The relationship between atmosphere pressure (P_atm), gauge pressure (P_gauge) and absolute pressure (P_abs) is given by:

Asked in SSC JE 2014, EVENING

Detailed Explanation

The three standard concepts of pressure—absolute, atmospheric, and gauge—are linked by a simple linear relationship based on the choice of datum.

1. Pressure datum definitions:

• Absolute zero pressure: Datum of complete void/vacuum where molecular momentum is zero.
• Local atmospheric pressure (\(P_{\text{atm}}\)): Pressure exerted by the surrounding air mass at that elevation.
• Gauge pressure (\(P_{\text{gauge}}\)): Net pressure measured above local atmospheric pressure.

2. The governing equation is:

\[ P_{\text{abs}} = P_{\text{atm}} + P_{\text{gauge}} \]

3. Rearranging for other forms:

\[ P_{\text{gauge}} = P_{\text{abs}} - P_{\text{atm}} \]

\[ P_{\text{vacuum}} = P_{\text{atm}} - P_{\text{abs}} \]

Why “P_abs = P_atm + P_gauge” Is Correct

Gauge pressure is the pressure measured relative to atmospheric pressure. Adding atmospheric pressure to the gauge pressure restores the absolute pressure measured from absolute zero datum.

Why the Other Options Are Wrong

• A. P_abs = P_atm − P_gauge: P_abs = P_atm − P_gauge is incorrect; this formula applies to vacuum pressure (P_abs = P_atm − P_vac).
• B. P_atm = P_abs + P_gauge: P_atm = P_abs + P_gauge is mathematically inverted (it would imply P_atm > P_abs for positive gauge pressure).
• C. P_atm = P_gauge − P_abs: P_atm = P_gauge − P_abs would yield a negative value for atmospheric pressure.

Key Concepts for Students

• Absolute pressure is always positive or zero; it cannot be negative.
• Gauge pressure can be positive, zero, or negative.
• When a pressure gauge reads zero, the absolute pressure inside equals local atmospheric pressure.

Practice more: this is question 32 in Measurement of Pressure MCQs – Part 3. Try the whole set and check every answer instantly.