Values of constants in power-law fluid relation

[JamesBennettBeta]

NO TEMPLATE, MISPLACED HOMEWORK

Summary: What are the values of constants in power-law fluid relation when the fluid behaves as an ideal fluid, a Newtonian fluid and a non-Newtonian fluid?

τ = A(du/dy)^n +B

Where A, B and n are constants that depend upon the type of fluid and conditions imposed
on the flow. Comment on the value of these constants so that the fluid may behave as:

1. an ideal fluid
2. a Newtonian fluid
3. a non-Newtonian fluid

 

[vanhees71]

Which constants are you talking about?

 

[JamesBennettBeta]

Which constants are you talking about?

I updated the information. I spent a day reading and searing whole internet and still couldn't get the answers.

 

[Chestermiller]

I updated the information. I spent a day reading and searing whole internet and still couldn't get the answers.

Tell us about your thinking so far.

 

[JamesBennettBeta]

1. A=0 B=? n=?
In an ideal fluid the viscosity should be equal to zero.

2. A=? B=? n=1
In a Newtonian fluid the flow behavior index is equal to 1 (Experimentally)

3. A=? B=? n≠1
In a non-Newtonian fluid the flow behavior index is bot equal to 1

This is the far that I could understand.

 

[vanhees71]

I still have no clue which parameters these should be. If you do not even formulate the question accurately, how can you expect to find an answer or get one from us?

 

[JamesBennettBeta]

I still have no clue which parameters these should be. If you do not even formulate the question accurately, how can you expect to find an answer or get one from us?

I updated the information.

Formula is
τ = A(du/dy)^n +B,

constants are A, B and n

 

[256bits]

I updated the information. I spent a day reading and searing whole internet and still couldn't get the answers.

Probably because you have to digest the information that you were reading.

Start with understanding viscosity.
What is viscosity?
https://en.wikipedia.org/wiki/ViscosityUsually the definition is given in terms of understanding a Newtonian fluid.

There is a picture under the heading Newtonian and non-Newtonian fluids showing some fluids under shear stress. What does that tell you? especially about your constant B.
What would B be for " normal" shear thinning and shear thickening non-Newtonian fluids?
What about a Bingham plastic - what is its B?

Also,
What do you think B represents after figuring out the above?

What can you say about the constant "n" then , for Newtonian, shear thinning/thickening fluids?
ie slope is constant, slope increasing, slope decreasing.

You can also look at the Wikii on power law fluids.
https://en.wikipedia.org/wiki/Power-law_fluid
Your answer to items 1 and 2 should a singlet.
The answer to item 3 can become more involved depending on type on non-Newtonian fluid you wish to describe.

( By the way, I think your equation is not necessarily the equation for the fluid power law, but that the Herschel-Bulkley Model for Bingham Plastics, as seen in the figure )

 

[Chestermiller]

1. A=0 B=? n=?
In an ideal fluid the viscosity should be equal to zero.

2. A=? B=? n=1
In a Newtonian fluid the flow behavior index is equal to 1 (Experimentally)

3. A=? B=? n≠1
In a non-Newtonian fluid the flow behavior index is bot equal to 1

This is the far that I could understand.

In my expert judgment (my PhD thesis was in viscoelastic fluids/rheology), these answers are all correct, except that, in the case of a general non-Newtonian fluid, the general equation is more like $\tau=\tau(du/dy)$ where $\tau$ is a monotonic odd function of its argument.