Various liquids are poured into vertical communicating vessels on top of mercury: in one vessel there

Various liquids are poured into vertical communicating vessels on top of mercury: in one vessel there is a column of water 80 cm high, and in the other alcohol 15 cm high. Determine the difference in the levels of mercury in the vessels.

The sum of the pressures of mercury and water at the bottom in one vessel should be equal to the sum of the pressures of mercury and alcohol in the other vessel:

Prv + Pv = Prc + Pc;

ρрghрв + ρвghв = ρрghрс + ρсghс

g is the acceleration of gravity;
ρр, ρв, ρс – specific gravity of mercury, water and alcohol;

Pillars:
hrv – mercury under water;
hрс – mercury under alcohol;
hв – water;
hc – alcohol.

ρрhрв + ρвhв = ρрhрс + ρсhс;

ρр (hрв – hрс) = ρсhс – ρвhв;

hрв – hрс = (ρсhс – ρвhв) / ρр;

hрv – hрс = (789 kg / m ^ 3 * 0.15 m – 1000 kg / m ^ 3 * 0.8 m) / (13600 kg / m ^ 3) =

= -0.05 m.

Multiply both sides of the equality by -1.

hрс – hрв = 0.05 m.

Answer: the difference in the levels of mercury in the vessels will be 0.05 m or 5 cm. The level of mercury in the vessel with alcohol will be higher than the level of mercury in the vessel with water.