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GATE 2016 ME (ME3) – Question 51

Fluid Mechanics · Differential equations of continuity and momentum, velocity potential · 2 marks · Multiple choice

The two-dimensional velocity field is $\mathbf u=x/(x^2+y^2)\hat i+y/(x^2+y^2)\hat j$. Which statements are correct? (1) The flow is incompressible. (2) The flow is unsteady. (3) $a_y=-y/(x^2+y^2)^2$. (4) $a_x=-(x+y)/(x^2+y^2)^2$.

  1. (2) and (3)
  2. (1) and (3)
  3. (1) and (2)
  4. (3) and (4)

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Show answer and explanation

Correct answer: (B) (1) and (3)

Explanation

Let S=x²+y². Differentiation gives ∂u/∂x+∂v/∂y=0 away from the singular origin; there is no explicit time dependence, so flow is steady. Convective acceleration is(a_x,a_y)=−(x,y)/S². Thus statements1 and3 are correct, **B**; statement4 has an erroneous x+y numerator.