---
title: "Bulk modulus of compressed liquid"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:bulk-modulus-numerical"
source: https://www.bctengineer.com/q/semester_6/hydro_power/bulk-modulus-numerical
site: BCT Engineering
---

# Bulk modulus of compressed liquid

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2074 Bhadra, 4 marks
- Video: [Bulk Modulus of Elasticity and Compressibility - Fluid Mechanics - Physics Practice Problems](https://www.youtube.com/watch?v=ugxgSIGIHrg) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/bulk-modulus-numerical
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

A liquid compressed in a cylinder has a volume of 3600 cm³ at pressure 4 MN/m² and a volume of 3200 cm³ at pressure 8 MN/m². What is bulk modulus of elasticity?

## Short answer

Pressure increase dp = 4 MN/m², volume change dV = −400 cm³, volumetric strain 400/3600 = 0.1111. Bulk modulus K = dp/(−dV/V) = 36 MN/m² (3.6×10⁷ N/m²).

## Answer

Bulk modulus is the ratio of the increase in pressure to the resulting volumetric strain:
$$
K = \frac{dp}{-\,dV/V}
$$

**Given:** $V_1 = 3600$ cm³ at $p_1 = 4$ MN/m², $V_2 = 3200$ cm³ at $p_2 = 8$ MN/m².

$$
\begin{aligned}
dp &= 8 - 4 = 4\ \text{MN/m}^2 \\
dV &= 3200 - 3600 = -400\ \text{cm}^3 \\
-\frac{dV}{V} &= \frac{400}{3600} = 0.1111 \\
K &= \frac{4}{0.1111} = 36\ \text{MN/m}^2
\end{aligned}
$$

(The initial volume 3600 cm³ is used as the reference volume.)

**Answer:** $K = 36$ MN/m² $= 3.6 \times 10^7$ N/m².

## Check yourself

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

1. Volume falls from 3600 to 3200 cm^3. Using 3600 as reference, the volumetric strain is:
   A. 0.125
   B. 0.1111
   C. 400
   D. 0.0889
   Answer: B. -dV/V = 400/3600 = 0.1111. (Key point: Volumetric strain)

2. With dp = 4 MN/m^2, the bulk modulus is:
   A. 0.44 MN/m^2
   B. 4 MN/m^2
   C. 36 MN/m^2
   D. 144 MN/m^2
   Answer: C. K = 4/0.1111 = 36 MN/m^2 = 3.6 x 10^7 N/m^2. (Key point: Result)

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