For a Newtonian fluid, a plot of shear stress (on Y axis) against shear rate (on X
axis) will result in a straight line ________.
Options:
(A) parallel to the X axis
(B) parallel to the Y axis
(C) with a negative slope
(D) with a positive slope
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2026 Q.45)**
**1. Governing Concept**:
- **Topic**: Fluid Mechanics & Rheology of Fluids
- Newton's law of viscosity states that shear stress ($\tau$) is directly proportional to the shear rate / velocity gradient ($\dot{\gamma} = \frac{du}{dy}$):
$\tau = \mu \dot{\gamma}$
where the proportionality constant $\mu$ is dynamic viscosity.
- For a **Newtonian fluid**:
- The relationship is strictly linear.
- The plot passes through the origin $(0, 0)$ (zero yield stress $\tau_0 = 0$).
- The slope of the line equals the fluid dynamic viscosity $\mu$, which remains constant regardless of shear rate.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: A curve with non-zero intercept represents a Bingham plastic.
- **Option (B) is INCORRECT**: A curve concave upward (shear-thickening / dilatant) or concave downward (shear-thinning / pseudoplastic) represents non-Newtonian behavior.
- **Option (C) is INCORRECT**: Viscosity cannot be variable in an ideal Newtonian fluid.
- **Option (D) is CORRECT**: A straight line passing through the origin with a constant slope equal to dynamic viscosity.
**3. Final Answer**:
- **Correct Option**: **D**
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