
The funnel dips 8.1 cm
Glitter at the edge of the core goes round about 14.3 times a second; glitter by the wall, 0.57 times. That is 25 laps in the middle for every one at the edge.
Real vortices have two parts. Right at the centre, a narrow core turns like a solid wheel, all of it together. Outside the core, the water obeys the skater’s rule and slows as one over the distance. Physicists call this pairing a Rankine vortex, and it describes the bottle, the bathtub, the tornado and the hurricane surprisingly well.
05The big idea
Pull in,
spin up.
Spin is hard to create and hard to destroy. Once something is turning, its angular momentum stays put unless a twist from outside changes it. Squeeze the spinning thing smaller and it has only one way to keep its angular momentum: turn faster.
That one sentence explains a skater’s spin, the savage winds in a tornado’s narrow core, the way a collapsing star becomes a neutron star spinning many times a second, and the funnel in your bottle. Nobody has to push harder. The spin was there all along; it was just spread out.
06The math
1 · Angular momentum
L = m v r
For a bit of water of mass m circling at speed v, at distance r from the axis. With nothing twisting it, this stays fixed, so v goes as 1/r.
2 · Pressure for a curve
dp/dr = ρ v² / r
Going round a circle of radius r at speed v needs pressure that rises outward this steeply. ρ is the water’s density.
3 · Rossby number
Ro = U / (f L)
Compares a flow’s own turning with the Earth’s. f = 2Ω sin(latitude) is the Earth’s spin where you are, U the speed and L the size of the swirl.
The second formula, applied right across the vortex, gives the shape of the funnel. Outside the core, the surface sits lower than the far-off water by v² / 2g, where v is the local speed. Water moving at 1 m/s near the core is about 5 cm below the outer surface, and the core itself dips about twice as far. That is why a strong swirl can stretch the funnel all the way to the neck.
The third explains the drain. The Earth turns once a day, so at 45° latitude f ≈ 0.0001 per second. For water drifting at 10 cm/s across a 40 cm sink, Ro ≈ 0.1 / (0.0001 × 0.4) ≈ 2,500. The water’s own motion is thousands of times stronger than the Earth’s nudge. For a hurricane 500 km across with 30 m/s winds, Ro is below 1, and the Earth’s spin is in charge. Try your own swirls:
The Earth’s spin has no say
Rossby number 2,424. The sideways push of the Earth’s spin on this water is about 1/951,278 of gravity.
07Real life
From ice rinks to oceans, the same rule turns gentle rotation into fierce rotation wherever things are drawn toward a centre.
Figure skaters
A skater starts a spin with arms wide, then pulls them in and whirls several times faster. Nothing pushed them round harder: pulling mass toward the axis made it go faster to keep the same angular momentum. The water in the bottle does the same thing.
Hurricanes
Air drawn in toward a low-pressure centre over a warm ocean speeds up as it closes in, by the same rule as the water. Hurricanes are so big that the Earth’s spin steers them: they turn anticlockwise north of the equator and clockwise south of it.
Cyclone separators
Sawmills and many vacuum cleaners blow dusty air into a cone so it spins hard. The heavy dust can’t follow the tight curve inward and is flung to the wall, where it slides down into a bin, while the clean air leaves up the middle.
Wingtip vortices
Every aircraft wing leaves a pair of spinning tubes of air trailing from its tips. Behind a big airliner they can roll a small plane right over, which is why air traffic control leaves a gap of a few minutes between landings.
Rivers that bend
In a stirred cup of tea, the leaves gather in the middle of the bottom, not at the edge. Einstein showed in 1926 that the same slow circulation along the bottom of a river’s bend wears away the outside bank and builds up the inside one, so bends grow into loops.
Whirlpools
Where strong tides squeeze through narrow channels, as at Saltstraumen in Norway or Corryvreckan in Scotland, the water is set spinning and whirlpools several metres across open and close in a few minutes, funnels and all.
1926
In 1926 Albert Einstein wrote a short paper about a cup of tea. He asked why stirred tea leaves gather in the middle of the bottom of the cup instead of being flung outward. His answer: friction slows the water touching the bottom, so it can’t keep up its spin, and the pressure that holds the faster water above in its circle pushes the slow bottom water inward, sweeping the leaves to the centre.
He used the same idea to explain why rivers meander, and why their bends keep growing. The water in your bottle does it too: watch where the sunken glitter ends up. Newton had puzzled over a spinning bucket of water two and a half centuries earlier, in 1687; the underwater volcano shows the other great engine of moving water, heat.
08Is and isn’t
Centripetal force makes the water spin.
Your hand made it spin. “Centripetal” just names the inward push any curving motion needs. Here that push is a pressure difference, high at the wall and low in the middle, and the low pressure is what hollows out the funnel.
Water drains clockwise in one hemisphere and anticlockwise in the other.
In a sink or bath, the Earth’s spin is millions of times too weak to matter; whichever way the water was already moving wins. Ascher Shapiro only managed to detect it in 1962, in a wide, carefully settled tank at MIT, and colleagues later saw the opposite turn in the Southern Hemisphere.
Spinning flings everything out to the edge.
Sinking glitter gathers in a heap in the middle of the bottom, just like tea leaves. The water near the floor is slowed by friction, so it can’t hold its curve and is pushed inward along the bottom, carrying the flakes with it.
The bottle makes a small tornado.
It makes a vortex, which shares a tornado’s shape and its fast-spinning core. A real tornado is driven by the rising air of a thunderstorm and runs on its energy; the bottle’s whirl only runs down.
09Go further
A
The two-bottle race
Tape two bottles neck to neck, one full and one empty. Time how long the water takes to pour through with and without a swirl. The swirled one often wins by half.
B
Watch the tea leaves
Stir a cup of loose tea, or water with a pinch of sand, and stop. The leaves gather in a neat heap in the middle of the bottom. That is Einstein’s 1926 puzzle in your kitchen.
C
Newton’s bucket
Spin a glass of water on a turntable or lazy Susan. Once the water has caught up with the glass, its surface is a smooth curved bowl, a different shape from the bottle’s sharp funnel.
D
Test the drain myth
Fill a sink, let it sit for ten minutes, then stir it gently clockwise and pull the plug. Repeat anticlockwise. It drains whichever way you stirred, in either hemisphere.
E
Skater on a stool
Sit on a swivel chair holding two heavy books at arm’s length. Have someone spin you gently, then pull the books in to your chest. Hold on.
10Questions
Fill a clear plastic bottle three-quarters full of water, add a drop of washing-up liquid and a pinch of glitter, and cap it tightly. Turn it upside down, swirl it quickly in small circles for a few seconds, then hold it still. A funnel of air forms down the middle of the spinning water.
Water near the centre spins fastest. To keep moving in a tight circle it needs a strong push toward the middle, which comes from a pressure difference: high pressure at the outside, low pressure at the centre. The water surface dips where the pressure is lowest, and air fills the hollow.
Swirling water keeps its angular momentum. As it moves closer to the axis, its speed has to rise to make up for the smaller radius, exactly like a figure skater who pulls in their arms and spins faster.
Not in a sink or a bath. The Coriolis effect from the Earth’s rotation is millions of times weaker than gravity at that scale, and the direction is set by how the water was already moving. It does decide the direction of hurricanes, which are hundreds of kilometres across.
It isn’t needed to make the vortex. A drop makes small bubbles last longer, and because bubbles are drawn into the low-pressure centre, they help outline the funnel.
Safety · Check the cap is tight before swirling, and do it over a sink in case it isn’t. Glitter is hard to clean up and bad for drains and rivers; biodegradable glitter or small bits of coloured paper work just as well.
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