Gasoline is poured in the left knee of communicating vessels, and oil in the right knee. The difference in oil levels in the right and left knees is 71 cm. Find the height of the gasoline column. (Density of gasoline 710 kg / m3. Density of oil 800 kg / m3)
1. Let’s translate given in the SI system:
h1 = 71 cm = 0.71 m
2. In a homogeneous fluid at rest, the pressures at points lying in the same horizontal plane (at the same level) are the same.
This means that the pressure in the left knee, at the interface between gasoline and oil, is equal to the oil pressure in the right knee at a depth of h1.
p1 = ρ1 * g * h1
Where ρ1 is the oil density, g is the free fall acceleration of a body raised above the Earth, g = 9.8 m / s2, h1 is the difference in oil levels in the right and left knees.
Gasoline pressure at the lower border of the column:
p2 = ρ2 * g * h2
Where ρ2 is the density of gasoline, g is the free fall acceleration of a body raised above the Earth g = 9.8 m / s2, h2 is the height of the column of gasoline in the left knee.
3.P1 = P2, according to Pascal’s law
ρ1 * g * h1 = ρ2 * g * h2
4. Let us express h2 from the previous expression and substitute the numerical values:
h2 = ρ1 * h1 / ρ2 = 800 * 0.71 / 710 = 0.81 m
Answer: the height of the petrol column is 0.81 m
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