A manometer measures pressure by comparing the height difference of a liquid in its U-shaped tube.
Understanding Manometer Pressure Measurement
Manometers, particularly U-tube manometers, are used to measure pressure by balancing the weight of a liquid column against the applied pressure. The principle is quite straightforward:
- The Setup: A U-shaped tube is partially filled with a liquid, usually water, mercury, or oil.
- Pressure Application: Pressure is applied to one side of the manometer.
- Liquid Displacement: The applied pressure forces the liquid down on one side of the tube and up on the other side.
- Reading the Pressure: The difference in height between the liquid levels in the two legs of the tube directly indicates the magnitude of the applied pressure. As stated, "The difference in height between the two legs of liquid represents the pressure pushing the liquid down one leg and up the other".
Types of Manometers and How They Work
U-Tube Manometer
This is the most basic type of manometer.
- One end of the U-tube is connected to the pressure source you want to measure.
- The other end is usually open to the atmosphere.
- The liquid levels will move depending on the pressure difference.
- The pressure is proportional to the height difference and the density of the liquid.
Inclined Manometer
An inclined manometer is a modified U-tube manometer with one leg inclined.
- The inclined leg makes it easier to measure smaller pressure differences.
- The change in liquid level is amplified along the length of the inclined tube, making measurements more precise.
Calculation of Pressure from Manometer Readings
The pressure P measured by a manometer is given by the formula:
- P = h ρ g
- P is the pressure difference
- h is the height difference between the liquid levels
- ρ is the density of the manometer fluid
- g is the acceleration due to gravity (approximately 9.8 m/s²)
Practical Examples
- If a manometer filled with water shows a height difference of 10 cm (0.1 m), the pressure is calculated as follows (using ρ of water as 1000 kg/m³):
- P = 0.1 m 1000 kg/m³ 9.8 m/s² = 980 Pascals
- If mercury is used (ρ ≈ 13600 kg/m³) with the same 10 cm difference:
- P = 0.1 m 13600 kg/m³ 9.8 m/s² ≈ 13328 Pascals.
Key Considerations
- The liquid used in the manometer impacts the measurement range and accuracy.
- Mercury, being dense, allows for measurement of higher pressures with smaller height differences compared to water.
- Ensure the manometer is correctly zeroed and that the tube is free of obstructions.
- The temperature of the liquid can affect its density; this may need to be considered for precise measurements.
