---
title: "Two-compartment vessel gauges: reading of gauge C"
subject: "Fundamental of Thermodynamics & Heat Transfer"
chapter: 1
key: "semester_2/fundamental_of_thermodynamics_and_heat_transfer:two-compartment-gauges-a4bar-b2bar"
source: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/two-compartment-gauges-a4bar-b2bar
site: BCT Engineering
---

# Two-compartment vessel gauges: reading of gauge C

Fundamental of Thermodynamics & Heat Transfer · Chapter 1: Introduction

- Asked in: 2069 Bhadra, 5 marks
- Video: [THERMODYNAMICS: PRESSURE SAMPLE PROBLEM #4](https://www.youtube.com/watch?v=Y1IIF6OzSa0) — Hayson Darren Bautista
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_2/fundamental_of_thermodynamics_and_heat_transfer/two-compartment-gauges-a4bar-b2bar
- Whole chapter: https://www.bctengineer.com/md/semester_2/fundamental_of_thermodynamics_and_heat_transfer/chapter-1

## Question

A vessel shown has two compartments as shown in figure below at different pressures. The pressure gauge A reads 4 bar and B reads 2 bar. The barometer reads 760mm of Hg. Calculate the reading of gauge C. [Take ρ = 13600 kg/m³ and g = 9.81 m/s²]
[Figure: a vessel with two compartments; gauge C on the left end, gauge B on the partition region, gauge A on the right end.]

## Short answer

Gauge C reads 2 bar. Atmospheric pressure is 1.014 bar; absolute pressure in the compartment with gauge A is 5.014 bar, and in the other compartment 3.014 bar, giving gauge C = 3.014 - 1.014 = 2 bar.

## Answer

**Given:** gauge A = 4 bar, gauge B = 2 bar, barometer = 760 mm Hg, ρ = 13600 kg/m³.

**Assumption:** Gauge A reads one compartment above atmosphere, gauge B reads the pressure difference across the partition, and gauge C reads the other compartment above atmosphere (the arrangement in the standard two-compartment problem).

**Step 1: Atmospheric pressure**
P_atm = 13600 × 9.81 × 0.760 = 101 396 Pa = 1.014 bar

**Step 2: Compartment with gauge A**
P_a = P_atm + 4 = 1.014 + 4 = 5.014 bar (abs)

**Step 3: Other compartment** (gauge B reads the difference)
P_c = P_a − P_B = 5.014 − 2 = 3.014 bar (abs)

**Step 4: Gauge C reading**
P_C = P_c − P_atm = 3.014 − 1.014 = **2 bar (gauge)**

Equivalently, C = A − B = 4 − 2 = 2 bar.

**Answer: Gauge C reads 2 bar (absolute pressure there = 3.014 bar).**

Note: if the figure shows the compartment with gauge C at the higher pressure (gauge B reading it above the compartment with gauge A), then C = A + B = 6 bar (absolute 7.014 bar).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The barometer reads 760 mm Hg with rho = 13600. P_atm in bar is about
   A. 0.76 bar
   B. 1.014 bar
   C. 10.14 bar
   D. 13.6 bar
   Answer: B. 13600 x 9.81 x 0.76 = 101 396 Pa = 1.014 bar. (Key point: Atmospheric pressure)

2. What does gauge B (2 bar) measure?
   A. The pressure difference across the partition
   B. Absolute pressure in compartment A
   C. Atmospheric pressure
   D. Gauge pressure of compartment C
   Answer: A. B reads the difference between the two compartments. (Key point: Gauge B meaning)

3. The compartment with gauge A has P_a = 1.014 + 4 = 5.014 bar abs. The other compartment's absolute pressure is
   A. 7.014 bar
   B. 2.0 bar
   C. 3.014 bar
   D. 1.014 bar
   Answer: C. P_c = P_a - P_B = 5.014 - 2 = 3.014 bar. (Key point: Absolute pressure of other compartment)

4. What does gauge C read?
   A. 1.014 bar
   B. 3.014 bar
   C. 6 bar
   D. 2 bar
   Answer: D. P_C = 3.014 - 1.014 = 2 bar gauge, i.e. A - B, independent of P_atm. (Key point: Gauge C reading)

## Related in Fundamental of Thermodynamics & Heat Transfer

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- [Three pressure gauges on two compartments](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Athree-pressure-gauges-two-compartments) — Fundamental of Thermodynamics & Heat Transfer, chapter 1
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