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GATE 2021 CH – Question 37

Fluid Mechanics and Mechanical Operations · Fluid properties, fluid statics and fluid kinematics · 2 marks · Multiple choice

Consider a fluid confined between two horizontal parallel plates and subjected to shear flow. In the first experiment, the plates are separated by a distance of 1 mm. It is found that a shear stress of $2\ \mathrm{N\,m^{-2}}$ has to be applied to keep the top plate moving with a velocity of $2\ \mathrm{m\,s^{-1}}$, while the other plate is fixed. In the second experiment, the plates are separated by a distance of 0.25 mm. It is found that a shear stress of $3\ \mathrm{N\,m^{-2}}$ has to be applied to keep the top plate moving with a velocity of $1\ \mathrm{m\,s^{-1}}$, while the other plate is fixed. In the range of shear rates studied, the rheological character of the fluid is

  1. Newtonian
  2. Pseudoplastic
  3. Dilatant
  4. Ideal and inviscid

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Show answer and explanation

Correct answer: (B) Pseudoplastic

Explanation

The shear rate between the plates is $\dot\gamma=U/h$. Thus $\dot\gamma_1=2/0.001=2000\ \mathrm{s^{-1}}$ and $\dot\gamma_2=1/0.00025=4000\ \mathrm{s^{-1}}$.

The apparent viscosities are $\mu_{app,1}=2/2000=0.001$ Pa·s and $\mu_{app,2}=3/4000=0.00075$ Pa·s. Viscosity **decreases** as shear rate increases: the fluid is shear-thinning, or **pseudoplastic (B)**.

A power-law check gives $n=\ln(3/2)/\ln2=0.585<1$, consistent with this classification.