Why does tap water get thinner as it falls?
― No water is vanishing. It's just in a hurry
Open a tap just a little, and the stream of water is thickest at the spout and gets thinner as it falls. The water isn't disappearing along the way. As it falls it speeds up, so the same amount of water fits through a narrower channel. And once the stream gets thin enough, it slices itself into drops.
You turn the kitchen tap gently to fill a glass. The water that comes out looks like a clear glass rod — so still it almost seems frozen in place.
Look closely, though, and that rod is thick at the top and tapers as it goes down. Near the bottom of the sink, the surface sometimes turns bumpy and scatters into little drops.
We see this every single day, yet almost nobody ever explains why it happens.
Just two reasons
The amount of water leaving the tap each second is the same at every height. Lower down, the water is moving faster, so a thinner stream is enough to carry the same amount.
Water's surface always tries to shrink to the smallest area possible. A long thin column wastes a lot of surface area, so a pinch point grows and grows until the stream snaps into drops.
The first reason explains why the shape tapers; the second explains why it finally breaks. Let's look at each in turn.
Thinner, exactly in proportion to how much faster it goes
Tap water neither gains nor loses volume along the way. One second after leaving the spout, the water has always moved down to the next level. So the amount of water passing any cross-section each second is the same — right at the spout, 10cm below, or 20cm below.
But the water keeps speeding up as it falls. Fast-moving water can carry the same amount through a narrower channel. It's a bit like a road: where cars move faster, they spread further apart. Water does something similar, except instead of spreading apart, the column itself gets narrower.
Try the slider in Figure 1 to change how hard the tap is opened (the water's speed at the spout). Open it gently, and the stream accelerates a lot right after the spout, so it narrows sharply. Open it hard, and the water is already fast, so falling barely changes its speed ratio — the stream stays almost straight.
If the spout thickness is 1cm and the speed is 0.5m per second, falling 20cm roughly quadruples the speed. The cross-sectional area drops to a quarter, so the thickness (diameter) is almost halved. Figure 1's starting values are exactly this case.
A thin stream snaps itself into drops
Water's surface behaves like a stretched rubber membrane, always pulling itself inward. This is surface tension. For the same amount of water, a round drop needs less surface area than a long thin column.
Tiny, invisible ripples are always present on the stream's surface, stirred up by small vibrations in the tap. Where the stream pinches in, the surface curves more sharply, pushing inward harder. The water squeezed out there escapes into the bulging parts nearby, so the pinch keeps getting tighter (Figure 2).
As in the bottom of Figure 2, once the column breaks it leaves a row of round drops. A tiny drop often gets trapped between two larger ones. The thinner the falling stream gets (reason 1), the stronger surface tension's effect becomes, relatively speaking. That's why a gently-opened, thin stream turns into drops over a shorter distance.
Open the tap wide, and the stream loses its glass-rod clarity, turning whitish and rough-looking. The flow becomes turbulent inside the spout, and the surface ripples finely, scattering light in all directions. If you want to see a clear stream, the trick is to open the tap just a little.
The way a liquid column breaks into evenly-spaced drops has been used by some printers to produce uniform ink droplets. The very phenomenon you see in your kitchen sink has also become a manufacturing tool.
In short
Tap water gets thinner going down not because water is disappearing, but because it speeds up as it falls. Since the same amount passes any point each second, a faster spot needs only a thinner column. And once the stream is thin enough, surface tension pinches it in and it finally splits into drops.
Water gets thinner the faster it hurries.
Once too thin, it rounds itself up into drops.
For more on the "round shape" that surface tension makes, see Why does a soap film stay round even on a square frame?, and for how poured liquid clings to an edge, see Why does liquid poured slowly from a kettle dribble down the outside?
- Open the tap just a little to make a clear stream. Hold a ruler right behind the flow and compare the thickness just below the spout with the thickness about 15cm lower.
- Open the tap bit by bit and watch the tapering become more gradual (the same as moving Figure 1's slider to the right).
- Film near the bottom of the sink in slow motion on your phone. You may catch the moment the stream pinches and snaps into drops.
Don't leave the water running — turn it off as soon as you've checked. It's easier to see with a dark background and light from the side.
Want to go deeper? ― terms, formulas, and textbook linksWe mark which level each part belongs to, from middle-school science to university-level courses
- MSCovered in middle-school science
- HSCovered in high-school physics
- HS+Advanced high-school content, or a textbook sidebar topic
- UnivNot covered in high school — a university specialist subject (fluid dynamics)
- ResearchNot yet settled even at university level — something researchers are actively studying
MSTerms: this phenomenon has names
- Flow rate: the volume of water passing a cross-section each second. If no water is gained or lost along the way, it's the same at every height.
- Free fall: motion under gravity alone. Speed increases with time.
- Surface tension: a liquid surface's tendency to shrink to the smallest area. It's why water drops are round.
MSHSChecking with a formula: how thick is the stream 20cm down?
