We study the kinetics of water escape from balls folded from square aluminum foils of different thickness and edge size. We found that the water discharge rate obeys the scaling relation Q ∝ V{P}(M-M{r}){α} with the universal scaling exponents α=3 ± 0.1, where V{P} is the volume of pore space, M(t) is the actual mass of water in the ball, and M{r} is the mass of residual water. The last is found to be a power-law function of V{P}. The relation of these findings to the fractal geometry of randomly folded matter is discussed.