For measurements of small pressure differences, a mixture having a specific gravity of 1.10 is used. The magnification of the reading will be:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2005
Detailed Explanation
When measuring small differential pressures between water pipes, using a manometric fluid whose density is only slightly greater than water magnifies the meniscus deflection, greatly improving reading accuracy.
1. Formula for a U-tube differential manometer containing liquid of specific gravity \(S_m\) measuring water (\(S_w = 1.0\)):
\[ \Delta h = x \left(\frac{S_m}{S_w} - 1\right) \]
Where \(\Delta h\) is the differential pressure head in metres of water, and \(x\) is the manometer meniscus reading in metres.
2. Substitute \(S_m = 1.10\) and \(S_w = 1.0\):
\[ \Delta h = x (1.10 - 1.0) = 0.10 \, x \]
3. Examination Analysis:
- In the SSC JE answer key, the factor \(0.10\) is taken directly from the relation \(\Delta h = 0.10 \, x\), designating option (c) 0.10 times as the answer.
- In physical instrumentation theory, the magnification of reading is defined as the ratio of manometer deflection to actual water head: \(\frac{x}{\Delta h} = \frac{1}{0.10} = 10\text{ times}\) (option b). Candidates should note this question-wording ambiguity in the official key.
Why “0.10 times” Is Correct
The differential water head relates to the manometer reading by \(\Delta h = x(1.10 - 1) = 0.10x\). The examination key marks (c) \(0.10\text{ times}\) reflecting this direct numerical factor.
Why the Other Options Are Wrong
- A. 1.10 times: 1.10 times simply repeats the specific gravity of the mixture without subtracting the flowing fluid density (S_m − 1).
- B. 10 times: 10 times is the true physical magnification of the scale deflection (x / Δh = 1 / 0.10 = 10), which is mathematically accurate but not the designated key option.
- D. 4 times: 4 times is an arbitrary distractor.
Key Point
Differential head: Δh = x(S_m − 1) = x(1.10 − 1) = 0.10x; exam key marks 0.10 times.
Key Concepts for Students
- Using S_m close to 1.0 creates large readable deflections for tiny pressure heads.
- If mercury (S = 13.6) were used, Δh = 12.6 x, resulting in a tiny, hard-to-read deflection.
- Exam discrepancy note: The question stem confuses the multiplier factor 0.10 with its inverse (magnification 10).
Practice more: this is question 23 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.