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GATE 2024 CE (CE2) – Question 24

Fluid Mechanics · Properties of fluids, fluid statics · 1 mark · Multiple choice

The following figure shows a plot between shear stress and velocity gradient for materials/fluids P, Q, R, S, and T.

[Figure: shear stress against velocity gradient. P is an almost vertical line through the origin, Q is a straight line with a positive intercept on the stress axis, R is a curve that rises steeply and then flattens, S is a straight line through the origin and T is along the horizontal axis.]

Which one of the following options is CORRECT?

Diagram for GATE 2024 CE (CE2) question 24
  1. P → Ideal Fluid; Q → Ideal Bingham plastic; R → Non-Newtonian fluid; S → Newtonian fluid
  2. P → Real solid; Q → Ideal Bingham plastic; S → Newtonian fluid; T → Ideal Fluid
  3. P → Ideal Fluid; Q → Ideal Bingham plastic; R → Non-Newtonian fluid; T → Real solid
  4. P → Real solid; Q → Newtonian fluid; R → Ideal Bingham plastic; T → Ideal Fluid

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Show answer and explanation

Correct answer: (B) P → Real solid; Q → Ideal Bingham plastic; S → Newtonian fluid; T → Ideal Fluid

Explanation

A solid needs a very large stress for a tiny velocity gradient (a nearly vertical line), so P is a real solid. A Bingham plastic has a yield stress (an intercept) and then a linear rise, so Q is an ideal Bingham plastic. A Newtonian fluid has stress proportional to the gradient, a straight line through the origin: S. An ideal fluid has no shear stress at any gradient, which is the horizontal axis T. R is a non-Newtonian fluid, but option B is the only one with all the other labels right.