The Manometer
Simple Explanation
A manometer is a U-shaped tube containing liquid, used to measure the pressure of a gas by comparing it to atmospheric pressure. The gas is connected to one side of the tube; the height difference between the liquid levels in the two arms directly indicates the pressure difference.
Why Do We Need It?
Manometers provide a simple, direct, and highly visual way to measure gas pressure, widely used in laboratories and industrial settings where a precise pressure reading is needed.
Formula
Manometer Pressure Difference
ΔP = hρg
A manometer measures the pressure of a gas by comparing it to atmospheric pressure, using the height difference between two liquid columns connected to the gas and the open air.
- ΔP
- — The pressure difference between the gas and the atmosphere, in Pa
- h
- — The height difference between the two liquid columns in the manometer, in metres
- ρ
- — Density of the manometer liquid, in kg/m³
- g
- — Acceleration due to gravity, 9.8 m/s²
When to use it: Use to find a gas's pressure relative to atmospheric pressure from the height difference observed in a manometer's liquid columns.
Worked Example
Finding gas pressure from a manometer reading
A manometer connected to a gas supply shows the liquid on the gas side is 0.15 m LOWER than the open side (mercury, ρ = 13,600 kg/m³, g = 9.8 m/s², atmospheric pressure = 101,300 Pa).
Why Does This Work?
If the gas pressure exceeds atmospheric pressure, it pushes the liquid down on the gas side and up on the open side; the resulting height difference directly balances (and therefore measures) the pressure difference, following the same hρg relationship used for a barometer.
Real-Life Example
Checking blood pressure with a mercury sphygmomanometer
Traditional blood pressure measurement devices use a mercury column (a form of manometer).
The height of mercury the cuff pressure can support directly indicates blood pressure — this is a direct medical application of the same manometer principle used to measure gas pressure in a laboratory.
Practice
A water manometer (ρ = 1000 kg/m³, g = 9.8 m/s²) shows a height difference of 0.20 m. Find the pressure difference this represents.
MediumCommon mistake
Forgetting to determine whether the gas pressure is above or below atmospheric based on which side of the manometer is lower — the height difference alone only gives the MAGNITUDE of the pressure difference, not whether to add or subtract it from atmospheric pressure.
Quick Review
- A manometer measures gas pressure by comparing liquid column heights in a U-tube.
- ΔP = hρg gives the pressure difference from the observed height difference.
- Determine from which side is lower whether the gas pressure is above or below atmospheric.