Three Holes in a Bottle: Pressure Grows With Depth

Punch three holes up the side of a bottle, fill it with water, and almost everyone predicts the same thing: the bottom hole will squirt furthest, because the pressure down there is highest. The pressure part is right. The prediction is wrong. In this water pressure depth experiment the middle hole wins, and the top and bottom holes land in very nearly the same place as each other. That is not a quirk of your bottle. It falls out of two lines of algebra, and showing a child a confident prediction being beaten by a measurement is the most useful thing that can happen in an afternoon.

Key Takeaways

• You’ll punch three 2 mm holes up the side of a clear bottle, keep it topped up, and measure how far each jet lands.
• It teaches hydrostatic pressure, that pressure depends only on depth, and that exit speed and flight time pull in opposite directions.
• Best for ages 8 to 14. The algebra is for 12 and up; the measuring works from 8.
• The one thing that ruins it: letting the water level drop while you measure. Keep refilling.
• The maximum range you can get equals the height of the water column. That is a real result, not an approximation.

What You’ll Need

Item	How much	Where to get it	If you don’t have it
Clear, straight-sided plastic bottle, 1.5–2 L	1	A soda or mineral-water bottle. Straight sides matter, because the sides tell you the water height	A tall rectangular juice carton, opened at the top
Small nail or 2 mm drill bit	1	Hardware drawer	A metal skewer. A drawing pin alone makes holes too small
Pliers and a candle or lighter, adult only	1 set	Kitchen	A 2 mm drill bit in a hand drill, which is tidier and safer
Masking tape	a few strips	Stationery	Electrical tape. Not clear sticky tape, which lifts when wet
Ruler or tape measure	1, at least 50 cm	—	A printed sheet of graph paper laid on the ground
Jug of water for topping up	2 L, refilled	Tap	A garden hose running gently into the bottle
Permanent marker	1	—	Masking tape as markers
Chalk, or a few coins	3	—	Anything to mark where each jet lands

Time: prep 10 min, experiment 20 min, cleanup 5 min Cost: everything is probably in your kitchen Mess level: do this outside, on a driveway, patio or lawn

Do the Experiment

Step 1 — Mark the three hole positions

Stand the bottle on a flat surface and mark three dots in a straight vertical line at 4 cm, 12 cm and 20 cm above the base. Those exact numbers matter later, so use a ruler, not a guess. Then mark a fill line at 24 cm. You now have holes at depths of 20, 12 and 4 cm below the water surface.

Step 2 — Make the holes, adult only

Heat the nail tip with pliers over a candle flame for about ten seconds and push it through each mark, twisting slightly to open the hole to roughly 2 mm. A clean 2 mm drill bit is the better option if you have one. Hole size is the single most common thing people get wrong: at 1 mm or less, surface tension turns the jet into a dribble, and at 4 mm the bottle empties before you can measure anything.

Step 3 — Tape over the holes and fill to the line

Cover all three holes with one strip of masking tape, pressed hard. Fill the bottle to the 24 cm mark and leave the cap off. Stand it on the ground at the edge of your driveway, with the holes facing out across a clear 50 cm of flat surface.

Step 4 — Take the prediction, in writing

Ask: “Which hole will throw water the furthest?” Then ask the harder version: “Will the top and bottom holes land in different places?” Nearly everyone says the bottom wins and that the top will fall shortest. Write it down and date it.

Step 5 — Pull the tape and mark the landing points

Peel the tape off in one movement and immediately mark where each of the three jets hits the ground with chalk or a coin. Have a second person pouring water into the top from a jug the whole time, keeping the level at the 24 cm line.

What you should see: three arcs of different shapes landing in surprising places. The middle jet lands furthest, at around 20 to 24 cm from the bottle. The top and bottom jets land at nearly the same distance as each other, around 15 to 18 cm. The bottom jet is visibly the fastest and flattest; the top jet is slow but starts high and has longer to fall.

Step 6 — Re-tape and measure properly, three times

Tape the holes, refill, and repeat twice more. Record all three distances each time in a small table.

What you should see: repeatable numbers, within about 2 cm run to run, provided you keep the water topped up. If your numbers drift downward across the three runs, you let the level drop.

Step 7 — Put the cap on while it’s running

With water flowing, screw the cap on tight.

What you should see: all three jets weaken within a second or two and may stop altogether. Take the cap off and they resume. Water cannot leave unless air can get in to replace it, which means the atmosphere pressing on the open surface is part of what drives every jet.

What’s Actually Going On in This Water Pressure Depth Experiment

Hydrostatic pressure is the pressure a still fluid exerts because of the weight of fluid above it, and it follows one short equation: P = ρgh, where ρ is the fluid’s density, g is gravitational acceleration and h is the depth below the surface. HyperPhysics sets out the derivation and its consequences. Note what is absent: the width of the container, its shape, and the total volume of water. Only depth matters. A bottle and a swimming pool have the same pressure 20 cm down.

