Pressure · Model
Pressure in liquids
Punch three holes down the side of a full can — near the top, halfway, near the bottom. The bottom jet comes out hardest and fastest, every single time.
Start here
Three holes, one can, three different jets.
The top hole dribbles. The middle one arches out. The bottom one comes out hard and flat, fast enough to feel. Same can, same water, holes the same size.
Why does the bottom jet come out fastest?
Nothing about the water changes as it sinks. A litre near the bottom weighs exactly what a litre near the top weighs. What changes is how much water is stacked above the hole: at the bottom hole the whole depth of water is pressing, and at the top hole only a few centimetres are. More weight above, on the same area, means more pressure — and a faster jet.
A liquid presses on everything it touches. Go deeper and there is more liquid stacked above you, so more weight is pressing on each square metre and the pressure is higher. At any one depth a liquid presses equally in every direction — down on the bottom, sideways on the walls, and upwards on anything underneath — which is why water comes out sideways through a hole in the side of a can rather than just running down the inside.
At the bench · a pressure probe on a cable
Same probe. Same liquid. Just lower.
Change a control to begin
The probe has a face of 0.02 m², and it reads the pressure of the liquid alone. Lower it, and change what the tank is filled with.
Commit first. You lower the probe from 1 m down to 2 m down in the same tank. What happens to the reading?
What the tank holds
—
Depth
—
Liquid above the face
—
Pressure on the face
—
Turn the face over
—
The relationship · a stack, not a triangle
Pressure at a depth = weight of the liquid above ÷ the area it presses on
P = W ÷ A
Every layer adds its weight to what is below it.
Twice the depth, twice the weight above, twice the pressure.
Worked example · one step at a time
A probe with a 0.05 m² face sits 2 m down. The water above its face weighs 1000 N. What is the pressure on it?
Step 0 of 5
Convert
1000 N stays 1000 N · 0.05 m² stays 0.05 m²
The weight is already in newtons and the face already in square metres, so there is nothing to convert.
Formula
pressure = weight of the liquid above ÷ area
The same relationship as any other pressure. Only the force has a new name.
Insert
pressure = 1000 N ÷ 0.05 m²
The area is the probe face, not the area of the whole tank.
Fine-tune
1000 ÷ 0.05 = 20 000
Newtons divided by square metres leaves newtons per square metre.
Answer
pressure = 20 000 Pa
Twenty thousand pascals, which is what 2 m of water comes to.
Worked example · one step at a time
A probe face of 250 cm² has 600 N of water above it. What is the pressure on the face?
Step 0 of 5
Convert
250 cm² ÷ 10 000 = 0.0250 m²
A pascal is a newton per square metre, and there are 10 000 square centimetres in a square metre.
Formula
pressure = weight of the liquid above ÷ area
Force shared out over the face it presses on.
Insert
pressure = 600 N ÷ 0.0250 m²
The converted area goes in. The 250 never does.
Fine-tune
600 ÷ 0.0250 = 24 000
Newtons divided by square metres leaves newtons per square metre.
Answer
pressure = 24 000 Pa
Insert 250 instead of 0.0250 and the answer comes out 2.4 Pa.
Your turn · the same five steps
Your probe: 600 N of fresh water above a 0.02 m² face, 3.0 m down.
Write all five lines before you check. The numbers are the ones your own tank is showing.
The five lines, marked
Convert
600 N stays 600 N · 0.02 m² stays 0.02 m²
The weight is already in newtons and the face already in square metres, so there is nothing to convert.
Formula
pressure = weight of the liquid above ÷ area
Force over area, with the weight of the column as the force.
Insert
pressure = 600 N ÷ 0.02 m²
Both figures come off the bench above.
Fine-tune
600 ÷ 0.02 = 30 000
Newtons divided by square metres leaves newtons per square metre.
Answer
pressure = 30 000 Pa
At 3.0 m down in fresh water, pressing equally in every direction.
The five lines give 30 000 Pa, and the shaded column on the bench is the 600 N those lines used.
A hatch of 400 cm² in the side of a tank has 1600 N of water above it. What is the pressure on the hatch?
This one needs the Convert line to do some work.
The five lines, marked
Convert
400 cm² ÷ 10 000 = 0.0400 m²
A pascal needs square metres, and there are 10 000 square centimetres in one.
