Dilatant fluids exhibit shear-thickening behavior, where apparent viscosity increases with shear rate due to their power-law flow characteristics defined by consistency index K and flow behavior index n > 1. For this fluid with K = 0.415 (CGS units, g·cm⁻¹·sⁿ) and n = 1.23 at a shear rate of 60 s⁻¹, the apparent viscosity is calculated using the standard formula μ_a = K × (shear rate)^(n-1).

Step-by-Step Solution

Common Errors to Avoid

• Using μ_a = K × γ̇^n (yields ~35, incorrect – this equals shear stress τ, not viscosity)
• Assuming Newtonian η = K (0.415, ignores shear rate dependence)
• Forgetting to subtract 1 from n in the exponent (n-1 = 0.23, not 1.23)

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Apparent viscosity dilatant fluid calculations are essential for GATE Biotechnology aspirants tackling non-Newtonian flow problems with consistency index K 0.415 and flow behavior index n 1.23 at shear rate 60 s⁻¹. This guide breaks down the power-law formula μ_a = K × γ̇^(n-1), yielding ~1.17 (rounded to 1) in CGS units (g·cm⁻¹·s⁻¹).

Power-Law Fluids Explained

• Dilatant (shear-thickening, n>1): Cornstarch slurry – viscosity increases with shear
• Pseudoplastic (shear-thinning, n<1): Paint, blood – viscosity decreases with shear
• Newtonian (n=1): Water, simple oils – constant viscosity

Here, n=1.23 confirms dilatant nature, where viscosity rises with shear rate γ̇.

Detailed Calculation Walkthrough

1. Identify formula: μ_a = K γ̇^(n-1)
2. Plug in values: γ̇^(0.23) = 60^0.23 ≈ 2.817
3. Multiply: 0.415 × 2.817 ≈ 1.169
4. Round: 1 (nearest integer)

GATE Exam Relevance

This mirrors GATE BT 2023 Q.62, testing CGS units and rounding for numerical answers. Practice similar problems boosts scores in fluid mechanics/biochemical engineering sections. Perfect for IIT JAM and GATE Biotechnology preparation.