---
title: "U-Tube Manometer & Barometer Interactive Lab | Sandbox Physics"
description: "Do two liquid heights tell you an absolute pressure or a pressure difference?"
canonical_url: "https://sandboxphysics.com/labs/manometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/manometer/"
last_modified: "2026-10-28"
---

IN04 · Pressure needs a reference

# U-Tube Manometer & Barometer

**Do two liquid heights tell you an absolute pressure or a pressure difference?** The liquid-height difference measures the pressure difference between the two surfaces. An open end supplies atmospheric pressure as the reference; an evacuated end supplies a nearly zero reference. Add the reference pressure to recover the unknown absolute pressure.

Connect the U-tube to air, a trapped gas or an ideal vacuum. Move the pressure dial and ruler datum, check the zero and infer pressure from saved height pairs.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Static incompressible liquid and ideal gas share one vertical height scale; tube widths are enlarged. The two ports are at the same height. Gas weight, capillarity, vapour pressure, glass expansion and liquid oscillations are omitted. A closed gas pocket changes pressure with its volume and temperature. Density and fill volume use declared teaching expansion coefficients between ten and thirty-five degrees Celsius. Zero checking precedes a fresh reference connection. Each record freezes heights, noise specification, reference, temperature, density and differential zero. The reported height uncertainty excludes density, reference-pressure and material-model uncertainty.

Saved simulated heights

## A difference becomes a pressure

Pressure difference $800\,\mathrm{Pa}$

Reference pressure $800\,\mathrm{Pa}$

Unknown absolute pressure $800\,\mathrm{Pa}$

Height contribution to uncertainty $800\,\mathrm{Pa}$

Inspect a saved pair

Raw ruler readings share the saved datum

| No. | Left | Right | Zero | Head after zero |
| --- | --- | --- | --- | --- |

Calibration & reference provenance

$$
p_L=p_R+\rho g\bigl[(r_R-r_L)-b_0\bigr]
$$

An equal-pressure check measures the difference of the two reading offsets. The sealed pocket uses its recorded initial volume, initial absolute pressure and temperature. Its current volume follows from the measured head and liquid-volume conservation.

Model limits & sources

Static, incompressible liquid and ideal gas; both ports share a height. Liquid density and volume use a constant teaching expansion coefficient between ten and thirty-five degrees Celsius. The gas cell is prepared at twenty degrees each time it is connected; zero checking takes place before that connection. The vacuum reference has zero pressure and the model liquid has no vapour pressure. Gas weight, capillarity, tube expansion and dynamic sloshing are omitted. The height uncertainty includes reading scatter, ruler resolution and the saved zero-mean uncertainty; density, reference-pressure and material-model uncertainties remain separate. Tube widths are enlarged; vertical heights retain one scale.

- [AMETEK Pressure Measurement Guide, 2016, pp.34–39](https://www.ametekcalibration.com/-/media/ametekcalibration/download_links/pressure/deadweight%20testers/deadweight-tester-precision-pressure-measurement-guide-us.pdf)
- [OpenStax, University Physics 1, section 14.2](https://openstax.org/books/university-physics-volume-1/pages/14-2-measuring-pressure)

Physics tutorial

## The liquid compares two pushes

**Background** Gas presses on both liquid surfaces. A deeper column supplies more pressure at the bottom, so unequal pushes settle at unequal heights.

**Why it matters** A height becomes an absolute pressure only after you identify what pushes on the other side.

Start with the essentials

- **Focus question**: Do two liquid heights tell you an absolute pressure or a pressure difference?
- **One-sentence intuition**: The liquid balances a difference; the reference supplies the missing absolute level.

### Core mathematical model

#### Follow the connected liquid

$$
p_L-p_R=\rho g(z_R-z_L)
$$

Height increases upward. Extra pressure on the left lowers that surface and raises the right. All heights are converted to metres.

#### A trapped gas supplies a changing reference

$$
\frac{p_R V_R}{T_R}=\frac{p_{R0}V_{R0}}{T_0}
$$

The gas pocket was closed at a known initial pressure, volume and temperature. Kelvin temperatures and absolute pressures are required.

#### Correct the two scale readings

$$
h=(r_R-r_L)-b_0
$$

Both readings share a ruler datum. Equalizing the pressures measures only the difference of the reading offsets.

### Common difficulties

#### Zero gauge pressure still has an absolute pressure

**Typical misconception** Equal liquid levels mean that neither surface is under pressure.

**Better mental model** Both surfaces can be pressed equally by the atmosphere. Their pressures cancel in the height difference, and the absolute pressure remains.

### Run the experiment

1. 01

   #### Shift the ruler

   Drag the gold datum rail, then save another pair.

   **What to observe:** Both raw ruler readings shift together. Their difference and the inferred pressure stay nearly the same, within rounding.

2. 02

   #### Change the reference

   Drag the gold hose plug from Air to Gas pocket.

   **What to observe:** The right side compresses a gas pocket. The reference pushes back, so the same source pressure produces a smaller head.

3. 03

   #### Measure an absolute pressure

   Choose A vacuum reference. Then change the liquid to Water-like liquid.

   **What to observe:** The dense-liquid column fits the tube; the water column would need more than ten metres and cannot be saved in this apparatus.

4. 04

   #### Check a shifted zero

   Change Differential reading offset, then choose Equalize & check zero and return to Positive gauge pressure.

   **What to observe:** The new calibration changes later measurements. Earlier height pairs keep their original zero check.

Physical conclusion

Read both surfaces, subtract the saved differential zero and add the correct reference pressure.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Which pressure does a liquid column measure?**](https://sandboxphysics.com/stories/instruments/manometer/)

Motion & dynamics · Starter path

## From a falling ball to an orbit

Start by measuring gravity and splitting motion into components. Then add contact forces and collisions, and follow the same laws all the way to an orbit.

[Start here → **Free Fall & Measuring Gravity** Capture a few drops and fit the camera positions to estimate gravitational acceleration. Then add air damping and watch the fit drift from the truth. Observe · 14 min](https://sandboxphysics.com/labs/free-fall/)

1. [1 Free Fall & Measuring Gravity](https://sandboxphysics.com/labs/free-fall/)
2. [2 Projectile Flight Designer](https://sandboxphysics.com/labs/projectile-flight/)
3. [3 Inclined Plane & Friction](https://sandboxphysics.com/labs/inclined-plane/)
4. [4 One-Dimensional Collision Bench](https://sandboxphysics.com/labs/collision-bench/)
5. [5 Mass–Spring Oscillator](https://sandboxphysics.com/labs/mass-spring/)
6. [6 How Orbits Take Shape](https://sandboxphysics.com/labs/orbit/)

[View the full path →](https://sandboxphysics.com/topics/mechanics/#starter-path)