Formula
pressure = weight of the liquid above ÷ area
Force shared out over the area it presses on.
Insert
pressure = 1600 N ÷ 0.0400 m²
The converted area goes in. The 400 never does.
Fine-tune
1600 ÷ 0.0400 = 40 000
Newtons divided by square metres leaves newtons per square metre.
Answer
pressure = 40 000 Pa
Insert 400 instead of 0.0400 and the answer comes out 4 Pa.
The five lines give 40 000 Pa. The whole question turned on the first one.
Key fact
Pressure in a liquid increases with depth, because the deeper you go the more liquid is stacked above you. At any one depth the liquid presses equally in every direction, and it is the depth that decides the pressure — not how much liquid there is in total.
Think again
“More water means more pressure, so a lake presses harder than a bucket.”
Only if it is deeper. Stand a narrow tube of water 2 m tall next to a swimming pool 2 m deep and the pressure at the bottom of each is the same, to the pascal. What sits above your square metre of floor is a column 2 m tall in both cases, and the water off to the sides in the pool is not resting on your square metre — it is resting on its own. This is why a water tower works: what matters for the pressure at your tap is how high the water is above it, not how many litres the tower holds.
“Water is heavier at the bottom.”
It is not. A litre from the bottom of the tank and a litre from the top balance each other exactly — and a liquid is very nearly impossible to squash, so the water down there is not even packed tighter. Nothing about the water changes with depth. What changes is how much of it is above you, which is a fact about your position, not about the water.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
A pressure probe has a face of 0.05 m². At the depth it is hanging, the water above its face weighs 1500 N. What is the pressure on the face?
Rung 2 · The one that catches people
A swimming pool is filled to 2 m deep. Beside it stands a thin pipe of water, also 2 m tall, open at the top. Where is the pressure greater at the bottom?
Rung 3 · Explain
A concrete dam is thin at the top and much thicker at the base. Explain why, using depth, pressure and the water above.
Rung 4 · Take it somewhere new
You punch three holes down the side of a full can and watch the jets. Predict what the three jets look like, then say what happens to all three as the can empties, and explain both using pressure.
Key note
The pressure in a liquid rises with depth, because each layer of liquid adds its weight to everything below it. Work it out the same way as any other pressure: the weight of the liquid above, divided by the area it presses on. At a given depth the push is the same in every direction, and it depends on the depth and the liquid — not on how much liquid there is or how wide the container is.
Going further
Every dam in the world is built to this fact. The pressure at the top of the wall is almost nothing and the pressure at the base is enormous, so a dam is thin at the top and thick at the bottom — the shape is a drawing of the pressure it has to hold. Submarines are the same story from the inside: a hull that is comfortable at 100 m is in serious trouble at 500 m, and the deep-sea vehicles that visit the bottom of the Mariana Trench sit inside spheres with walls several centimetres thick, because a sphere is the only shape that has no flat side for the water to work on.
The same idea runs your taps. Water is pumped up into a tower or a reservoir on high ground, and the pressure at your kitchen sink comes from the height of that water above it — nothing else. That is why the top flat in a block often has feeble water pressure and the ground floor does not, and why a hosepipe on a hill runs harder than the same hose at the top of the slope. Turn it round and you get a way to measure: a column of liquid whose height tells you a pressure, which is what a manometer is, and which is why blood pressure is still quoted as millimetres of mercury.
Before this lesson
Connects to
At GCSE this becomes
- Pressure in a column of liquid as height × density × gravitational field strength, pressure differences in fluids, and how those give upthrust.
Where to next
Ask Mr Badmus AI
Got a depth of your own in mind — a pool, a dam, a dive?
Ask your teacher before making holes in a can. Cut edges are sharp.
The tank is a teaching model. Water is taken as 1000 kg in every cubic metre, sea water as 1025 and paraffin as 800, and weight as mass × 10 N/kg; real values shift with temperature and, for sea water, with saltiness. The probe reads the pressure of the liquid alone — the atmosphere is pressing on the surface as well, and adds about 100 000 Pa everywhere in the tank. The tank is drawn to scale in depth; the probe face is drawn larger than 0.02 m² would be so that it can be seen.
Lesson content © MrBadmusAI.