Which of the following pressure units represent at least pressure ?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2004
Detailed Explanation
Pressure intensity is expressed in a variety of scientific, engineering, and meteorological units. Converting each unit to standard SI units (Pascals, \(\text{N/m}^2\)) enables direct quantitative comparison.
1. Convert each unit to Pascals (\(\text{N/m}^2\)):
- (a) 1 millibar (\(\text{mbar}\)): \[ 1\text{ bar} = 10^5\text{ Pa} \;\implies\; 1\text{ mbar} = 10^{-3}\text{ bar} = 10^{-3} \times 10^5\text{ Pa} = 100\text{ N/m}^2 \]
- (b) 1 mm of mercury (\(\text{mmHg}\)): \[ 1\text{ mmHg} = \rho_{\text{Hg}} g h = 13,600 \times 9.80665 \times 0.001 \approx 133.322\text{ N/m}^2 \]
- (c) 1 N/mm²: \[ 1\text{ N/mm}^2 = \frac{1\text{ N}}{(10^{-3}\text{ m})^2} = 10^6\text{ N/m}^2 = 1,000,000\text{ Pa} = 1\text{ MPa} \]
- (d) 1 kgf/cm²: \[ 1\text{ kgf/cm}^2 = \frac{9.80665\text{ N}}{(10^{-2}\text{ m})^2} = 98,066.5\text{ N/m}^2 \approx 98.07\text{ kPa} \approx 1\text{ at (technical atmosphere)} \]
2. Arrange in ascending order of magnitude:
\[ 1\text{ millibar } (100\text{ Pa}) < 1\text{ mmHg } (133.3\text{ Pa}) < 1\text{ kgf/cm}^2 (98,066.5\text{ Pa}) < 1\text{ N/mm}^2 (1,000,000\text{ Pa}) \]
Therefore, 1 millibar represents the least pressure intensity.
Why “milibar” Is Correct
At \(100\text{ N/m}^2\), 1 millibar is significantly smaller than 1 mm of Hg (\(133.3\text{ N/m}^2\)), 1 kgf/cm² (\(98,066.5\text{ N/m}^2\)), and 1 N/mm² (\(1,000,000\text{ N/m}^2\)), making it the smallest unit among the choices.
Why the Other Options Are Wrong
- B. mm of mercury: 1 mm of mercury equals 133.322 N/m², which is 33.3% larger than 1 millibar (100 N/m²).
- C. N/mm²: 1 N/mm² equals 1,000,000 N/m² (1 MPa), which is ten thousand times larger than 1 millibar.
- D. kgf/cm²: 1 kgf/cm² equals 98,066.5 N/m², which is nearly one thousand times larger than 1 millibar.
Key Point
Pressure unit comparison: 1 millibar (100 Pa) < 1 mm Hg (133.3 Pa) < 1 kgf/cm² (98.07 kPa) < 1 N/mm² (1 MPa).
Key Concepts for Students
- 1 bar = 10⁵ Pa = 100 kPa = 1000 mbar.
- 1 atmosphere = 1.01325 bar = 1013.25 mbar = 760 mmHg = 101.325 kPa.
- 1 N/mm² = 10 bar = 10.197 kgf/cm² = 1 MPa.
Practice more: this is question 38 in Measurement of Pressure MCQs – Part 3. Try the whole set and check every answer instantly.