Purpose of manometers: A manometer is primarily used to measure what quantity in fluid systems?

Introduction / Context:
Manometers employ one or more columns of fluid to balance unknown pressure differences by hydrostatic head. They remain fundamental laboratory and field instruments because they are simple, accurate, and require minimal calibration when fluid properties are known.

Given Data / Assumptions:

• Hydrostatic principle applies: p2 - p1 = ρ_m * g * Δh (with sign conventions).
• Using a manometric fluid (e.g., mercury or a colored liquid).
• Small temperature variation so density remains essentially constant.

Concept / Approach:
Simple (open) manometers measure gauge pressure at a single tapping relative to atmosphere, whereas differential manometers connect two points and directly read their pressure difference. Because the most general use is measuring Δp between two points, the best answer here is the differential function.

Step-by-Step Solution:

Verification / Alternative check:
For a venturimeter, two pressure tappings (upstream and throat) are indeed joined to a differential manometer to find the pressure drop used in discharge calculations, exemplifying the “difference of pressures” purpose.

Why Other Options Are Wrong:

• Atmospheric pressure: Typically measured by a barometer, not a manometer (though conceptually related).
• Absolute pressures in pipes/channels/venturimeters: A simple manometer reads gauge (relative) unless one limb is evacuated; differential use is canonical.

Common Pitfalls:
Ignoring fluid density differences between the manometric fluid and the line fluid; using wrong sign convention; neglecting elevation corrections of tapping points.

Final Answer:
difference of pressures between two points in a pipe