A smooth stream leaves the faucet with one width and becomes visibly thinner as it falls. Nothing is squeezing the lower stream through a second nozzle, and water is not disappearing in midair. Gravity increases the downward speed. Because nearly the same volume must pass every height each second, faster water needs a smaller cross-sectional area.
The short answer
A falling faucet stream narrows because gravity speeds the water up while steady, nearly incompressible flow conserves mass. The lower water moves faster, so a smaller cross section carries the same volume per second.
Observation and interpretation
| Visible in the clip | Interpretation from sources | Not measured |
|---|---|---|
| A connected, smooth stream extends below the outlet. | Mass flow through successive cross sections is approximately conserved. | The actual flow rate. |
| The stream is narrower farther below the faucet. | Greater downward speed requires less area for the same steady volume flow. | Speed and diameter at each height. |
| The outline may become uneven farther down. | The continuous-stream approximation eventually becomes less accurate. | The breakup position and resulting droplet size. |
Step 1: gravity accelerates water after it leaves the outlet
Inside a pipe, pressure and the pipe walls guide the water. After the stream leaves the faucet, its surface is exposed to the air. As it falls, gravitational potential energy decreases and downward kinetic energy increases. If air drag and viscous losses are modest over this short distance, the average speed is greater at a lower point.
The Bernoulli relation in the Illinois notes connects lower elevation in a free stream with greater speed when pressure is approximately the same at both exposed points. The video does not measure that speed, but motion tracking offers a check: a marked parcel in the lower section should cover more vertical distance during the same frame interval.
Step 2: steady water cannot pile up between two heights
Imagine two horizontal planes cutting the same smooth stream. If the faucet setting is steady, water passing the upper plane cannot keep accumulating between the planes. The mass entering that region per second must closely match the mass leaving it per second. Liquid water also changes density very little under these ordinary conditions.
OpenStax writes the volume flow rate as Q=Av and gives A₁v₁=A₂v₂ for steady flow of an incompressible fluid. A is cross-sectional area and v is average speed. The University of Illinois Physics 101 notes use a narrowing falling faucet stream as a direct continuity-equation example and state that mass flow rate remains the same everywhere when fluid is not accumulating or disappearing.
Step 3: a faster stream needs less area to carry the same flow
Consider the water that passes one level during one second. Near the outlet it moves a shorter distance in that second, producing a shorter, wider cylinder of water. Lower down, the same volume moves through a longer vertical distance. If the volume is unchanged while the length is larger, the cross-sectional area must be smaller.
Union University explains that gravity accelerates the falling faucet water and that the cross section must shrink so the same amount of water passes each level per unit time. Area, rather than diameter, is the quantity directly paired with speed in Q=Av. For a nearly circular stream, area depends on diameter squared, so its width does not need to shrink in simple inverse proportion to speed.
There is no invisible lower nozzle
A nozzle narrows a pipe and can drive faster flow through pressure differences. The free stream below a faucet has no solid wall forming a second constriction. Its exposed surface is close to atmospheric pressure along the short smooth section. The causal order here is therefore useful: gravity increases the speed after release, and continuity requires a smaller area for the same flow rate.
Where surface tension enters
Surface tension alone is not a sufficient explanation for the first smooth narrowing below the tap. It matters strongly when the stream develops necks and breaks into drops, while the systematic speed-area change in the connected upper stream follows first from gravitational acceleration and conservation of mass.
Separating the connected upper stream from the droplet region prevents two stages from being merged into one explanation. Continuity explains why the smooth column becomes thinner; surface tension and disturbances become central when that column develops necks and separates.
A prediction visible with a phone camera
With the tap left at a steady setting, water lower in the smooth connected stream should travel farther between successive video frames and have a smaller width than water near the outlet. Repeating the shot from the side against a fixed grid should preserve both trends.
Keep the camera perpendicular to the stream and leave zoom and focus fixed. A ruler or printed grid behind the water helps distinguish real narrowing from perspective. Compare two heights within the same steady take, since changing the tap setting changes the flow rate and creates a different case.
Rewatching the opening shot
The lower water is not a smaller quantity of water. It is the same continuing flow stretched over more vertical distance because it is moving faster. The thinner outline records two facts at once: gravity has accelerated the falling stream, and mass conservation has adjusted the area needed to carry the steady flow.
Sources checked
Sources & further reading
- openstax.org — 14 5 fluid dynamics
- courses.physics.illinois.edu — Handout18.pdf
- www.uu.edu — Why does a stream of water from a faucet become smaller at it falls
References checked 2026-09-15. This is an adapted English edition, not an endorsement by the cited organizations.
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