Compute tube movement sensitivity for tiny pressure differences. Check angle and density effects for scaling. Get cleaner readings with safe unit conversions every time.
An inclined manometer converts a small pressure difference into a longer tube movement. The vertical head is h = L·sinθ.
The pressure difference is ΔP = (ρm − ρf)·g·h, where ρm is manometer fluid density and ρf is process fluid density.
Sensitivity (movement per pressure) is S = dL/dP = 1 / ((ρm − ρf)·g·sinθ).
| ρf (kg/m³) | ρm (kg/m³) | θ (deg) | S (mm/Pa) | ΔP for L=50 mm (Pa) |
|---|---|---|---|---|
| 1.2 | 1000 | 10 | 0.0059 | 8.46 |
| 1.2 | 1000 | 5 | 0.0118 | 4.23 |
| 998 | 13600 | 15 | 0.0003 | 159.2 |
Professional article (400 words)
Inclined manometers help when pressure differences are so small that a vertical column is difficult to read. Tilting the tube converts a tiny vertical head into a longer movement along the scale. Sensitivity tells how far the meniscus travels per unit pressure change, guiding readability. It also indicates whether your scale length suits the planned test.
The vertical rise is h = L·sinθ, where L is distance along the tube and θ is inclination from horizontal. The pressure difference is ΔP = (ρm − ρf)·g·h. Combining gives sensitivity S = dL/dP = 1/((ρm − ρf)·g·sinθ).
Angle controls the scale stretch. When θ decreases, sinθ decreases, so S increases and the same ΔP produces a longer L. Dropping θ from 10° to 5° nearly doubles sensitivity because sin5° is about half of sin10°. Avoid angles too close to 0° to keep travel manageable.
Density difference Δρ = ρm − ρf sets pressure per unit head. Water versus air gives Δρ near 1000 kg/m³, which is useful for very low pressures. Mercury (≈13,600 kg/m³) greatly increases Δρ, reducing sensitivity but allowing larger ΔP without excessive tube length.
In airflow, duct, and filter testing, ΔP often lies around 1–250 Pa, with angles commonly 5–15°. For water–air at 10°, sensitivity is about 0.0059 mm/Pa, so a 10 Pa change moves the meniscus about 0.059 mm. Lower angles increase movement.
If your scale resolution is δL, the smallest pressure step is δPmin ≈ (ρm − ρf)·g·(δL·sinθ). Finer graduations, better lighting, or camera reading lowers δPmin. A smaller angle also lowers δPmin, but requires more tube length for the same ΔP.
Density varies with temperature, especially for water and light oils. For better accuracy, use temperature-corrected density and verify the angle with a protractor or inclinometer. Meniscus shape, tube diameter, and wetting can shift readings, so repeat measurements and keep eye position consistent to reduce parallax.
Inclined manometers are common in HVAC commissioning, fan curves, and wind-tunnel pressure taps. Keep the body level side-to-side, remove bubbles, and let the meniscus settle before recording. Use the calculator to compare design choices and document sensitivity in test notes.
Sensitivity is the tube movement per unit pressure change, typically expressed as mm/Pa. Higher sensitivity means a small pressure difference produces a larger, easier-to-read displacement along the inclined scale.
The pressure relation uses Δρ = ρm − ρf. If Δρ is zero or negative, the instrument will not provide a stable differential head in the expected direction, and the sensitivity formula becomes invalid.
Lowering the angle increases sensitivity because sinθ decreases, stretching the scale. The same pressure causes a longer displacement, improving readability, but it can also require a longer tube to cover the desired pressure range.
Yes. Enter your pressure difference in the unit you use, and the calculator converts internally to SI. You can also select output units for sensitivity so results match your lab or field reporting format.
Using a measurable resolution δL, the calculator estimates δPmin. It helps you decide whether the instrument and angle can resolve the smallest pressure changes you care about, before you run the experiment.
Yes. Fluid density changes with temperature, affecting Δρ and therefore sensitivity and ΔP calculations. For precise work, use temperature-corrected densities and allow the apparatus to reach thermal equilibrium before taking final readings.
Air bubbles, a tilted base, dirty tube walls, and parallax during reading can all distort the meniscus position. Purge bubbles, level the instrument, clean the tube, and always read at eye level for repeatable results.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.