Rheological Behavior of Fluids Push each fluid down the same channel with the same force. Water (Newtonian) makes a clean parabola. Ketchup and paint (shear-thinning) run flatter — they thin out where they’re worked hardest. Toothpaste (Bingham) has a solid unsheared plug riding down the middle until the stress at the walls beats its yield strength. The journey: Newton assumed stress ∝ shear rate. Real fluids don’t: τ = K (γ̇)ⁿ (power law) or τ = τᵧ + μ γ̇ (Bingham). Feeding those laws through the same force balance gives these profiles; the dashed line is the Newtonian parabola for comparison.