Gauge pressure at a point is equal to :
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2009
Detailed Explanation
Pressure gauges record the difference between the absolute pressure inside a vessel and the surrounding atmospheric pressure.
1. Basic pressure relationship:
\[ p_{\text{abs}} = p_{\text{atm}} + p_{\text{gauge}} \]
2. Solve for gauge pressure (\(p_{\text{gauge}}\)):
\[ p_{\text{gauge}} = p_{\text{abs}} - p_{\text{atm}} \]
3. Physical interpretation:
- If \(p_{\text{abs}} > p_{\text{atm}}\): \(p_{\text{gauge}}\) is positive.
- If \(p_{\text{abs}} = p_{\text{atm}}\): \(p_{\text{gauge}} = 0\).
- If \(p_{\text{abs}} < p_{\text{atm}}\): \(p_{\text{gauge}}\) is negative (called vacuum).
Why “Absolute pressure minus atmospheric pressure” Is Correct
By definition, gauge pressure is the pressure measured above the local atmospheric datum, obtained by subtracting atmospheric pressure from absolute pressure.
Why the Other Options Are Wrong
- A. Absolute pressure plus atmospheric pressure: Absolute pressure plus atmospheric pressure is a fictitious sum with no physical meaning.
- C. Vacuum pressure plus absolute pressure: Vacuum pressure plus absolute pressure equals atmospheric pressure (P_vac + P_abs = P_atm), not gauge pressure.
- D. None of the above: Option (b) is the correct standard definition; 'None of the above' is incorrect.
Key Point
Gauge pressure = Absolute pressure − Atmospheric pressure.
Key Concepts for Students
- Gauge pressure is positive when pressure exceeds atmospheric.
- Gauge pressure is zero when pressure equals atmospheric.
- Most industrial dial gauges and sensors read gauge pressure directly.
Practice more: this is question 34 in Measurement of Pressure MCQs – Part 3. Try the whole set and check every answer instantly.