Force F equals the weight of a column of liquid of height h and of the same cross-section as the disk S, i.e, hSpg, where p is the density of the liquid. On the other hand force F₂ is determined by the momentum carried away by the stream of water flowing out in unit time, which equals mv = Svpv = Sv²p. From Torricelli's formula, v, the velocity of the flow of a liquid out of an opening lying at depth h, equals √2gh. Therefore
F₂ = 2hSpg = 2F₁.
The fact that force F₂ is greater than F₁ can be explained by the redistribution of pressure inside the liquid while it is flowing out. When liquid flows out of a wide vessel through a small hole, the lines of flow cluster round the opening and consequently the pressure on the wall of the vessel near the opening decreases, as follows from Bernoulli's law. Therefore the reaction to liquid flowing out is greater than the force of the static pressure on the area of the opening.