📂Fluid Mechanics

Fluids and the Definition of Fluid Dynamics

Definition

Fluid — what is it?

1. A term that collectively refers to liquids and gases
2. A collection of molecules randomly arranged and clustered together¹

3. In the stationary state, normal stress acts, and in the flowing state, when shear stress is applied, the material undergoes continuous deformation and flows²

Explanation

Although called a definition, it is not very strict. However, even without a rigorous definition we naturally know what a fluid is, and that is sufficient. Common properties of fluids include fluidity and viscosity. Fluidity (the ability to flow) is literally the property of flowing, and viscosity characterizes resistance to shear stress and fluid friction³. Simply put, viscosity denotes the degree of stickiness or thickness.

Fluid mechanics is the discipline that studies the motion of fluids. Fluid mechanics is divided into two subfields depending on the state of the fluid: fluid statics, which deals with stationary fluids, and fluid dynamics, which deals with moving (flowing) fluids. The Navier–Stokes equations, famed as the ‘ultimate’ differential equations and the subject of one of the Millennium Prize problems — “existence and smoothness of solutions to the Navier–Stokes equations” — arise 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, $\mathbf{u}$ denotes the fluid velocity, $\mathbf{f}$ denotes the external force per unit volume, $\rho$ denotes the density, $p$ denotes the pressure, and $\nu$ denotes the viscosity coefficient.