Answer:
(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.
