🔬 U-Tube Manometer Calculator
Calculate gauge pressure or differential pressure from U-tube manometer readings using the hydrostatic pressure formula ΔP = ρgh. Enter the manometer fluid density, height difference, and gravity. Supports multiple units and includes a step-by-step solution.
What Is a U-Tube Manometer?
A U-tube manometer is a simple and accurate instrument for measuring pressure or pressure difference. It consists of a U-shaped glass tube filled with a manometer fluid (such as mercury, water, or oil). When pressure is applied to one side, the fluid level changes, and the height difference (h) between the two columns indicates the pressure.
The fundamental equation for a U-tube manometer is:
ΔP = ρ · g · h
where ΔP = pressure difference (Pa), ρ = manometer fluid density (kg/m³), g = gravitational acceleration (m/s²), h = height difference (m)
Types of U-Tube Manometer Measurements
There are two common configurations:
- Gauge Pressure: One side of the U-tube is open to the atmosphere, while the other is connected to the pressure source. The pressure is P = ρgh.
- Differential Pressure: Both sides are connected to different pressure points. If both sides contain the same process fluid, the differential pressure is ΔP = (ρ_m − ρ_f)gh, where ρ_m is the manometer fluid and ρ_f is the process fluid density.
Common Manometer Fluids
- Mercury (Hg): ρ ≈ 13,600 kg/m³ — used for high pressures, compact tube length.
- Water (H₂O): ρ ≈ 1,000 kg/m³ — used for low pressures, non-toxic.
- Oil: ρ ≈ 800–900 kg/m³ — used when mercury contamination is a concern.
- Ethanol: ρ ≈ 789 kg/m³ — used for very low pressures.
How to Use This Calculator
- Select the calculation type — gauge pressure or differential pressure.
- Enter the manometer fluid density (e.g., 1000 kg/m³ for water, 13600 kg/m³ for mercury).
- If calculating differential pressure, enter the process fluid density.
- Enter the height difference (h) and select the unit.
- Enter gravity (default 9.81 m/s²).
- Press "Calculate Pressure" to see the result in multiple units.
Why Use This Calculator?
- Instant results: Get pressure in Pa, kPa, PSI, and mmHg.
- Multiple units: Enter density and height in your preferred units.
- Step-by-step breakdown: See exactly how the calculation is performed.
- Free & private: No registration, no data storage — all calculations are done in your browser.
❓ U-Tube Manometer Calculator FAQ
What is the formula for a U-tube manometer?
The formula is ΔP = ρgh, where ρ is the manometer fluid density, g is gravitational acceleration, and h is the height difference between the two fluid columns.
What is the difference between gauge and differential pressure?
Gauge pressure is measured relative to atmospheric pressure (one side open to atmosphere). Differential pressure is the pressure difference between two points, accounting for the density of the process fluid as well as the manometer fluid.
What fluid is used in a U-tube manometer?
Mercury (13,600 kg/m³) is used for high pressures because its high density allows a compact tube. Water (1,000 kg/m³) is used for low pressures and is non-toxic. Oil and alcohol are used for very low pressures or when mercury is not suitable.
How do I convert the height difference to pressure?
Multiply the height difference by the fluid density and gravity: P = ρgh. For example, 100 mm of water (ρ = 1000 kg/m³, g = 9.81 m/s²) gives P = 1000 × 9.81 × 0.1 = 981 Pa.
What is the differential pressure formula?
When both sides of the manometer contain the same process fluid, the differential pressure is ΔP = (ρ_m − ρ_f)gh, where ρ_m is the manometer fluid density and ρ_f is the process fluid density.
Why is mercury used in manometers?
Mercury has a very high density (13,600 kg/m³), which means a relatively short column can measure large pressures. It is also opaque and has a clear meniscus, making readings easy.
What are the common applications of U-tube manometers?
U-tube manometers are used in HVAC systems (duct pressure), laboratory calibration, process control (pipeline pressure), medical equipment (blood pressure), and aerodynamics (wind tunnel testing).
How accurate is this calculator?
This calculator uses the exact hydrostatic pressure formula ΔP = ρgh. Accuracy depends on the precision of the input values. You can adjust the decimal precision in the output.
Is this calculator free?
Yes, this calculator is completely free to use. No registration or personal data storage is required.
What units does this calculator support?
Density: kg/m³, g/cm³, lb/ft³. Height: mm, cm, m, in, ft. Gravity: m/s², ft/s². Pressure is displayed in Pa, kPa, PSI, and mmHg.