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Manometer for gas

Calculates gas pressure difference from a manometer-fluid column.

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P_{1} - P_{2} = ρ_{m} g h = P_{h}

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Core idea

Overview

For gas manometers, the gas density is often small compared with the manometer-fluid density. The pressure difference is then well approximated by rho_m g h.

When to use: Use this gas-manometer approximation when the manometer liquid is much denser than the gas being measured.

Why it matters: It provides a simple way to measure low gas pressure differences with a liquid column.

Symbols

Variables

$P_{1}$ - $P_{2}$ = Pressure Difference, $ρ_{m}$ = Manometer Fluid Density, g = Gravitational Acceleration, h = Height Difference

P_{1} - P_{2}

Pressure Difference

ρ_{m}

Manometer Fluid Density

k g / m^{3}

g

Gravitational Acceleration

m / s^{2}

h

Height Difference

m

Walkthrough

Derivation

Derivation of Manometer for gas

The gas manometer relation is the manometer pressure difference with gas density neglected compared with the manometer liquid.

The gas density is negligible compared with the manometer-fluid density.
The manometer liquid is static and has constant density.
The height difference is vertical.

Start with a liquid-column pressure difference

The manometer liquid column creates a pressure difference equal to its weight per area.

Δ P = ρ_{m} g h

Apply to gas taps

For gases, the gas-column correction is commonly small, leaving the manometer-liquid term.

P_{1} - P_{2} = ρ_{m} g h = P_{h}

Result

P_{1} - P_{2} = ρ_{m} g h = P_{h}

Source: Munson, Young, Okiishi, Huebsch, and Rothmayer, Fundamentals of Fluid Mechanics, Wiley, 2013; OpenStax University Physics Volume 1, Pressure Gauges and Manometers, accessed 2026-04-09

Free formulas

Rearrangements

Solve for $ρ_{m} = \frac{P _{1} - P _{2}}{g h}$

Solve for Manometer Fluid Density

\frac{P _{1} - P _{2}}{g h} = ρ_{m}

Isolate density by dividing both sides of the equation by gravity and height.

Difficulty: 2/5

Solve for $h = \frac{P _{1} - P _{2}}{ρ _{m} g}$

Solve for Height Difference

\frac{P _{1} - P _{2}}{ρ _{m} g} = h

Isolate height by dividing both sides of the equation by density and gravity.

Difficulty: 2/5

Solve for $g = \frac{P _{1} - P _{2}}{ρ _{m} h}$

Solve for Gravitational Acceleration

\frac{P _{1} - P _{2}}{ρ _{m} h} = g

Isolate gravity by dividing both sides of the equation by density and height.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph shows a straight line passing through the origin, representing the pressure difference in a manometer for gas as it relates to the height difference of the fluid. For a student, this means that if you double the height difference, you also double the pressure difference, assuming the manometer fluid and gravity stay the same. The most important feature is that the pressure difference is directly proportional to the height difference. This relationship is a direct consequence of the manometer equation.

Graph type: linear

Why it behaves this way

Intuition

The gas pushes the manometer liquid until the liquid-column weight balances the gas pressure difference.

P_{1} - P_{2}

Gas pressure difference

The pressure imbalance between two gas points.

ρ_{m}

Manometer-fluid density

The liquid density that sets pressure per metre of height.

h

Height difference

The visible offset between liquid levels.

Free study cues

Insight

Canonical usage

This equation is used to calculate the pressure difference between two points in a fluid system by measuring the height difference of a manometer fluid and knowing the fluid's density and the local gravitational.

Common confusion

Students may incorrectly use the density of the gas being measured instead of the density of the manometer fluid.

Dimension note

This equation yields a quantity with physical dimensions (pressure), not a dimensionless number.

Unit systems

$P_{1} - P_{2}$ Pa · The pressure difference is the primary output, typically in Pascals in SI.

$ρ_{m}$ kg/m^3 · The density of the manometer fluid is a critical input.

$g$ m/s^2 · Gravitational acceleration, which can be approximated by standard gravity or a locally measured value.

$h$ m · The height difference in the manometer column.

One free problem

Practice Problem

A water manometer measuring gas pressure has $r h o_{m}$ = 1000 kg/ $m^{3}$ , h = 0.25 m, and g = 9.81 m/ $s^{2}$ . What is the pressure difference?

Manometer Fluid Density1000 kg/m^3

Gravitational Acceleration9.81 m/s^2

Height Difference0.25 m

Solve for: pressureDifference

Hint: Use deltaP = $r h o_{m}$ g h.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Measuring a small pressure difference in a ventilation duct using an inclined liquid manometer.

Study smarter

Tips

Use the manometer-fluid density.
Check whether gas density can be neglected.
Use vertical height difference only.

Avoid these traps

Common Mistakes

Using gas density instead of manometer-fluid density.
Forgetting that this is usually a pressure difference, not absolute pressure.

Common questions

Frequently Asked Questions

The gas manometer relation is the manometer pressure difference with gas density neglected compared with the manometer liquid.

Use this gas-manometer approximation when the manometer liquid is much denser than the gas being measured.

It provides a simple way to measure low gas pressure differences with a liquid column.

Using gas density instead of manometer-fluid density. Forgetting that this is usually a pressure difference, not absolute pressure.

Measuring a small pressure difference in a ventilation duct using an inclined liquid manometer.

Use the manometer-fluid density. Check whether gas density can be neglected. Use vertical height difference only.

References

Sources

Munson, Young, Okiishi, Huebsch, and Rothmayer, Fundamentals of Fluid Mechanics, Wiley, 2013
OpenStax University Physics Volume 1, Pressure Gauges and Manometers, accessed 2026-04-09
NIST CODATA
IUPAC Gold Book
Wikipedia: Manometer
Fundamentals of Fluid Mechanics by Munson, Young, and Okiishi
NIST Chemistry WebBook
Britannica

Manometer for gas

Overview

Variables

Derivation

Start with a liquid-column pressure difference

Apply to gas taps

Rearrangements

Graph

Intuition

Insight

Practice Problem

Real-World Context

Tips

Common Mistakes

Related Formulas

Hydrostatic pressure

Hydrostatic head

General manometer

Differential manometer

Frequently Asked Questions

Sources