---
title: "Thin copper shell: pressure from extra 80 cc liquid"
subject: "Strength of Materials"
chapter: 5
key: "semester_3/strength_of_materials:thin-copper-shell-extra-liquid-80cc"
source: https://www.bctengineer.com/q/semester_3/strength_of_materials/thin-copper-shell-extra-liquid-80cc
site: BCT Engineering
---

# Thin copper shell: pressure from extra 80 cc liquid

Strength of Materials · Chapter 5: Thin Walled Vessels

- Asked in: 2071 Chaitra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/strength_of_materials/thin-copper-shell-extra-liquid-80cc
- Whole chapter: https://www.bctengineer.com/md/semester_3/strength_of_materials/chapter-5

## Question

A thin walled cylindrical shell made up of copper plate has been filled with a liquid at atmospheric pressure. An additional 80cc of liquid is then pumped into 3 m cylindrical shell whose internal diameter is 300 mm and wall thickness 14 mm. Find the values of pressure developed on the wall of cylinder due to this extra liquid. Take Poisson ratio = 0.36 and Modulus of elasticity $E = 10^6\ \text{kg/cm}^2$.

## Short answer

Volume V = 212058 cm³, volumetric strain = 80/V. Using ε_v = pd(5−4ν)/(4tE) with ν=0.36, E=10⁶ kg/cm², solve p = 19.78 kg/cm² (1.94 MPa).

## Answer

The extra liquid fills the space created by the expansion of the shell. The liquid is assumed incompressible (no bulk modulus is given), so $\delta V_{shell} = 80\ \text{cm}^3$.

**Data:** $L = 300$ cm, $d = 30$ cm, $t = 1.4$ cm, $\nu = 0.36$, $E = 10^6\ \text{kg/cm}^2$.

#### Volumetric strain of a thin cylinder
$$
\varepsilon_v = 2\varepsilon_c + \varepsilon_l = \frac{pd}{2tE}\left(\frac{5}{2} - 2\nu\right) = \frac{pd}{4tE}(5-4\nu)
$$

#### Volume and pressure
$$
V = \frac{\pi}{4}(30)^2(300) = 212057.50\ \text{cm}^3
$$

$$
\frac{\delta V}{V} = \frac{80}{212057.50} = 3.7726\times10^{-4} = \frac{p(30)}{4(1.4)(10^6)}(5 - 4\times0.36) = 1.9071\times10^{-5}\,p
$$

$$
p = 19.781\ \text{kg/cm}^2 \approx 1.940\ \text{N/mm}^2
$$

**Answer: pressure developed $\approx 19.78\ \text{kg/cm}^2$ (1.94 MPa).**

## Check yourself

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

1. What condition lets us equate the 80 cc of extra liquid to the shell's volume increase?
   A. The shell does not expand at all
   B. The liquid compresses by 80 cc
   C. Longitudinal strain is zero
   D. The liquid is incompressible, so the added volume equals the shell expansion
   Answer: D. With no bulk modulus given, liquid compressibility is ignored. (Key point: Condition)

2. Which formula gives volumetric strain of a thin cylinder?
   A. pd(5 - 4 nu)/(4 t E)
   B. pd(5 - 4 nu)/(2 t E)
   C. pd(3 - 4 nu)/(4 t E)
   D. pd(1 - 2 nu)/(2 t E)
   Answer: A. eps_v = 2 eps_c + eps_l simplifies to pd(5 - 4 nu)/(4tE). (Key point: Volumetric strain formula)

3. Which consistent data set is used?
   A. L = 3 cm, d = 300 cm
   B. L = 300 cm, d = 30 cm, t = 1.4 cm, E in kg/cm^2
   C. d = 300 mm with E in kg/cm^2
   D. t = 14 cm
   Answer: B. Volume is in cm^3 and E is in kg/cm^2, so lengths must be in cm. (Key point: Units)

4. What pressure is obtained?
   A. About 1.98 kg/cm^2
   B. About 198 kg/cm^2
   C. About 19.8 kg/cm^2
   D. About 3.8 kg/cm^2
   Answer: C. dV/V = 3.77e-4 = 1.9071e-5 p gives p = 19.78 kg/cm^2. (Key point: Result)

## Close variants set in other exams

- [Thin copper shell: pressure from extra 50 cc liquid](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Athin-copper-shell-extra-liquid-50cc) — Strength of Materials, chapter 5, asked 2×

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