In a U-tube manometer used to measure the pressure of a flowing gas, why is mercury often used as the manometric fluid instead of water?
- AMercury has a lower vapor pressure.
- BMercury is more colorful and easier to see.
- CMercury's high density allows for a smaller, more manageable column height for high pressures.Correct
- DMercury is less viscous than water.
Solution
Concept
Manometric fluid density and column height relation
Formula
h = P / (ρ × g)
Step-by-step solution
1. Hydrostatic balance in a manometer is expressed as P = ρ × g × h, giving column height h = P / (ρ × g). 2. The column height needed to balance a given fluid pressure is inversely proportional to the density of the manometric liquid. 3. Mercury has a high relative density (13.6), whereas water has a relative density of 1.0. 4. Consequently, a mercury column is 13.6 times shorter than a water column, allowing high pressures to be measured within compact tube lengths. Answer: C
Explanation
In a U-tube manometer measuring gas or liquid pressure, the required balancing column height is inversely proportional to fluid density (h = P / (ρ × g)). Because mercury has a high relative density of 13.6, the required manometric fluid column height is roughly 14 times shorter than water, keeping the apparatus compact and physically manageable.
Why the other options are wrong
A) Mercury has low vapor pressure, but its high density is the governing factor that prevents excessively tall manometers. B) Fluid color is a visual preference, not the engineering reason for selecting mercury. D) Mercury is more viscous than water.
Shortcut
High fluid density (ρHg = 13.6 ρw) -> Compact, manageable manometer column height.
Common mistake
Assuming mercury is selected solely for vapor pressure, overlooking that density determines physical tube height.
Correct answer: C) Mercury's high density allows for a smaller, more manageable column height for high pressures.