U-tube differential manometer

Solves ΔP from the level difference, or finds the reading required, including the line fluid density and the elevation difference between taps.

Configuration and reading

Variable conocida Gauge fluid Gauge fluid density · Level difference h · Line fluid density · Elevation zᵦ − zₐ · Positive if tap B is higher Gravedad local ·

Differential pressure Pₐ−Pᵦ

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Column reading h

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Line fluid head

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Gauge fluid density

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Pressure direction

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Density ratio

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Visual response of the U-tube

Hydrostatic balance

\[P_A-P_B=(\rho_m-\rho_l)gh+\rho_l g(z_B-z_A)\]

\[h=\frac{\Delta P-\rho_lg\Delta z}{(\rho_m-\rho_l)g}\]

The sign shows which tap is at the higher pressure. A gauge fluid with the same density as the process fluid destroys the sensitivity of the reading.

U-tube manometer reading

A differential manometer turns a pressure difference into a measurable level change. The balance is built by walking the column: pressure rises going down through a fluid and falls going up.

Reference gauge fluid densities

Fluido	Approximate density	Application
Mercurio	13 546 kg/m³	Large pressure differences
Water	998 kg/m³	Low pressures and gases
Light oil	850 kg/m³	More sensitive than water in aqueous lines

Elevation correction

If the taps are not at the same elevation, the ρgΔz term must be retained. Ignoring it can significantly bias low-pressure measurements.

Preguntas frecuentes

What does a negative ΔP mean?

That the pressure at B is higher than at A, under the sign convention used here.

Can I use the same liquid in the line and in the manometer?

The density difference vanishes and the instrument no longer produces a useful differential reading.

Does temperature matter?

Yes. The density of each fluid must be taken at the actual measurement temperature.