Let's find the thickness of a thin stream, 1cm thick at the spout with a speed of 0.5m per second there, after falling 20cm.
| In symbols | A₀ × v₀ ＝ A × v , v ＝ √( v₀² ＋ 2 × g × h ) , d ＝ d₀ × √( v₀ ÷ v ) |
| In words | (Cross-sectional area × speed) is the same at every height. The speed after falling is set by the speed at the spout and the height fallen. The thickness (diameter) shrinks in proportion to the square root of the speed ratio. |
| Where it comes from | The first comes from water neither gaining nor losing volume along the way (conservation of mass = the continuity equation). The second comes from potential energy turning into kinetic energy while falling (conservation of energy). Since cross-sectional area is proportional to the square of the diameter, the third formula follows. |
| Symbol | Meaning and unit |
|---|---|
| A₀, A | Cross-sectional area of the stream at the spout, and after falling (square metres) |
| v₀, v | Speed of the water at the spout, and after falling (m/s) |
| d₀, d | Thickness (diameter) of the stream at the spout, and after falling (cm) |
| g | Gravitational acceleration (about 9.8 m/s²) |
| h | Height fallen from the spout (m) |
| Thickness at spout | 1 cm |
| Speed at spout | 0.5 m/s |
| Height fallen | 20 cm (0.2 m) |
| Gravitational acceleration | 9.8 m/s² |
| 2 × gravitational acceleration | 2 × 9.8 ＝ 19.6 |
| Multiply by height fallen | 19.6 × 0.2 ＝ 3.92 |
| Speed at spout, squared | 0.5 × 0.5 ＝ 0.25 |
| Add together | 0.25 ＋ 3.92 ＝ 4.17 |
| Speed after falling | the square root of 4.17 is about 2.04 (about 2 m/s) |
| How many times faster | 2.04 ÷ 0.5 ≒ 4.1 |
| Fraction of original cross-section | 1 ÷ 4.1 ≒ 0.24 |
| Thickness ratio | the square root of 0.24 is about 0.49 |
| Thickness 20cm down | 1 × 0.49 ＝ 0.49 (cm) |
Falling just 20cm roughly quadruples the speed, cuts the cross-section to about a quarter, and nearly halves the thickness to about 5mm. That's why the stream visibly thins over the short drop to the sink.
HSHS+One step further on speed and thickness
HSThe falling-speed formula is exactly the constant-acceleration equation "v² − v₀² ＝ 2gh". Air resistance is considered negligible at this speed and distance. Each part of the stream is simply doing the same free-fall motion, just starting at a different moment.
HS+The smaller the spout speed, the bigger the speed ratio after falling, and the thinner the stream becomes. Conversely, if the spout speed is large, the ratio stays close to 1 and the stream barely narrows. The difference you see with Figure 1's slider is exactly this ratio. Bernoulli's principle also applies directly to the flow inside the pipe and near the spout.
UnivHow the column snaps into drops: the Plateau–Rayleigh instability
In fluid dynamics, the way a liquid column pinches and breaks into drops is called the Plateau–Rayleigh instability, studied experimentally by Plateau and theoretically by Lord Rayleigh in the 19th century. Only ripples with a wavelength longer than the column's circumference grow, and the fastest-growing wavelength is about 9 times the column's radius. As a result, the size of the resulting drops is largely set by the column's thickness, with a diameter a little under twice that of the column. The "Weber number", which compares surface tension against inertia, and the "Ohnesorge number", which captures the effect of viscosity, are used to classify how the breakup happens.
📖 For the derivation and further reading: Continuity equation (Japanese Wikipedia) ／ Plateau–Rayleigh instability (English Wikipedia)
ResearchWhat's still not fully understood
- Predicting where it breaks Where a column breaks into drops depends on tiny disturbances — vibration in the tap, air movement, and so on. Accurately predicting "how many cm down" it breaks at a real sink is still said to be far from easy.
- Behaviour at the moment of breakup Just before a pinch narrows to the point of breaking, the neck's thickness heads toward zero in theory. The shape and speed changes at that instant are studied as a mathematical singularity, and research continues.
- How small drops form How to avoid the tiny "satellite droplets" that form between larger drops is an important problem in printing and drug manufacturing too.
In other words, even this article is only "the explanation as far as we currently understand it." Even the water in your everyday sink still holds unanswered questions.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| MS | Science, "Motion and energy" | Falling faster as it goes down |
| HS | Physics, "Uniformly accelerated linear motion" / "Conservation of mechanical energy" | Calculating the speed 20cm down |
| HS+ | Physics (advanced), "Fluids / Bernoulli's principle" | The continuity equation and stream thickness |
| Univ | Fluid dynamics, "Interface instability" | How the column breaks into drops |
| Research | Interfacial fluid dynamics / droplet formation | Where it breaks, satellite droplets |
| ― | Everyday connections | How far you open the tap, ink droplets, sprays |
- Wikipedia, "連続の方程式" (Continuity equation, Japanese Wikipedia)
- Wikipedia, "表面張力" (Surface tension, Japanese Wikipedia)
- Wikipedia, "Plateau–Rayleigh instability"
- J. Eggers, "Nonlinear dynamics and breakup of free-surface flows", Reviews of Modern Physics 69, 865 (1997)
- Lord Rayleigh, "On the instability of jets", Proceedings of the London Mathematical Society 10, 4–13 (1878)
※This article is a general-audience science explainer. The figures given are approximations to help build understanding. The actual stream thickness and breakup point depend on the shape of the tap and the water pressure.