Water is poured into one knee of communicating vessels up to a height of 6 cm. To what height should

Water is poured into one knee of communicating vessels up to a height of 6 cm. To what height should kerosene be poured into the other knee in order to achieve equilibrium of liquids in the knees of the vessel?

To achieve an equilibrium of fluids in the knees of communicating vessels, it is necessary that the pressure of the fluids on the bottom in both knees is the same. The pressure of the liquid p at the bottom is determined by the formula:

р = ρ · g · h, where the coefficient g = 9.8 N / kg, and ρ is the density of the liquid.

From the condition of the problem it is known that water is poured into one knee of communicating vessels up to a height of h 6 = 6 cm = 0.06 m, having a density ρ₁ = 1000 kg / m ^ 3, it exerts pressure on the bottom of the knee p g = ρ₁ · g · h₁.

Kerosene, height h₂ and density ρ₂ = 800 kg / m ^ 3, is poured into the other knee, it exerts pressure p₂ = ρ₂ · g · h₂ on the bottom of the knee.

Since р₁ = р₂, we obtain ρ₁ · g · h₁ = ρ₂ · g · h₂ or ρ₁ · h₁ = ρ₂ · h₂, then:

h₂ = (ρ₁ h₁) / ρ₂.

Substitute the values ​​of physical quantities in the calculation formula:

h₂ = (1000 kg / m ^ 3 0.06 m) / 800 kg / m ^ 3;

h₂ = 0.075 m.

Answer: in order to achieve equilibrium of liquids in the knees of the vessel, kerosene must be poured to a height of 0.075 m.