Look at a big dam from the side and it is shaped like a wedge: a few metres thick at the top, often 30 metres or more at the base. All that extra concrete costs a fortune. Why do engineers put it there?
Start with something you know
Dive to the bottom of a swimming pool and your ears start to hurt. Nothing touched you, yet something is pushing on your eardrums. That something is the weight of all the water above you.
Imagine a tall column of water standing on a small patch at the bottom. The patch has to hold the whole column up. The deeper the patch, the taller and heavier the column. Pressure is that weight shared over the area, the force on each square metre.
Try it
Try this
- Drag the probe from the surface to the bottom. Does the gauge rise steadily or in jumps?
- Move the probe sideways at the same depth. Does the pressure change?
- Switch to mercury. How much deeper would you need to go in water for the same reading?
- Try the funnel shape. Does the shape of the tank change the pressure at the bottom?
What is happening
A column of liquid with height h and area A weighs ρ g h A. Divide by the area and A cancels out, leaving:
- p
- pressure at that depth (Pa)
- patm
- air pressure at the surface, about 101,325 Pa
- ρ
- density of the liquid (kg/m³)
- g
- gravity, 9.81 m/s²
- h
- depth below the surface (m)
The part ρ g h is called gauge pressure, because it is what a tyre gauge or pool gauge reads: the pressure above the surrounding air. Every 10 metres of water adds about 98 kPa, almost one extra atmosphere.
Two surprising facts
At any point in a still liquid, the pressure pushes equally in every direction. That is why the arrows on the probe are all the same length, and why water squirts sideways out of a hole in the side of a bottle.
Pressure depends only on depth, not on the width or shape of the container. A narrow pipe 10 metres tall and a lake 10 metres deep have the same pressure at the bottom. This is called the hydrostatic paradox.
Back to the dam
Water pushes on a dam wall with a pressure that grows from zero at the surface to its largest value at the bottom. Draw that push and you get a triangle: small at the top, large at the base. Engineers make the wall thick where the push is biggest and thin where it is small. Notice that the length of the lake behind the dam does not matter at all, only the depth of water against the wall.
Where you see it
- The water tank on your roofTaps on the ground floor get a stronger flow than taps on the top floor, because they sit deeper below the water level in the tank.
- SubmarinesAt 300 metres down the water presses about 30 times harder than the air at the surface, so hulls are thick, round and very strong.
- Blood pressureIt is measured at the height of the heart. A reading taken at the ankle would be higher because of the blood standing above it.
- Ears while divingSwallowing lets air into the middle ear and balances the pressure on both sides of the eardrum.
Easy to mix up
- Pressure is not force. A small area and a large area at the same depth feel the same pressure, but the large one feels a bigger total force.
- More water does not mean more pressure. A deep narrow well pushes harder at its bottom than a wide shallow pond.
Check your understanding
5 questions.Pressure Quiz