A manometer is a simple pressure measuring device that uses a liquid column to compare pressures. It is common in engineering labs, fluid systems, HVAC work, and process equipment because it turns an invisible pressure difference into a visible height difference. The basic idea is that a heavier fluid column creates more pressure at its bottom, so a height change can be converted into pressure.
A U-tube manometer is especially useful because the two liquid levels can be read directly against a scale.
In a U-tube manometer, the pressure difference between the two arms supports a difference in liquid height, usually written as Delta P = rho g Delta h. If one side is open to the atmosphere, the device measures gauge pressure relative to atmospheric pressure. If both sides are connected to different points in a system, it acts as a differential manometer and measures the pressure difference between those points.
Absolute pressure is found by adding atmospheric pressure to gauge pressure when the gauge pressure is positive, so Pabs = Patm + Pgauge.
Key Facts
- Hydrostatic pressure in a fluid column is P = rho g h.
- For a simple U-tube manometer with the same gas above both liquid surfaces, Delta P = rho_m g Delta h.
- Gauge pressure is pressure measured relative to atmospheric pressure: Pgauge = Pabs - Patm.
- Absolute pressure is measured relative to a perfect vacuum: Pabs = Patm + Pgauge.
- A differential manometer measures the pressure difference between two points: P1 - P2 depends on liquid densities and height differences.
- Denser manometer fluids, such as mercury, give smaller height differences for the same pressure difference.
Vocabulary
- Manometer
- A device that measures pressure or pressure difference by balancing it against the height of a liquid column.
- U-tube manometer
- A manometer made from a U-shaped tube in which unequal liquid levels show a pressure difference between the two sides.
- Differential pressure
- The difference between two pressures, often written as Delta P = P1 - P2.
- Gauge pressure
- Pressure measured relative to local atmospheric pressure.
- Absolute pressure
- Pressure measured relative to a perfect vacuum.
Common Mistakes to Avoid
- Using the total liquid height instead of the height difference is wrong because the pressure difference depends on Delta h between the two free surfaces, not the full length of the tube.
- Forgetting the liquid density is wrong because the same height difference gives different pressures for water, oil, mercury, or other manometer fluids.
- Mixing up gauge and absolute pressure is wrong because a manometer open to the atmosphere usually reads pressure relative to atmospheric pressure, not relative to vacuum.
- Assigning the pressure increase to the higher liquid side is wrong because the side with the lower manometer liquid level usually has the higher applied pressure pushing the fluid down.
Practice Questions
- 1 A U-tube manometer contains mercury with density 13600 kg/m^3. One side is open to the atmosphere and the height difference is 0.120 m. Find the gauge pressure of the gas connected to the other side using g = 9.81 m/s^2.
- 2 A water manometer shows a height difference of 35.0 cm between two air ducts. Using rho = 1000 kg/m^3 and g = 9.81 m/s^2, calculate the pressure difference in pascals.
- 3 A U-tube manometer connected to a tank has the liquid level lower on the tank side and higher on the open atmospheric side. Explain whether the tank pressure is above or below atmospheric pressure, and describe how you know.