Differential manometer Calculator

Formula first

Overview

When the same process fluid fills both connection legs, the differential manometer simplifies to the density difference between the manometer fluid and the process fluid times gravity and height difference.

Symbols

Variables

$P_1$ - $P_2$ = Pressure Difference, ${\rho }_m$ = Manometer Fluid Density, $\rho$ = Process Fluid Density, g = Gravitational Acceleration, h = Height Difference

Apply it well

When To Use

When to use: Use this simplified form for a U-tube differential manometer connected between two points in the same fluid.

Why it matters: The equation turns a visible column-height difference into a pressure difference across a pipe, filter, or restriction.

Avoid these traps

Common Mistakes

• Using $rh{o}_m$ alone when the process-fluid density is not negligible.
• Swapping P1 and P2 without changing the sign convention.

One free problem

Practice Problem

A differential manometer uses mercury with density 13600 kg/$m^3$ to measure a water line with density 1000 kg/$m^3$. If h = 0.080 m and g = 9.81 m/$s^2$, what is P1 - P2?

Solve for: pressureDifference

Hint: Use the density difference.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Munson, Young, Okiishi, Huebsch, and Rothmayer, Fundamentals of Fluid Mechanics, Wiley, 2013
2. Engineering LibreTexts, 4.3.2.3: Magnified Pressure Measurement, accessed 2026-04-09
3. NIST CODATA
4. IUPAC Gold Book
5. Wikipedia: Differential manometer
6. Textbook: Fluid Mechanics by Frank M. White
7. NIST Chemistry WebBook
8. University Physics with Modern Physics by Hugh D. Young and Roger A. Freedman