GATE BT 2023 • Q62 NAT • 2 Marks

Section 2: General Biotechnology

Biomolecules, enzyme kinetics

Subtopic: Fundamentals of Biomolecules, enzyme kinetics

Question Statement:

The values of the consistency index ' K ' and the flow behavior index ' n ' of a dilatant fluid are 0.415 (in CGS units) and 1.23, respectively. The value of the apparent viscosity (in 11..g cm s-- ) of this fluid at a shear rate of 160 s- (rounded off to the nearest integer) is ___________.

Official Answer Key:

1 to 1

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2023 Q.62)** **1. Governing Concept & Definition**: - **Topic**: Bioprocess Rheology & Non-Newtonian Power-Law Fluids - For an Ostwald-de Waele power-law dilatant (shear-thickening) fluid ($n > 1$): $\tau = K \dot{\gamma}^n$ - The apparent viscosity ($\eta_{\text{app}}$) is: $\eta_{\text{app}} = \frac{\tau}{\dot{\gamma}} = K \dot{\gamma}^{n-1}$ **2. Detailed Step-by-Step Calculation**: - **Given in CGS units**: - Consistency index $K = 0.415\text{ g cm}^{-1}\text{ s}^{n-2}$ - Flow behavior index $n = 1.23$ - Shear rate $\dot{\gamma} = 60\text{ s}^{-1}$ - **Exponent Calculation**: $n - 1 = 1.23 - 1 = 0.23$ - **Apparent Viscosity Evaluation**: $\eta_{\text{app}} = 0.415 \times (60)^{0.23}$ - $\ln(60) \approx 4.09434$ - $0.23 \times \ln(60) \approx 0.23 \times 4.09434 \approx 0.9417$ - $60^{0.23} = e^{0.9417} \approx 2.5643$ $\eta_{\text{app}} = 0.415 \times 2.5643 \approx 1.064\text{ g cm}^{-1}\text{s}^{-1} \approx 1\text{ g cm}^{-1}\text{s}^{-1}$ **3. Final Answer**: - **Calculated Value**: **1 g cm⁻¹ s⁻¹** - **Official GATE Accepted Range**: **1 to 1**

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test