2.3 Gas Pressure
A manometer consists of a glass U-tube containing liquid such as coloured water or mercury. It is used to measure gas pressure by determining the difference between the gas pressure and atmospheric pressure based on the difference in liquid column levels.
Learning Objectives
- Explain how a manometer functions to measure gas pressure.
- Determine gas pressure using a water manometer or a mercury manometer.
- Solve numerical problems involving gas pressure and atmospheric pressure in units such as cm Hg, m H₂O, and Pa.
U-tube Manometer Connected to a Gas Supply
See how the difference in liquid height h corresponds to the difference between gas pressure and atmospheric pressure at the same horizontal reference line.
Before connecting to gas supply
Both arms are open to the atmosphere, so the liquid levels in both arms are equal.
After connecting to gas supply
Gas pressure pushes the liquid down on the gas side, while the open side rises by height h.
Short Explanation
What is a Manometer?
A manometer consists of a glass U-tube containing liquid such as coloured water or mercury. It measures gas pressure by comparing the gas pressure with atmospheric pressure.
Operating Principle
At equilibrium, two points at the same horizontal level in the same continuous liquid have the same pressure. Therefore, \(P_{\text{gas}} = h + P_{\text{atm}}\).
Pressure Difference
The height, \(h\), of the liquid column represents the difference between gas pressure and atmospheric pressure: \(\Delta P = P_{\text{gas}} - P_{\text{atm}} = h\).
Pressure Conversion
To convert liquid column height to pascals, use \(P = h\rho g\), where \(\rho\) is liquid density and \(g\) is gravitational acceleration.
| Quantity | Symbol | SI Unit |
|---|---|---|
| Gas pressure | \(P_{\text{gas}}\) | Pa |
| Atmospheric pressure | \(P_{\text{atm}}\) | Pa |
| Liquid column height | \(h\) | m |
| Liquid density | \(\rho\) | kg m⁻³ |
| Gravitational acceleration | \(g\) | m s⁻² |
Try to Answer First
Answer in your mind, then press “Check Answer”.
Why is mercury preferred over water in a manometer when measuring high gas pressures?
Check Answer
If the diameter of the glass tube of a manometer is doubled, what happens to the height difference, h, of the liquid columns?
Check Answer
A mercury manometer shows a liquid column height difference of 40 cm. Given that \(P_{\text{atm}} = 76\ \text{cm Hg}\), what is the pressure of the gas supply in cm Hg?
Check Answer
Common Mistakes
- Forgetting to add atmospheric pressure (\(P_{\text{atm}}\)) to the height difference \(h\) when calculating total gas pressure.
- Assuming that increasing the diameter of the U-tube manometer will reduce the height difference \(h\).
- Directly using height in centimetres instead of converting to metres before applying the formula \(P = h\rho g\).
- Confusing units of pressure by directly adding values with different units, such as adding cm Hg directly to Pa or kPa without conversion.
Concept Misunderstandings
A wider manometer tube requires more force to push the liquid, so the height difference \(h\) will be smaller.
Pressure depends only on vertical depth, liquid density, and gravitational acceleration (\(P = h\rho g\)). It is independent of the surface area or diameter of the tube.
The height difference \(h\) directly equals the total gas pressure.
The height difference \(h\) represents only the difference between the gas pressure and atmospheric pressure (\(P_{\text{gas}} - P_{\text{atm}}\)). To find the total gas pressure, atmospheric pressure must be added.
Summary
- A manometer is a U-tube containing liquid used to measure gas pressure.
- When connected to a gas supply with pressure higher than atmospheric pressure, the gas pushes the liquid column down on its side.
- Formula for gas pressure: \(P_{\text{gas}} = h + P_{\text{atm}}\), where \(h\) is the height difference between the liquid levels.
- Pressure conversion to SI unit (Pa): \(P = h\rho g\).
- Tube diameter does not affect the liquid column height \(h\).
- Mercury is used for high pressures due to its high density, while digital manometers with pressure transducers are widely used today for safety, portability, and accuracy.
Short Activity
Objective: Test your understanding of manometer principles, pressure calculations and key terms.
A. Objective Quiz
1 What happens to the height difference, \(h\), between the liquid levels in a manometer if the glass tube is replaced with one of larger diameter?
2 A mercury manometer connected to a gas tank has a mercury level difference of 25 cm. If atmospheric pressure is 75 cm Hg, what is the gas pressure in cm Hg?
B. Fill in the Blanks
3 In a manometer, the height difference \(h\) represents the difference between the gas pressure and pressure.
4 Digital manometers that use a pressure are more common nowadays because they are portable and provide accurate readings without using toxic mercury.
C. Matching / Drag and Drop
Match each manometer term or parameter with its correct description. If using a phone, tap the answer first, then tap the matching box.
