Question

Which of the followings statements related to pressure are correct ?
(A) Gage pressure = Absolute pressure \(-\) Atmospheric pressure
(B) Absolute pressure = Gage pressure \(-\) Atmospheric pressure
(C) Absolute pressure = Atmospheric pressure \(+\) Vacuum pressure
(D) Gage pressure = Atmospheric pressure \(+\) Vacuum pressure
Choose the correct answer from the options given below:

• A. (A) only.
• B. (A), (B) and (C) only.
• C. (A) and (C) only.
• D. (B), (C) and (D) only.

Hint:

Remember the reference datum:
- If you measure from absolute zero \(\rightarrow\) Absolute Pressure.
- If you measure from atmospheric pressure \(\rightarrow\) Gage Pressure (above atmospheric) or Vacuum Pressure (below atmospheric).
- Formula: \(P_{\text{abs}} = P_{\text{atm}} + P_{\text{gauge}}\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Pressure is defined as force per unit area.
In fluid mechanics, pressure is measured with respect to different datums:
- Absolute Pressure (\(P_{\text{abs}}\)): Measured relative to a perfect vacuum (absolute zero pressure).
- Gage Pressure (\(P_{\text{gauge}}\)): Measured relative to the local atmospheric pressure.
- Vacuum Pressure (\(P_{\text{vac}}\)): Measured below atmospheric pressure.
Key Formula or Approach:
The standard relationships between these pressures are:
\[ P_{\text{abs}} = P_{\text{atm}} + P_{\text{gauge}} \quad (\text{for pressures above atmospheric}) \]
\[ P_{\text{abs}} = P_{\text{atm}} - P_{\text{vac}} \quad (\text{for pressures below atmospheric}) \]

Step 2: Detailed Explanation:
Let us evaluate each of the statements:
- Statement (A): "Gage pressure = Absolute pressure \(-\) Atmospheric pressure"
Rearranging our standard formula:
\[ P_{\text{gauge}} = P_{\text{abs}} - P_{\text{atm}} \]
This statement is correct.
- Statement (B): "Absolute pressure = Gage pressure \(-\) Atmospheric pressure"
This is incorrect. Absolute pressure is the sum, not the difference, of gage and atmospheric pressures:
\[ P_{\text{abs}} = P_{\text{gauge}} + P_{\text{atm}} \]
- Statement (C): "Absolute pressure = Atmospheric pressure \(+\) Vacuum pressure"
This is incorrect. Vacuum is negative gage pressure, so:
\[ P_{\text{abs}} = P_{\text{atm}} - P_{\text{vac}} \]
- Statement (D): "Gage pressure = Atmospheric pressure \(+\) Vacuum pressure"
This is incorrect.
Therefore, only statement (A) is correct.

Step 3: Final Answer:
The correct option is (A).