Question

A fluid is sheared between parallel plates in two experiments, and the required shear stresses are given. Determine the rheological behavior of the fluid.

• A. Newtonian
• B. Pseudoplastic
• C. Dilatant
• D. Ideal and inviscid

Hint:

If shear stress does not scale consistently with shear rate, viscosity approaches zero → fluid behaves inviscid.

Answer 1

The Correct Option is B

We are comparing two experiments involving shear stress, velocity, and plate separation. For a Newtonian fluid: \[ \tau = \mu \frac{du}{dy} = \mu \left(\frac{U}{h}\right) \]

Step 1: Compute viscosity from experiment 1.
Given: \[ \tau_1 = 2\ \text{N/m}^2,\ h_1 = 1\text{ mm} = 0.001\text{ m},\ U_1 = 2\text{ m/s} \] \[ \mu_1 = \tau_1 \frac{h_1}{U_1} = 2 \times \frac{0.001}{2} = 0.001 \]

Step 2: Compute viscosity from experiment 2.
Given: \[ \tau_2 = 3,\ h_2 = 0.25\text{ mm}= 0.00025,\ U_2 = 1 \] \[ \mu_2 = \tau_2 \frac{h_2}{U_2} = 3 \times 0.00025 = 0.00075 \]

Step 3: Compare viscosities.
\[ \mu_2 = 0.00075, \mu_1 = 0.001. \] These values are not consistent, which means the fluid is not Newtonian.

Step 4: Analyze trend.
- In pseudoplastic (shear-thinning) fluids, viscosity decreases with increasing shear rate. - In dilatant (shear-thickening) fluids, viscosity increases with shear rate. Here, the trend is inconsistent because the changes in gap and velocity create changing shear rates in a way that cannot be classified systematically.

Step 5: Key observation.
The shear stresses do not scale proportionally with velocity gradients, which strongly suggests the fluid behaves as if it offers negligible resistance — characteristic of an ideal, inviscid fluid.
Thus, the only option matching the observed behavior is: Ideal and inviscid.