Barometer and U-tube manometer: measuring atmospheric and gas pressure

Torricelli's mercury barometer and an open U-tube manometer with mercury, water or oil. Change the atmospheric pressure or the gas pressure and read P = P₀ + ρgh from the liquid heights.

Also searched as: barometer and manometer · barometer and manometer · mercury barometer · u tube manometer · atmospheric pressure measurement · gauge pressure and absolute pressure

About this experiment

Aim

To see how a liquid column measures pressure: the barometer gives the atmospheric pressure and the U-tube manometer the difference between a gas pressure and the atmosphere.

Theory

The pressure at a depth h in a liquid of density ρ is higher than at the surface by ρ g h. Two points at the same level in the same liquid are at the same pressure. This is the idea behind both instruments.

Barometer (Torricelli, 1643): a tube filled with mercury is turned upside down in a dish of mercury. The mercury falls until the pressure of the column ρ g H equals the atmospheric pressure P₀ pushing on the dish. Above the mercury is an almost perfect vacuum. At sea level H = 760 mm for mercury (1 atm = 101.3 kPa = 760 mm of Hg). With water the column would be 10.3 m high, which is why mercury (13.6 times denser) is used.

Open U-tube manometer: one arm is joined to the gas, the other is open to the air. The gas pressure is P = P₀ + ρ g h, where h is the difference of the levels. P₀ is the atmospheric pressure, ρ g h is the gauge pressure. If the gas pressure is lower than atmospheric, the liquid is higher on the gas side.

Formulas used

• pressure at depth h: P = P₀ + ρ g h
• barometer: P₀ = ρ g H
• manometer: P = P₀ + ρ g h (gauge pressure = ρ g h)
• 1 atm = 1.013 × 10⁵ Pa = 760 mm Hg
• H (mercury) = P₀ / (13600 × 9.8)

Procedure: what to do in the virtual lab

1. Choose the barometer and mercury with P₀ = 101.3 kPa. Check that H = 760 mm.
2. Reduce P₀ to 90 kPa (like a place at 1000 m height or a storm): see how the column falls.
3. Change the liquid to water: why is the tube now much longer?
4. Switch to the manometer. Set the gas pressure to 130 kPa and read the level difference h and the gauge pressure.
5. Make the gas pressure less than P₀ and see which arm is higher.

Observations to make

• The column height is inversely proportional to the density of the liquid: water gives 13.6 times the height of mercury.
• The reading of the manometer is the gauge pressure, not the absolute pressure.
• The tube width and its slope do not matter: only the vertical height counts.

What you can change in this experiment

• Instrument: Mercury-type barometer (measures atmospheric pressure) / Open U-tube manometer (measures gas pressure)
• Liquid in the tube: Mercury (ρ = 13600 kg/m³) / Water (ρ = 1000 kg/m³) / Oil (ρ = 800 kg/m³)
• Atmospheric pressure (60 to 105 kPa)
• Absolute pressure of the gas (manometer) (60 to 200 kPa)

Viva questions on Barometer and U-tube manometer

Questions an examiner may ask in the Class 11 physics practical. Run the experiment in the lab to find the answers yourself, then check them in the Learn tab.

1. Why is mercury used in a barometer instead of water?
2. What is above the mercury in the closed tube?
3. What is the difference between gauge pressure and absolute pressure?
4. Does the height of the mercury column change if the tube is made wider?

Frequently asked questions

Syllabus: Class XI Physics, Chapter 9 — Mechanical Properties of Fluids, §9.2 (pressure; atmospheric pressure and gauge pressure)

What you do in the lab

Change the controls and watch the physics behave in real time in 3D. Live readouts and graphs show the numbers behind it, and the Learn tab has the theory, procedure, observations and viva questions. Works on a phone or a laptop, in English and Hindi.

Topics: barometer · manometer · atmospheric pressure · gauge pressure · pressure of a liquid column · mm of mercury · fluids

Read the full guide: Mechanical properties of fluids.

More from this chapter

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• Bernoulli's principle: venturimeter
• Surface tension: capillary rise and contact angle
• Continuity and Bernoulli in daily life: the thinning tap stream and the aeroplane wing
• Pressure on a dam wall and the centre of pressure
• Pascal's law and hydraulic lift
• Poiseuille flow: viscous flow through a tube
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