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Liquid in a U-tube
Intermediate
Oscillates with period set by column length.
T = 2π√(L/2g)A liquid column of total length L oscillates with T = 2π√(L/2g) when disturbed, because the restoring force is the weight of the extra liquid column.
L = 0.5 m: T ≈ 1.4 s.
Independent of density.
In more detail
A liquid in a U-tube oscillates as the levels move up and down, with the liquid's weight providing the restoring force. The period depends on the length of the liquid column.
Real-world uses
- U-tube manometers are used to measure pressure, which relies on this behaviour.
- Physics labs demonstrate oscillations using liquid columns.
- Liquid sloshing in a tank or a U-tube manometer oscillates with a period set by its column length.
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Frequently asked questions
Is damping important?
Yes. Viscosity and friction gradually reduce the oscillations.
What sets the period?
The total length of the liquid column and g.
Why does a longer column swing more slowly?
A longer column has more mass to accelerate for the same restoring force, so its period is longer.
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