(c) indicate whether the fluid with the following characteristics is a newtonian or nonnewtonian.
(i) τ = ay + b and = 1 + 2 + 3^2
(ii) = ^[ (−1) ] = ^

(i) Newtonian

(ii) non-Newtonian

Explanation:

The general relation between shear stress and velocity gradient of a fluid is:

τ = A (du/dy)^n + B

"Indicate  whether  the  fluid  with  the  following  characteristics  is  a  Newtonian  or  non-Newtonian."

(i) τ = Ay + B and u = C₁ + C₂y + C₃y²

(ii) τ = Ay^(n(n−1)) and u = C(y^n)

(i) Find du/dy.

u = C₁ + C₂y + C₃y²

du/dy = C₂ + 2C₃y

For a Newtonian fluid, τ = μ du/dy.  Substituting:

τ = μ (C₂ + 2C₃y)

Distributing:

τ = 2μC₃y + μC₂

This fits the form of τ = Ay + B, where A = 2μC₃ and B = μC₂.  So the fluid is indeed Newtonian.

(ii) Find du/dy.

u = C(y^n)

du/dy = Cn(y^(n−1))

For a Newtonian fluid, τ = μ du/dy.  Substituting:

τ = μCn(y^(n−1)))

This does not fit the form τ = Ay^(n(n−1)).  So the fluid is non-Newtonian.

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