At a certain point, the absolute pressure and atmospheric pressure is given by 850 mm of Hg and 700 mm of Hg respectively. What is the value of gauge pressure (mm of Hg) at that point?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 22.1.2018 (Evening Shift)
Detailed Explanation
Gauge pressure measures how much a fluid's pressure exceeds or falls below the ambient atmospheric pressure. Subtracting local atmospheric pressure from absolute pressure gives gauge pressure.
1. Given values:
- Absolute pressure \(p_{\text{abs}} = 850\text{ mm of Hg}\)
- Atmospheric pressure \(p_{\text{atm}} = 700\text{ mm of Hg}\)
2. Apply the fundamental relationship:
\[ p_{\text{gauge}} = p_{\text{abs}} - p_{\text{atm}} \]
3. Substitute the values:
\[ p_{\text{gauge}} = 850\text{ mm of Hg} - 700\text{ mm of Hg} = 150\text{ mm of Hg} \]
Why “150” Is Correct
The measured absolute pressure of \(850\text{ mm of Hg}\) is \(150\text{ mm of Hg}\) higher than the ambient atmospheric level of \(700\text{ mm of Hg}\). This excess corresponds to a gauge pressure of \(150\text{ mm of Hg}\).
Why the Other Options Are Wrong
- A. 50: 50 mm Hg results from subtracting 800 − 750 or arbitrary arithmetic.
- B. 100: 100 mm Hg is an incorrect subtraction.
- D. 200: 200 mm Hg results from arbitrary rounding or miscalculation.
Key Point
Gauge pressure formula: p_gauge = p_abs − p_atm = 850 − 700 = 150 mm of Hg.
Key Concepts for Students
- Because both heads are expressed in mm of Hg, they can be subtracted directly without unit conversions.
- If p_abs was less than p_atm, the resulting negative gauge pressure would be called a vacuum.
- 150 mm of Hg corresponds to 150 × 133.322 Pa ≈ 20.0 kPa gauge pressure.
Practice more: this is question 21 in Measurement of Pressure MCQs – Part 2. Try the whole set and check every answer instantly.