U-tube: water and oil level difference

The left arm of a U-tube holds water with a 20 cm column (water density 1.0 g/cm³). The right arm holds oil of density 0.8 g/cm³, and the two columns balance. Find the height of the oil column and the difference in height between the two liquid surfaces.

Step-by-step

1. ρ_water·h_water = ρ_oil·h_oil (equal pressure at the same level)
   In connected vessels the same liquid has equal pressure at the same level
2. h_oil = ρ_water·h_water/ρ_oil = 1×20/0.8 = 25
   The lower the density, the taller the column needed to balance
3. Δh = |h_oil − h_water| = 5 cm
   Height difference between the two liquid levels

Why it works

In a connected liquid, pressure is equal on any horizontal level: ρ_water × h_water = ρ_oil × h_oil. A less dense liquid must stand higher to balance the same pressure.

Common mistakes

• Multiplying 20 cm by 0.8 instead of dividing by it.
• Assuming both arms must have the same liquid height.

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