U-Tube Manometer: Pressure Difference from Height
1 · Predict
A U-shaped tube holds water at different heights on each side, open to the air on both ends. What determines the pressure difference between the two columns?
- The pressure difference depends only on the height difference between the two sides.
- The pressure difference depends on the total amount of water in the tube.
- There is no pressure difference as long as both sides are open to the air.
2 · Set Up
- Open the fluid-utube preset and press Reset. Water sits at different levels on the left and right sides of the U-tube.
- Enable the pressure-difference readout.
- Set the left and right water heights for each trial and record the pressure-difference reading.
3 · Collect Data
| Left height h_L (m) | Right height h_R (m) | Pressure difference ΔP (Pa) |
|---|---|---|
| 0.1 | 0.16 | |
| 0.08 | 0.2 | |
| 0.05 | 0.25 |
Plot ΔP (y-axis) against the height difference h_R − h_L (x-axis) for your three trials. Is the line straight?
4 · Analyze
- For one trial, compute ΔP = ρg(h_R − h_L) using water density 1000 kg/m³ and g = 9.8 m/s², and compare it to the reading.
- Your three trials use different absolute heights but the same pattern. Explain why ΔP depends only on the height difference, not on how full the tube is overall.
5 · Extend
- A mercury barometer uses the same principle but with mercury (density 13,600 kg/m³) instead of water. For the same height difference, would the pressure difference be larger or smaller than with water? By roughly what factor?
- Divers feel pressure increase the deeper they go. Use ΔP = ρgΔh to explain why the pressure at 10 m underwater is roughly double the pressure at 5 m.
The Physics Behind This Experiment
Hydrostatic Pressure
Pressure in a fluid increases linearly with depth: P = ρgh. In a U-tube open to the air on both ends, the pressure difference between the two columns comes entirely from their height difference.