Using water’s density of about 998 kg/m³ from the USGS water-density table, the gauge pressure at your lowest hole, 20 cm down, is roughly 1,960 pascals. For comparison, NOAA notes that the atmosphere presses on you at sea level at 14.7 pounds per square inch, about 101,000 pascals, and that in the ocean the pressure goes up by one whole atmosphere for every 10.06 metres of depth. Your bottle’s biggest pressure is about 2% of an atmosphere. Small, and still enough to throw water across a driveway.

Now the part that makes the demo worth doing. The speed at which water leaves a hole is given by Torricelli’s result, v = √(2gh), which falls straight out of energy conservation: the water arrives at the hole having effectively fallen the depth h. So the bottom hole really does produce the fastest jet. But once the water is airborne it is a projectile, and the time it has before hitting the ground depends on how high the hole is. A hole at height y above the ground gives a flight time of √(2y/g).

Multiply speed by time and the g cancels completely:

range = 2 × √(depth × height) = 2√(h·y)

Now put your numbers in. Bottom hole: h = 20 cm, y = 4 cm, so range = 2√80 ≈ 17.9 cm. Middle: h = 12, y = 12, range = 2 × 12 = 24 cm. Top: h = 4, y = 20, range = 2√80 ≈ 17.9 cm again. The top and bottom holes are predicted to land in exactly the same place, and the middle one wins.

Two further consequences fall out for free. The range is largest when h equals y, which means the best hole is halfway up the water column, wherever that is. And the maximum range is then exactly 2 × (H/2) = H, the height of the water column itself. If your water stands 24 cm deep, no hole anywhere in that bottle can throw water further than 24 cm.

Real jets reach only 80 to 95% of the predicted distance, because the stream contracts as it leaves the hole and loses energy to friction at the edges. That gap is not a failure of the experiment. Engineers call it a discharge coefficient, and noticing it is more sophisticated than getting the “right” answer.

How to Explain It to Your Kid

Ages 5–8: Deeper water pushes harder

Fill the bath and have them hold a plastic cup upside down, pushing it slowly under. It gets harder the deeper they push. Tell them that water is heavy and all the water above a spot is sitting on it, so the deeper you go the harder the water pushes. Then let them peel the tape and shout out which squirt goes furthest. They will not care about the algebra and should not have to.

Ages 9–12: Two things fight each other

Give them the two halves separately. Fast but low, slow but high. Ask which matters more, let them guess, then measure. The result that top and bottom land in the same spot is the one to dwell on: strange enough to be memorable, simple enough to check twice. Point out too that pressure depends only on depth, not on how much water there is. A thin tube of water 20 cm tall pushes exactly as hard at the bottom as your fat bottle does.

Ages 13+: Derive it, then test the prediction

Have them write v = √(2gh) and t = √(2y/g), multiply, and watch g disappear. Then set them the real problem: given a bottle filled to height H, where should you put a single hole to maximise range, and what is that maximum? They should get H/2 and H. Then go and test it. Punch a fourth hole exactly at H/2 on the opposite side and check whether it beats the original middle hole. The discrepancy between predicted and measured range is the interesting data, not an embarrassment.

The question to ask: “If we refilled the bottle to only 16 cm instead of 24, which hole would win then, and how far would it go?”

Why Teaching This Early Pays Off

P = ρgh is one of a very small number of formulas a person actually uses outside an exam. It sets the pressure in a shower, the thickness of a dam at its base, the depth a submarine survives, the reason your ears hurt at the bottom of a pool. A child who has seen it predict three chalk marks on a driveway has a reason to believe it.

The more valuable lesson is procedural. Everyone predicts the bottom hole. The prediction is confident, reasonable and incorrect, and the correction comes from a measurement rather than from an adult. White and Gunstone built a whole instructional structure on this, Predict–Observe–Explain, in Probing Understanding (1992), and its central rule is that the prediction must be committed to before the tape comes off. Kirschner, Sweller and Clark add the counterweight: handing a child a bottle and a nail with no guidance is not teaching (Kirschner et al., 2006).

Do not oversell it. One experiment does not teach fluid mechanics, and no study shows that an afternoon with a bottle moves school results. What it does is make one equation feel like a tool instead of a thing to memorise.

