IPhO 2026, Теория — Задача 1.1. Hydrostatic gate

• T1-A1 0.5 m

  Official answer: a = Δh/(2√2) = 0.50 m.

T1-A [3.0 pts]. Hydrostatic gate

T1-A1 [3.0 pts].
Since the dam is perfectly sealed, the area of the opening is $a \cdot (a/\sqrt{2})$:

The horizontal force exerted by the water on either side is equal to the pressure at the centroid of the cube sections on the corresponding side times the effective area, as calculated previously:

With an effective application point at the centroid of the left region of the block. The other relevant forces are the block’s weight $\rho \times g \times vol$, the vertical component of the force exerted by the fluid (buoyant force) $\rho_0 \times g \times vol$, and the force that the hinge applies to the block (which exerts no torque).
At the critical $\Delta h$, the bottom edge of the opening applies zero force to the block. For the net torque to be 0,

Note: Arms are $a/(2\sqrt{2})$ from O either in the horizontal or vertical direction for pressure difference and effective weight respectively.

For $\rho = 3\rho_0$,