The communicating vessels contain mercury. The diameter of one vessel is twice the size of the other.

| May 21, 2021 | education

The communicating vessels contain mercury. The diameter of one vessel is twice the size of the other. A column of water 0.7 meters high is poured into a narrow vessel. How much will the level of mercury rise in one vessel and drop in another?

Data: hw (height of the poured water column) = 0.7 m; db (diameter of the larger vessel) = 2dm (diameter of the smaller vessel).

Constants: ρw (water density) = 10 ^ 3 kg / m3; ρrt (density of mercury) = 13.6 * 10 ^ 3 kg / m3.

1) The ratio of changes in mercury levels in vessels: Sb * hb = Sm * hm, from where we express: hm = Sb * hb / Sm = (0.25 * Π * db ^ 2) * hb / (0.25 * Π * dm2 ) = (2dm2) * hb / dm2 = 4hb.

2) Change in the height of mercury in the larger vessel: ρw * g * hw – ρrt * g * hm = ρrt * g * hb; ρw * g * hw = ρрт * g * hb + ρрт * g * hм; ρв * hв = 5ρрт * hb, whence we express: hb = ρв * hв / (5 * ρрт) = 10 ^ 3 * 0.7 / (5 * 13.6 * 10 ^ 3) = 0.01 m = 1 cm …

3) Change in the height of mercury in a smaller vessel: hm = 4hb = 4 * 1 = 4 cm.

Answer: Mercury will descend in a smaller vessel by 4 cm and rise in a larger one by 1 cm.



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