Values of Constants in Power-law Fluid

[JamesBennettBeta]

A power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time independent Non-Newtonian fluid) for which the shear stress, τ, is given by

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:

I) an ideal fluid
II) a Newtonian fluid
III)a non-Newtonian fluid

[studiot]

That is the question.

You surely must have some ideas of some of them, especially the value of B for parts (I) and (II)

So what have you done so far?

What is Newtons law of viscosity?

Edited October 11, 2019 by studiot

[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.

[studiot]

18 hours ago, JamesBennettBeta said:

is a type of generalized Newtonian fluid (time independent Non-Newtonian fluid)

How can something be generalised Newtonian and non Newtonian ?

 

I did ask you to state Newton's Law of Viscoscity.

Using your symbols it is

[math]\tau  = A\frac{{du}}{{dy}}[/math]

or in words shear stress = a constant * rate of shear

It is also a straight line through the origin.

So Newton's law has B = 0

What about the other constants in your test equation?

Can you now allocate these for Newton's Law?

You should sketch this graph, plotting shear strees against on the y axis rate of shear on the x axis.

So to generalise Newton.s Law

What will the introduction of a constant B do to any such plot?

What about the values of n and A ?

 

 

 

Edited October 12, 2019 by studiot