In the vast and complex world of physics, fluids occupy a central place, with applications ranging from engineering to the natural environment. To understand fluid dynamics, scientists often refer to two main categories: real fluids and ideal fluids.

**Real fluids,** like water, air, and oil, **have tangible properties that can be measured and observed**. Their dynamics are influenced by factors such as viscosity, which represents a form of internal friction between fluid particles. Understanding real fluids is essential for solving practical problems such as the flow of water through a pipe or the aerodynamics of an airplane.

On the other hand, **ideal fluids are a theoretical model used to simplify the analysis of flow problems**. In an ideal fluid, there are no internal frictional forces (zero viscosity), and the flow is irrotational. Although ideal fluids do not exist in nature, this model is a useful tool for understanding the basic laws of fluid flow and applying them to real situations.

In our article, we will delve into the differences between real fluids and ideal fluids, exploring the laws and principles that govern their behavior. Ready? Let’s start!

## Real fluids and ideal fluids

Fluid dynamics studies phenomena in which gases and liquids are in motion, i.e. in **dynamic conditions**.

Our knowledge of the **microscopic constitution** of fluids, i.e. of the behavior of the particles that compose them, allows us an in-depth study of static situations, but when6,022⋅10236,022⋅1 023particles per mole of fluid are set in motion, the work becomes complicated. Don’t you remember what **Avogadro’s number** is? Go to class!

Let’s think about **wind farms**, **hydroelectric power plants**, **wind tunnels, and** **dams**: these are circumstances in which knowledge of fluid dynamics is fundamental. It is complicated to study the motion of such “elusive” substances as gases and liquids taking into account all the real variables such as **density**, **viscosity**, **temperature**, **pressure** …

Considering that each substance tends to have different behaviors for each variation of the previously mentioned properties, the only way to study the motion of a fluid is **to build a model** that simplifies the work as much as possible.

## The ideal fluids

To study fluids in **dynamic situations**, such as water flowing through a pipe or gas expelled from a spray can, we introduce the **ideal fluid model**.

A model is a simplified approximation of the actual behavior of a phenomenon.

The model predicts that an ideal fluid:

- is
**incompressible**, so a change in pressure does not lead to a change in volume - is
**non-viscous**, so the microscopic motions of the particles occur without friction, and the various parts of the fluid slide over each other without resistance - has a
**laminar**or**stationary regime**, i.e. the velocity of the particles at each point does not vary over time (the**speeds**can be**different**in different parts of the fluid, but**not variable**)

Real liquids correspond with **good approximation** to incompressibility. The same cannot always be said of viscosity, a relevant property in real liquids. A fluid corresponds to the model only if the viscosity does not significantly **influence its motion**. For gases, which cannot be modeled exactly like liquids, it was necessary to build a more specific model, the **ideal gas**. Go to the lesson on **ideal gases**!

## How to use the ideal fluid model

We need to study the volume **flow rate** of water�which, via a section tubeTOTO, affects the blades of a water mill at speed�v.

**If we were to calculate the real** dynamic conditions of the fluid, we would have to take into consideration: the **temperature** of the water which defines its **density**, **viscosity**, **pressure**, the characteristics of the medium that transports it, the vortical and turbulent motions which cause the speed to vary and the flow of water on the mill…

The procedure would be very long, imprecise, and, above all, too particular to be able to derive a general law.

We treat the situation from the point of view of an **ideal fluid**.

Water is practically **incompressible**, and the variation in density is negligible as it is evident only for large temperature jumps, the **viscosity coefficient of** water is very low and does not affect its motion considerably therefore it is also **irrelevant**, furthermore, the Water flow in a pipe under ideal conditions has a **laminar** flow regime.

Having declared the necessary characteristics of the **ideal fluid model**, we can apply the **continuity equation** to calculate the approximate flow rate of the water in a pipe affecting the mill blades: TOQ = v TO.

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