Science Puzzle
Which Dam Needs to Be Stronger?
Two concrete dams are identical in height and width. Dam A holds back a reservoir 10 kilometres long. Dam B holds back a narrow channel of water only 5 metres long, trapped between the dam and a wall of solid rock. In both cases the water against the dam is 50 metres deep.
Which dam has to be built to withstand the bigger push from its water?
The Answer
Both dams feel exactly the same push. The 10 km lake and the 5 m channel press on their dams equally hard.
Water pressure at any point depends on how much water is stacked above that point, which means it depends only on depth. Fifty metres down, the pressure is about 490,000 pascals: nearly 50 tonnes pressing on every square metre. It makes no difference whether that water stretches back 5 metres or 10 kilometres. Nearly all the weight of the big lake presses down on the lake bed, not sideways on the dam. Only the water touching the dam pushes on it, and that push is set by the depth.
Add it up over the whole face and each metre of either dam's width holds back a sideways force of about 12 million newtons, roughly the weight of 1,250 tonnes. Because the pressure grows steadily from nothing at the surface to its biggest value at the bottom, dams are built much thicker at the base than at the top.
Engineers do treat the two dams slightly differently in real life. Wind blowing along a 10 km lake can whip up big waves, so dam A needs a little extra height to stop them slopping over. But the water pressure itself is identical. This surprising result is sometimes called the hydrostatic paradox.
The principle: Hydrostatic pressure. The pressure in a still liquid depends only on its depth and density, never on how much liquid there is or how far it stretches, so a dam's load is set by the depth of the water against it.