U-tube: water 9 cm, liquid 0.6 g/cm³

The left arm of a U-tube holds water to a height of 9 cm, and the right arm holds another liquid of density 0.6 g/cm³ (water density 1.0 g/cm³). At rest, how high is the liquid column in the right arm, and what is the height difference 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 = 1×9/0.6 = 15
   The lower the density, the taller the column needed to balance
3. Δh = |h_oil − h_water| = 6 cm
   Height difference between the two liquid levels

Why it works

The pressure at the bottom of the two arms is the same, so ρ_water × h_water = ρ_liquid × h_liquid. The lighter liquid forms a taller column, and the height difference is the gap between the two surfaces.

Common mistakes

• Multiplying 9 by 0.6 and getting 5.4 cm instead of dividing.
• Thinking the taller column means the higher pressure at the bottom.

Related

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