Before You Start: What Parents Should Know

Best age	8–14. From 8 for the measuring, from 12 for the derivation
Supervision	An adult makes the holes. After that a child can run the whole thing
Real hazards	A heated nail stays hot for minutes and burns on contact. Melting plastic gives off fumes, so do it outdoors or by an open window. Wet concrete is slippery
Don’t	Do not use a glass bottle, and do not make the holes with scissors or a knife, which cracks the plastic and leaves a sharp edge. Do not seal the cap and then shake it

When It Doesn’t Work

• The jets dribble down the side instead of arcing out. The holes are too small. Surface tension wins below about 1.5 mm. Reheat the nail and widen them, rotating as you push.
• Distances shrink with every run. The water level is falling. The whole prediction assumes a constant 24 cm head, so one person pours while the other measures. This is the single most common reason the numbers come out wrong.
• The bottom hole does win. Check your geometry. If the bottle is standing on a table and the jets are landing on the floor, then y is measured from the floor, every hole is high up, and the balance shifts toward the fastest jet. Stand the bottle on the same surface the water lands on.
• The jets cross each other and you can’t tell which is which. Food colouring in the water does not help, since all three come from the same bottle. Instead, tape over two holes and run one at a time.
• The holes tore into one long slot. You pushed the nail in too far or too fast. Start a new bottle; a slot cannot be fixed with tape.

Take It Further

1. Find the optimum empirically. Make a bottle with holes every 3 cm from 3 cm to 21 cm, run one at a time at a constant 24 cm head, and plot range against hole height. You should get an arch peaking at the middle. Compare your curve against 2√((24 − y)y).
2. Change the liquid. Run it with water and then with a 1:1 mix of water and dish soap, or with cooking oil in a separate bottle. Density cancels out of the range formula entirely, so in theory the range should not change. Viscosity, however, is not in the formula, and oil will fall short. Finding out which variables the formula ignores is a better lesson than confirming one it includes.
3. Measure your own house. Water pressure at a tap depends on how far below the tank or the mains the tap sits. Work out the height difference between your highest tap and your roof tank if you have one, convert to pressure with P = ρgh, and compare the flow rates. Pair this with the siphon experiment, which is the same pressure argument running uphill.

What to Watch For Over the Next 3 Months

• Week 4: they mention pressure and depth together without prompting, usually at a swimming pool or in the bath.
• Month 2: they start asking what a formula ignores, not just what it contains. That habit, applied to the range equation, is the single most transferable thing in this article.
• Month 3: the concept turns up somewhere else. A dam in a documentary, a diver equalising, a tall building’s water tanks, why a can crushes under atmospheric pressure. The question worth encouraging is “how deep can a submarine go, and what breaks first?”

Frequently Asked Questions

Why does the width of the bottle not matter?

Because pressure at a point in a still fluid comes from the depth of fluid above that point, not the total amount. A narrow straw of water 20 cm tall and a 20 cm deep lake exert the same pressure at the bottom. This is sometimes called the hydrostatic paradox, and it startles adults more than children.

Does this work the same at high altitude?

Yes, essentially. What drives the jet is the gauge pressure ρgh, the pressure above whatever the surrounding air is doing, and that depends on depth rather than on the local atmosphere. The air pressing on the open surface and the air pressing on the jet largely cancel out.

Can we use a glass bottle?

No. You cannot make a clean hole in glass with a nail, and attempts produce cracks and sharp fragments under a column of water. Plastic also lets you see the water level, which you need for Step 6.

Why do the jets stop when I put the cap on?

Because air has to get into the bottle to replace the water leaving it. Seal the top and the air inside expands slightly as water drains, its pressure drops below atmospheric, and the pressure difference driving the jets collapses. It is the same mechanism as the glug-glug when you empty a bottle of milk too fast.

Is this related to the Cartesian diver?

Loosely. Both involve pressure in fluids, but the diver is about compressing a trapped bubble and changing buoyancy, which you can explore in the Cartesian diver experiment.

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About the author

Ricky Flores is the founder of HiWave Makers and an electrical engineer with 15+ years of experience building consumer technology at Apple, Samsung, and Texas Instruments. He writes about how kids learn to build, think, and create in a tech-saturated world. Read more at hiwavemakers.com.

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Sources

1. Nave, C. R. “Pressure in a Fluid.” HyperPhysics, Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/pflu.html
2. NOAA National Ocean Service. “How does pressure change with ocean depth?” https://oceanservice.noaa.gov/facts/pressure.html
3. U.S. Geological Survey. “Water Density.” Water Science School. https://www.usgs.gov/special-topics/water-science-school/science/water-density
4. White, R., & Gunstone, R. (1992). Probing Understanding. Falmer Press.
5. Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). “Why Minimal Guidance During Instruction Does Not Work.” Educational Psychologist, 41(2), 75–86. https://doi.org/10.1207/s15326985ep4102_1
6. Chi, M. T. H., & Wylie, R. (2014). “The ICAP Framework: Linking Cognitive Engagement to Active Learning Outcomes.” Educational Psychologist, 49(4), 219–243. https://doi.org/10.1080/00461520.2014.965823
7. National Research Council. (2012). A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas. National Academies Press. https://doi.org/10.17226/13165