Pressure scales – Relation between absolute, gauge, and atmospheric Absolute pressure is related to gauge pressure and atmospheric pressure by which expression?

Introduction:
Engineering practice uses multiple pressure references. Gauge pressure measures pressure relative to ambient atmosphere, while absolute pressure is measured relative to an absolute vacuum. Understanding the relation among these is essential for thermodynamics, fluid statics, and instrumentation.

Given Data / Assumptions:

• Ambient atmospheric pressure is Patm (approximately 101.325 kPa at sea level).
• Gauge pressure Pg = Pabs − Patm by definition.
• Vacuum pressure Pvaccum refers to a pressure below atmosphere often reported as a magnitude beneath Patm.

Concept / Approach:

From Pg = Pabs − Patm, rearrange to Pabs = Pg + Patm. This identity holds regardless of whether Pg is positive (above atmosphere) or negative (below atmosphere). Conversions in instruments follow this identity to translate between scales.

Step-by-Step Solution:

Verification / Alternative check:

Consider a tire at 220 kPa absolute. With Patm ≈ 100 kPa, Pg ≈ 120 kPa. The identity Pabs = Pg + Patm is satisfied numerically, confirming correctness.

Why Other Options Are Wrong:

Gauge − atmosphere / atmosphere − gauge: Algebraically incorrect rearrangements.Gauge − vacuum: Terminology confusion; vacuum reading is not a linear subtractor to convert gauge to absolute.Vacuum + atmosphere: This can equal absolute only when “vacuum” is carefully defined as the deficit from absolute zero, which is not the usual industrial convention.

Common Pitfalls:

Mixing sign conventions for vacuum and gauge readings, or assuming Patm is constant across altitude and weather conditions without correction.

Final Answer:

gauge pressure + atmospheric pressure