Questions: Differential Manometer Types and Applications

Question 1

A U-tube manometer currently uses mercury (ρ ≈ 13,600 kg/m³) and shows a 50 mm height difference for a given pressure differential. An engineer replaces the mercury with water (ρ ≈ 1,000 kg/m³). Assuming the same pressure differential, what height difference will the water manometer show?

• A. Approximately 3.7 mm — water is denser in the effective reading
• B. Still 50 mm — the height reading depends only on the pressure difference, not the fluid
• C. Approximately 680 mm — water's lower density requires a much taller column to balance the same pressure
• D. Approximately 136 mm — the reading scales linearly with the density ratio

Answer: (C)

From ΔP = ρgh, the same pressure difference requires h = ΔP/(ρg). Switching from mercury (ρ = 13,600) to water (ρ = 1,000) increases the required height by the ratio 13,600/1,000 = 13.6. So 50 mm × 13.6 = 680 mm. This is why mercury is used for large pressure differences — its high density keeps the manometer compact. Water would require an impractically tall tube for the same measurement. This directly illustrates the key design principle: denser manometric fluid = smaller, more compact readings.

Question 2

Which manometer configuration is best suited for measuring a very small pressure difference (≈ 2 Pa) between two points in a water-filled pipe?

• A. U-tube with mercury — mercury's high density ensures a stable, readable column
• B. Standard U-tube with water as the manometric fluid
• C. Inverted U-tube with air trapped at the top — the low-density indicator fluid amplifies the height reading
• D. An inclined U-tube filled with mercury at a 45° angle

Answer: (C)

For very small pressure differences in liquid-filled systems, you want to *amplify* the reading, not compress it. An inverted U-tube with air (ρ_m ≈ 0) gives ΔP ≈ ρ_f·g·h, where the process fluid density drives the reading — this exaggerates the height difference, making it readable. Mercury (option A) would give an extremely tiny reading (h = ΔP/(ρ_mercury·g) ≈ 0.015 mm) — far too small to measure. Water-water (option B) is better than mercury but still gives only 0.2 mm. Inclined mercury (option D) wastes the amplification benefit of the incline on an already-compact fluid.

Question 3

An inclined manometer tilted at 10° from horizontal produces a larger length reading along the tube than a vertical manometer for the same pressure difference.

• T. True
• F. False

Answer: True

In an inclined manometer, a vertical rise of h appears as a tube-length reading of h/sin(θ). At θ = 10°, sin(10°) ≈ 0.174, so the tube length reading is approximately 5.8 times the actual vertical rise. This geometric amplification — with no change in manometric fluid — makes inclined manometers ideal for measuring small pressure differences that would be hard to read on a vertical tube. The pressure calculation still uses the vertical height h, not the along-tube length.

Question 4

A denser manometric fluid usually provides greater sensitivity — a larger height reading — for a given pressure difference in a U-tube manometer.

• T. True
• F. False

Answer: False

The opposite is true: a denser manometric fluid gives a *smaller* height reading for a given pressure difference. Since ΔP = ρ_m·g·h, a larger ρ_m means a smaller h for the same ΔP. High-density fluids like mercury produce compact, easy-to-handle readings for large pressure differences — but they have low sensitivity for small ΔP because the resulting column height is tiny. For small pressure differences, you want a *low-density* manometric fluid (inverted U-tube with air, or light oil) to amplify the reading.

Question 5

Explain why mercury is preferred over water for measuring large pressure differences in a U-tube manometer, and why this same property makes mercury unsuitable for measuring very small pressure differences.

Model answer: Mercury's high density (≈13,600 kg/m³, roughly 13.6× water) means a large pressure difference produces only a modest column height — the manometer stays compact and readable. For example, a 100 kPa difference requires only ≈750 mm of mercury versus ≈10 m of water. But for a very small pressure difference (say, 5 Pa), h = ΔP/(ρg) ≈ 0.037 mm of mercury — a height far too tiny to read accurately. Water, or better yet a light oil or air in an inverted configuration, would produce a readable height for the same small ΔP. The fundamental trade-off is: denser fluid → smaller readings (good for large ΔP, bad for small ΔP).

Fluid selection is always driven by matching the manometric fluid density to the expected pressure range. High-density fluid for large ΔP keeps the instrument compact; low-density fluid for small ΔP amplifies the signal to a measurable scale. Inclined manometers offer an additional geometric amplification strategy on top of fluid selection.