NapkinCalc

Fluid Mechanics — Flow & Pressure

Hydrostatic pressure — deeper means harder

ELI5: every metre of water above you adds weight, so pressure grows with depth: P = ρ·g·h. It depends only on depth and density, not on the shape of the container — a fact that surprises everyone the first time.

ρwater:=1000kg/m3\rho _{water} := 1000 kg/m^3 = 1000 kg / m^3 water density
gacc:=9.81m/s2g_{acc} := 9.81 m/s^2 = 9.81 m / s^2 gravity
hdepth:=10mh_{depth} := 10 m = 10 m depth below the surface
Phydro:=ρwater∗gacc∗hdepthinkPaP_{hydro} := \rho _{water} * g_{acc} * h_{depth} in kPa = 98.1 kPa gauge pressure ≈ 98 kPa — about one extra atmosphere
✓ pass abs(Phydro−98.1kPa)<0.5kPaabs(P_{hydro} - 98.1 kPa) < 0.5 kPa every 10 m of water ≈ one atmosphere

Real-world hook: this sizes dam walls (thick at the bottom), tells a diver the pressure on their lungs, and sets the water tower height that pressurises a town.