[유체] Chap 1. Basics of Fluid motion

Chap 1. Basics of fluid motion

1.1 Flows of matters

• Fluid : Substance deformed by infinitesimal shear

\[\tau = \mu {\partial u \over \partial y}\]

• Newtonian fluid : $\mu$ constant
• Distinct properties between liquid : if the substance takes its entire volume of the contained continer
• Viscosity : Dynamic $\mu$, Kinematic $\nu$ viscosity
  • $\mu$ (Pa sec) $\sim [ML^{-1}T^{-1}]$
  • $\nu$ ($m^2/s$) $\sim [L^2T^{-1}]$

\[\nu = {\mu \over \rho}\]

1.2 Continuum

• Assumtion (it treats fluid as continuous, homogeneous matter)
• $\rho$ (density) is almost constant over one material

1.3 Pressure & Stress

• Body force : force acting on entire volume segment
  • eg) Gravitation force, Buoyancy (Hydrostatic force + Body force)
• Surface force : force acting on surface of a segment
  • eg) Shear, Normal pressure
• Pascal’s law : Pressure Intensity is the same in all directions at a point. (regardless of motion of the fluid)

1.4 Ideal fluid

• The ideal fluid is invicid, incompressible fluid.
• invicid : no shear force acting on the fluid ($\mu = 0$)
  • i.e.) Force is always aligned normally to its surface
• incompressible fluid : $\rho = \text{const}$ or $\nabla \cdot \vec{u}=0$
  • i.e.) Satisfies the continuity equation.

1.5 Steady & Unsteady flow

• Unsteady : flow changes in time
• The steadiness of flow can be varied with the perspective of observing the fluid
  • i.e.) ${\partial (\cdot) \over \partial t}$: time change in local coordinate, ${d(\cdot) \over dt}$: time change in global coord.