In a differential manometer, the use of mercury is advantageous when the pressure difference is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2005
Detailed Explanation
The selection of manometric fluid in a differential manometer depends on the magnitude of the pressure difference to be measured. Heavy fluids keep column heights reasonable, while light fluids provide magnification for tiny pressure differences.
1. Differential manometer equation:
\[ \Delta p = x \cdot g \cdot (\rho_m - \rho_f) \;\implies\; x = \frac{\Delta p}{g \cdot (\rho_m - \rho_f)} \]
2. For a large pressure difference (\(\Delta p\)):
- If a light fluid (like water or oil) were used, the column deflection \(x\) would be enormous (several metres tall), requiring impractically long glass tubes.
- Using mercury (\(\rho_m = 13,600\text{ kg/m}^3\)) provides a large denominator \((\rho_m - \rho_f)\), keeping the column deflection \(x\) within a compact, easily readable height of 0.1 to 1.0 metre.
3. Conversely, for small pressure differences, mercury would yield an unreadably tiny meniscus displacement, so a lighter fluid (or inverted U-tube) is preferred.
Why “Large” Is Correct
Due to its high mass density (\(13,600\text{ kg/m}^3\)), mercury prevents manometer tubes from becoming unwieldy and tall when measuring large pressure differences.
Why the Other Options Are Wrong
- B. Small: For small pressure differences, mercury deflections are too tiny to read accurately; light fluids or inverted manometers are used instead.
- C. Either large or small: Mercury is unsuitable for very small pressure differences due to lack of resolution.
- D. None of the above: Option (a) is correct; 'None of the above' is incorrect.
Key Point
Mercury is advantageous in differential manometers for large pressure differences (S_m = 13.6 keeps tube height compact).
Key Concepts for Students
- For measuring small pressure differences, inverted U-tubes with air or light oil are used.
- Mercury does not wet glass (cohesion > adhesion) and forms a clear, distinct convex meniscus.
- Mercury has a very low vapor pressure, preventing vapor bubble formation in the column.
Practice more: this is question 36 in Measurement of Pressure MCQs – Part 3. Try the whole set and check every answer instantly.