The **key difference** between compressible and incompressible fluids is that the **compressible fluids occur in reality whereas the incompressible fluids is a concept developed for ease of calculations.**

Fluids are either gases or liquids that take the shape of the container. In fluid dynamics, the compressibility of a fluid is a very important factor. In nature, all the fluids are compressible, but we define incompressible fluids for our convenience of study. The concepts of compressible and incompressible fluids play a major role in fields such as fluid dynamics, fluid statics, aviation and many other fields. Therefore, it is vital to have a proper understanding of the concepts of compressibility of fluids in order to understand such fields.

### CONTENTS

1. Overview and Key Difference

2. What are Compressible Fluids

3. What are Incompressible Fluids

4. Side by Side Comparison – Compressible vs Incompressible Fluids in Tabular Form

5. Summary

## What are Compressible Fluids?

Every fluid we encounter in our daily lives is compressible. To understand what compressible fluids are, one must first understand what compressibility is. The compressibility of a fluid is the reduction of the volume of the fluid due to external pressures acting on it. Conversely, a compressible fluid will reduce its volume in the presence of external pressure. Therefore, we can take the quantitative measurement of the compressibility as the relative volume change of the liquid in response for a pressure change.

The symbol for compressibility is β or κ. Hence, we can define the compressibility mathematically as

** κ =(-1/v) ∂V/∂p,**

where V is the volume and p is the pressure.

In reality, every gas is highly compressible, but liquids are not highly compressible. Therefore, we can define the compressibility in two forms; adiabatic and isothermal compressibility.

The **adiabatic compressibility** describes the compressibility of the system when the temperature of the system is constant. We can denote it by β_{V}. Whereas, the** isothermal compressibility** refers to the compressibility measured under no energy transfer between the system and the surroundings. We can denote it by β_{S}. Since an adiabatic process is also isentropic, this process is a constant entropy process.

## What are Incompressible Fluids?

Incompressible fluids are a hypothetical type of fluids, which the scientists introduced for the convenience of calculations. An incompressible fluid is a fluid that does not change the volume of the fluid due to external pressure. Most of the basic calculations that we do in fluid dynamics depend on the assumption that the fluid is incompressible.

The approximation of incompressibility is acceptable for most of the liquids as their compressibility is very low. However, the compressibility of gases is high, so we cannot approximate gases as incompressible fluids. The compressibility of an incompressible fluid is always zero.

## What is the Difference Between Compressible and Incompressible Fluids?

Compressible fluids occur in reality. In fact, all of the fluids found in nature are compressible. Incompressible fluids are a concept that the scientists developed for the ease of calculations. Hence, this is the key difference between compressible and incompressible fluids. Accordingly, a significant difference between compressible and incompressible fluids is that the volume of compressible fluids decreases when we apply external pressure, but the volume of incompressible liquids remain constant. Besides, the fluid dynamic calculations for the incompressible fluids are very easy when compared to the calculations involving compressible fluids.

## Summary – Compressible vs Incompressible Fluids

A fluid is either a gas or a liquid. We can categorize fluids into two broad groups as compressible and incompressible fluids depending on their ability to undergo compression. However, there are no such fluids which do not undergo compression. Thus, the concept of incompressible fluids is hypothetical. The key difference between compressible and incompressible fluids is that the compressible fluids occur in reality whereas the incompressible fluids is a concept developed for ease of calculations.

##### Reference:

1. “Fluid.” Wikipedia, Wikimedia Foundation, 18 Sept. 2018. Available here

2. Celli , Vittorio. *Compressible Fluids*, 11 Oct. 1997. Available here

##### Image Courtesy:

1.”LPG cylinders” (CC BY 2.5) via Commons Wikimedia

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