Shear stress τ vs shear rate γ̇ for four fluid models — and channel flow profiles
Newtonian fluids: τ = μγ̇ (water, air). Power-law fluids: τ = Kγ̇ⁿ; n<1 is shear-thinning (ketchup, blood), n>1 is shear-thickening (cornstarch). Bingham plastics (toothpaste, mud) require a yield stress τ₀ before flowing: τ = τ₀ + μγ̇. Channel (Poiseuille) flow profiles are parabolic for Newtonian; flatter center and steeper edges for shear-thinning; plug flow for Bingham plastic where |τ| < τ₀.