文档介绍：Advanced Fluid Mechanics
Chapter 1 Introduction
Classification of a Fluid (A fluid can only substain tangential force when it moves)
1.) By viscous effect: inviscid & Viscous Fluid.
2.) pressible: pressible & Compressible Fluid.
3.) By Mack No: Subsonic, transonic, Supersonic, and hypersonic flow.
4.) By eddy effect: Laminar, Transition and Turbulent Flow.
The objective of this course is to examine the effect of tangential (shearing) stresses
on a fluid.
Remark:
For a ideal (or inviscid) flow, there is only normal force but tangential force between
two contacting layers.
Simple Notation of Viscosity
U F (tangential force required to move upper
plate at velocity of U )
h
Fluid (. water)
y
x
u(y) = y/h U
From observation, the tangential force per unit area required is proportional to U/h, or
du/dy. Therefore
U
τ≡ shear stress = tangential force per unit area (F/A) ∝
h
or
U ∂ u
τ= µ = µ 〝Newton’s Law of function〞()
h ∂ y
µ : Constant of proportionality
The first coefficient of viscosity
Remark:
. () provides the definition of the viscosity and is a method for measuring the
viscosity of the fluid.
Chapter1- 1
Advanced Fluid Mechanics
In generally, if ε XY represent the strain rate, then
τ xy= f ()ε xy ()
plastic
τ yielding fluids
Dilatent fluid Non- Newtonian
Pesudoplastic fluid fluid
Newtonian fluid
Yield stress
ε
Newtonian fluid: linear relation between τ and ε
Pesudoplastic fluid: the slope of the curve decrease as ε increase (shear-thinning) of
the shear-thinning effect is very strong. The fluid is called plastic
fluid.
Dilatent fluid: the slope of the curve increases as ε increases (shear-thicking).
Yielding fluid: A material, part solid and part fluid can substain certain stresses before
it starts to deform.
Note
Newton
1 Pa (Pascal) ≡(Pascal, a French philosopher and