📂Fluid Mechanics

Fluids and the Definition of Fluid Dynamics

Definition

Fluid — what is it?

1. A term used collectively for liquids and gases
2. A collection of molecules arranged randomly and gathered together¹

3. In the resting state normal (normal) stresses act, and in the flowing state when shear stress is applied, continuous deformation occurs and the material flows²

Explanation

Although called a definition, it is not particularly rigorous. Nevertheless, even without a strict definition we naturally know what a fluid is, and that is sufficient. Common properties of fluids include fluidity and viscosity. Fluidity is, literally, the property of flowing, and viscosity is the property that characterizes resistance to shear stress and to fluid friction³. Put simply, viscosity indicates how sticky or how thick a substance is.

Fluid mechanics is the discipline that deals with the motion of fluids. Fluid mechanics is further divided into two branches 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 — the paradigmatic nonlinear partial 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, $\mathbf{f}$ the external force per unit volume, $\rho$ the density, $p$ the pressure, and $\nu$ the viscosity coefficient.