Question

(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) ] = ^

Answer 1

(i) Newtonian

(ii) non-Newtonian

Step-by-step 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.