Manometer Calculator
Calculate gauge pressure from manometer fluid height, density, and gravity for U-tube and inclined manometers.
What Is a Manometer?
A manometer measures fluid pressure by balancing it against a liquid column. A U-tube manometer connects a pressurized vessel to a glass tube filled with a dense liquid such as mercury or water. The height difference between the two liquid surfaces reveals the gauge pressure at the connection point.
Manometer Pressure Formula
Hydrostatic pressure from a fluid column is:
$$P = \rho g h$$Here \(\rho\) is fluid density, \(g\) is gravitational acceleration, and \(h\) is the vertical height difference of the liquid column. For an inclined manometer, the measured length along the tube is converted to vertical height using \(h_v = L \sin(\theta)\), where \(\theta\) is the inclination angle.
U-Tube vs Inclined Manometers
U-tube manometers are simple and accurate for moderate pressure differences. Inclined manometers stretch the scale along a shallow angle, making small pressure changes easier to read. Both rely on Pascal's principle: pressure applied to a confined fluid is transmitted equally throughout the fluid.
Related tools: Fluid Pressure Calculator, Pipe Hydrostatic Calculator, and Ideal Gas Pressure Calculator.
Frequently Asked Questions
What is gauge pressure vs absolute pressure?
Gauge pressure is measured relative to atmospheric pressure. Absolute pressure adds atmospheric pressure to the gauge reading: P_abs = P_gauge + P_atm.
Why use mercury in manometers?
Mercury is dense (about 13,600 kg/m³), so it produces a shorter column for the same pressure. That keeps the instrument compact when measuring higher pressures.
What height difference does water give at 1 kPa?
Using P = ρgh with water at 1000 kg/m³ and g ≈ 9.81 m/s², h ≈ 0.102 m or about 10.2 cm for 1 kPa gauge pressure.
How does an inclined manometer improve resolution?
The liquid travels farther along the inclined tube for the same vertical rise. A longer scale makes small height changes easier to read with a ruler or scale.
Does temperature affect manometer readings?
Yes, slightly. Fluid density changes with temperature, and the vessel may expand. For precise work, note the fluid temperature and use corrected density values.