📂Physics

Fluids and the Definition of Fluid Dynamics

Definition

Fluid refers to:

1. A term that combines both liquid and gas
2. A collection of molecules that are randomly arranged and clustered together¹

3. In a stationary state, it is subject to vertical stress, and in a flow state, it undergoes continuous deformation and flows when subjected to shear forces²

Description

Although it’s called a definition, it’s not that strict. However, without pushing for a strict definition, we naturally understand what a fluid is, and that’s sufficient. Fluids have general properties such as fluidity and viscosity. Fluidity is, as the name implies, the characteristic of flowing, and viscosity characterizes the resistance to shear stress and fluid friction³. Simply put, viscosity is a term that describes the stickiness or thickness.

Fluid Mechanics is the study of the motion of fluids. Fluid mechanics is further divided according to the state of the fluid into fluid statics, which deals with the movement of fluids at rest, and fluid dynamics, which deals with the movement of moving (flowing) fluids. The Navier-Stokes equations, known as the ultimate differential equation and one of the Millennium Prize Problems, ‘Existence and smoothness of the Navier-Stokes equations’, is a central topic in fluid mechanics.

$$ \frac{ \partial \mathbf{u}}{ \partial t}+\left( \mathbf{u} \cdot \nabla \right)\mathbf{u}=\mathbf{f}-\frac{1}{\rho}\nabla p + \nu \nabla ^{2}\mathbf{u} $$

Here, $\mathbf{u}$ represents the velocity of the fluid, $\mathbf{f}$ represents the external force per unit volume, $\rho$ represents density, $p$ represents pressure, and $\nu$ represents the viscosity coefficient.