Constants definition - turbulent vel. profile

[jkr]

Homework Statement

Hello!

I need some help with a problem:

Problem: Turbulent flow beteween parallel flat plates.

It is defined:

[ tex ] \tau = \mu \frac{d\bar{u}}{dy}-\rho\bar{u'v'} [ \tex ]

The exercise gives that [ tex ] \tau = a y [ \tex ] and [ tex ] \rho\bar{u'v'} = \frac{by}{c+dy^2} [ \tex ], where [ tex ] a,b,c,d[ \tex ] are constants.

I need to know: How can I choose these constants? I'm looking for an aproximate solution.

Until now, I used just the no-slip condition at [ tex ] \pm H [ \tex ] and [ tex ] \frac{du(y=0)}{dy}=0 [ \tex ]

Tks for the help!

Homework Equations

[ tex ] \tau = \mu \frac{d\bar{u}}{dy}-\rho\bar{u'v'} [ \tex ]
[ tex ] \tau = a y [ \tex ]
[ tex ] \rho\bar{u'v'} = \frac{by}{c+dy^2} [ \tex ]

The Attempt at a Solution

 

[NascentOxygen]

Hello!

I need some help with a problem:

Problem: Turbulent flow beteween parallel flat plates.

It is defined:

$$\tau = \mu \frac{d\bar{u}}{dy}-\rho\bar{u'v'}$$

The exercise gives that $$\tau = a y$$ and $$\rho\bar{u'v'} = \frac{by}{c+dy^2}$$, where $$a,b,c,d$$ are constants.

I need to know: How can I choose these constants? I'm looking for an aproximate solution.

Until now, I used just the no-slip condition at $$\pm H$$ and $$\frac{du(y=0)}{dy}=0$$

Tks for the help!

Homework Equations

$$\tau = \mu \frac{d\bar{u}}{dy}-\rho\bar{u'v'}$$
$$\tau = a y$$
$$\rho\bar{u'v'} = \frac{by}{c+dy^2}$$

Hi jkr! http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

I'm astonished that you posted your question with its non-functioning itex formatting instructions. I have fixed them for you. Don't include unnecessary spaces inside the [...] instruction. And its [/tex] NOT [\tex].

I can't help you with a fluidics question, but now maybe someone else can.

 

[jkr]

Tks a lot for this! =D

 

[jkr]

Hi again,

If $$\rho \bar{u'v'} =0$$ at $$y = \pm H$$ then the model $$\rho \bar{u'v'}=\frac{by}{c+dy^2}$$ doesn't work because $$b=0.$$
However, for the case
$$\rho \bar{u'v'} =\frac{by+ey^3}{c+dy^2},$$ How does it work?

[]s

 

[DeeNos]

Hello!

The constants in this problem represent physical properties of the system, such as viscosity and density. In order to choose these constants, you will need to gather information about the specific system you are studying. This may include measurements of the flow, properties of the fluid being used, and any other relevant data. Once you have this information, you can use it to solve for the constants in the equations provided.

As for an approximate solution, you can use numerical methods or simplifications of the equations to find a solution. However, it is important to note that an exact solution may not be possible due to the complex nature of turbulent flow. It is also important to carefully consider the assumptions and limitations of your chosen solution method to ensure it accurately reflects the behavior of your system.

I hope this helps! Good luck with your problem.