文档介绍：Chapter 4 Differential Relations For Viscous Flow
Preliminary Remarks
* Two ways in analyzing fluid motion
Seeking an estimate of gross effects over a finite region or control volume.
Integral
(2) Seeking the point-by-point details of a flow pattern by analyzing an infinitesimal region of the flow.
Differential
1
Turbulent Flow VS. Laminar Flow
* Two forms of flow
Turbulent(湍,紊) flow, laminar(层)flow
* Viscous flow
Viscosity is inherent nature of real fluid.
Strain(剪切) is very strong in internal flow.
Transition
Reynolds number
Osbrone Reynolds
Reynolds tank
惯性力/粘性力
2
The Acceleration Field of a Fluid
Local acceleration
unsteady
Convective acceleration
nonuniform
Nonlinear terms
3
In the like manner
Any property Φ
Substantial (Material) derivative
随体(物质、全)导数
4
Example
Given .
Find the acceleration of a particle.
5
X inlet (mass flow)
X outlet
dx
y
z
x
dz
dy
Infinitesimal fixed CV
X flow out
Differential Equation of Mass Conservation
In the like manner
Flow out off the CV
6
Loss of mass in the CV
7
For steady flow
For pressible flow
Example 1
Under what conditions does the velocity field
represents an pressible flow which conserves mass? ( where )
8
Solution
Continuity for pressible flow
Example 2
An pressible velocity field:
u=a(x2-y2),w=b, a,b are const,what v=?
Solution
An arbitrary function of x,z,t
9
Assignment:
P264: (a), , ,(a)
10