Question

Consider the following statements regarding the pressure measured at a point in a fluid.
S1: Absolute pressure is gauge pressure plus atmospheric pressure.
S2: Gauge pressure is measured by considering absolute zero pressure as datum.
S3: Absolute pressure is measured by considering atmospheric pressure as datum.
S4: Vacuum pressure is negative pressure obtained by subtracting absolute pressure from atmospheric pressure.
Which ONE of the following options lists all the TRUE statements?

• A. S1 and S2
• B. S2 and S3
• C. S1 and S4
• D. S1, S2, and S4

Hint:

Write out P_abs = P_atm + P_gauge and P_vac = P_atm - P_abs, then check each statement's datum claim against these standard relations.

Answer 1

The Correct Option is C

Another way to sort this out is to draw a simple vertical pressure scale with three reference lines: zero at the bottom representing a perfect vacuum (absolute zero), the atmospheric line somewhere above it, and the actual point pressure marked wherever it happens to fall.

If the point pressure lies above the atmospheric line, the gap above atmospheric is the gauge pressure, and adding that gauge value to the atmospheric value gives back the absolute pressure. That is exactly $P_{abs}=P_{atm}+P_{gauge}$, so statement S1 checks out on the diagram.

Since gauge pressure is just the distance from the atmospheric line upward or downward, its zero mark sits at the atmospheric line, not at the bottom absolute-zero line. So S2, which claims gauge pressure uses absolute zero as its datum, contradicts the diagram and is wrong. Likewise, absolute pressure is always measured from the bottom line (true zero), never from the atmospheric line, so S3 is also wrong.

If the point pressure lies below the atmospheric line, the gap below atmospheric, given by $P_{vac}=P_{atm}-P_{abs}$, is the vacuum pressure, and this matches statement S4 exactly.

So only S1 and S4 survive the diagram check.

\[\boxed{\text{Answer: (C) S1 and S4}}\]