# Values of constants in power-law fluid relation

• JamesBennettBeta
In summary: I updated the information. Formula isτ = A(du/dy)^n +B, constants are A, B and nI 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.
JamesBennettBeta
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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

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Which constants are you talking about?

vanhees71 said:
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.

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

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.

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?

vanhees71 said:
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

JamesBennettBeta said:
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.

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
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 )

JamesBennettBeta said:
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.

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## What is the power-law fluid relation?

The power-law fluid relation is a mathematical equation that describes the relationship between the shear stress and the shear rate of a fluid. It is commonly used to model the behavior of non-Newtonian fluids, such as polymer solutions and pastes.

## What are the values of constants in the power-law fluid relation?

The values of constants in the power-law fluid relation are the consistency index (K) and the flow behavior index (n). These values are specific to each fluid and can be determined experimentally by measuring the shear stress and shear rate at different conditions.

## What is the significance of the consistency index in the power-law fluid relation?

The consistency index (K) is a measure of the fluid's resistance to flow. A higher value of K indicates a more viscous fluid, while a lower value indicates a less viscous fluid. It is an important parameter in determining the flow behavior of non-Newtonian fluids.

## How does the flow behavior index affect the power-law fluid relation?

The flow behavior index (n) determines the type of non-Newtonian behavior of the fluid. A value of n less than 1 indicates shear-thinning behavior, where the viscosity decreases with increasing shear rate. A value of n greater than 1 indicates shear-thickening behavior, where the viscosity increases with increasing shear rate. A value of n equal to 1 indicates Newtonian behavior, where the viscosity is constant regardless of shear rate.

## Can the values of constants in the power-law fluid relation change over time?

Yes, the values of constants in the power-law fluid relation can change over time, especially for non-Newtonian fluids. This is because the properties of these fluids can be affected by factors such as temperature, pressure, and chemical composition, which can alter the values of K and n. Therefore, it is important to regularly measure and update these values to accurately model the behavior of the fluid.

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