How to play Deep Dive
- Choose a dive and read the depth or the hull's limit, and the water's density, on the card.
- Pressure grows steadily with depth: p = p₀ + ρ·g·h, with ρ·g·h in Pa (divide by 1000 for kPa).
- For a force, multiply the pressure difference by the area: F = Δp·A. Type your prediction and press Dive.
- Watch the gauge and the graph: the orange marks show your prediction next to the real pressure.
Why does pressure grow with depth?
At any depth, the water has to hold up the weight of all the water above it. A column of water h deep over 1 m² has a mass of ρ·h kg and a weight of ρ·g·h N, so the water adds a pressure ρ·g·h. In the sea that is about 10 kPa for every metre, roughly one extra atmosphere every 10 m. On top of that sits the air, p₀ ≈ 101 kPa, so the total pressure is p = p₀ + ρ·g·h. The pressure depends only on the depth and the liquid, not on the shape or size of the water: a lake and an ocean press the same at 10 m if their water has the same density. Fresh water is less dense than seawater, so its pressure grows a little more slowly. Pressure pushes on every surface, at right angles to it, and the force is pressure times area. That is why a submarine's windows must be thick, and why a dam is thicker at the bottom, where the water presses hardest.
A focused learning model
The water is still and does not compress, so its density is the same at every depth, and g = 9.8 m/s². The air presses p₀ = 101 kPa on the surface. The submarine or diver goes down steadily for 2 s from its starting depth to its target; if the pressure reaches the hull's limit first, the alarm stops the dive at exactly that depth (within 0.05% of the limit still counts as safe). Inside the submarine the air stays at 101 kPa, so a window feels only ρ·g·h. A dive depth is right if it is safe with at most 2% to spare; every other prediction within 2%. Plays in real time.